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The boiling crisis phenomenonPart II: dryout dynamics and burnout

T.G. Theofanous *, T.N. Dinh, J.P. Tu, A.T. Dinh

Center for Risk Studies and Safety, University of California, Santa Barbara, 6740 Cortona Drive, Goleta CA 93117, USA

Accepted 10 December 2001

Abstract

This is Part II of a two-part paper on the boiling crisis phenomenon. Here we report on burnout experiments conducted on fresh

and aged heaters in pool boiling. Critical heat fluxes (CHFs) were found to vary from 50% to 140% of the hydrodynamic limit,

previously thought to exist at well-wetting conditions. The burnout events were captured in action (for the first time), using high-

speed, high-resolution infrared thermometry. Based on these observations and in conjunction with the levels of CHF reached, we are

led to conclude that the phenomenon cannot be (macro)hydrodynamically limited, at least at normal pressure and gravity conditions.

Based on infrared thermometry, and aided by X-ray radiography data on void fraction, the case for a scale separation phe-

nomenon in high heat flux pool boiling is argued. This indicates that boiling crisis is controlled by the microhydrodynamics and

rupture of an extended liquid microlayer, sitting and vaporizing autonomously on the heater surface. Further, the detailed dynamics

of this microlayer, as revealed by our experiments, demonstrates that all previous thermally based models of boiling crisis are in-

appropriate.

Ó 2002 Elsevier Science Inc. All rights reserved.

Keywords: Boiling crisis; Burnout; Critical heat flux

1. Introduction

More than half a century ago Kutateladze [1–3] in-

troduced his ‘‘hydrodynamic’’ concept for burnout.

Twenty years later [4], he followed with his famous

‘‘barbotage’’ experiments that specifically related burn-

out (in pool boiling) to a ‘‘liquid repulsion’’ mechanism

due to the counter-current flow of vapor at the heater

surface. The experiments involved injection of different

gases through microporous surfaces, and the incidence

of ‘‘repulsion’’ was identified by the formation of astable gas ‘‘cushion’’ in the immediate vicinity of the

surface. The ‘‘cushion’’ was detected by loss of electrical

contact between an electrode (wire) embedded flush with

the microporous surface, and an electrode immersed in

the bulk of the liquid. This break of stability was found

to be captured well by a fixed value of a grouping now

known as the Kutateladze number (Ku). Namely,

Ku ¼ U cr

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2

v

r g ðq‘ À qvÞ

4

s ð1Þ

where U cr is the critical gas velocity for instability, q‘

and qv are the liquid and vapor densities respectively, r

is the surface tension, and g is the acceleration due to

gravity. Gogonin and Kutateladze [5] went on to show

by means of extensive experiments boiling ethanol on

stainless steel plates, that

(a) Ku ¼ 0:145 within Æ15%, and(b) the results were independent of the heater size for

dÃP 2,

where dÃ is the heater length scale, L, made dimension-

less by the capillary length d $ r= g ðq‘ À qvÞf g1=2

. In

boiling, the vapor flow is related to the heat flux as

U cr ¼ qcr= H lvqv ð2Þ

where qcr is the critical heat flux (CHF) (burnout flux),

and H lv is the latent heat of vaporization. Eqs. (1) and

(2) lead to the Kutateladze–Zuber equation, discussed in

Part I:

Experimental Thermal and Fluid Science 26 (2002) 793–810

www.elsevier.com/locate/etfs

* Corresponding author. Tel.: +1-805-894-4900; fax: +1-805-893-

4927.

E-mail address: [email protected] (T.G. Theofanous).

0894-1777/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved.

PII: S 0 8 9 4 - 1 7 7 7 ( 0 2 ) 0 0 1 9 3 - 0

http://mail%20to:%[email protected]/

http://mail%20to:%[email protected]/



qcr ¼ C kqv H lvr g ðq‘ À qvÞ

q2v

1=4

ð3Þ

Due to variation of thermodynamic properties, the CHF

predicted by Eq. (3) for ethanol exhibits a broad maxi-

mum with pressure, rising from 0.5 MW/m2 at 1 bar

to $1.2 MW/m2 at $24 bar, and then gradually falling

off to 0.7 MW/m2 at $50 bar (the critical pressure of

ethanol is 63.8 bar), and this was borne out by the data

as well (within Æ15%).

As noted in Part I, the Kutateladze constant was

obtained theoretically by Zuber [6,7], and the idea of burnout limited solely by external (to the heater) hy-

drodynamics was pursued most prominently by the ex-

tensive works of Lienhard, Dhir and their co-workers

[8,9], as well as by Katto and his co-workers [10,11]. The

renditions (and interpretations) varied widely in their

specifics, as well as degree of specificity, but the result,

being the same, became entrenched at least as an upper

limit both quantitatively as well as conceptually [12].

But there have also been objections in principle to the

various specific hydrodynamic models (Zuber, Katto),

as well as detracting experimental evidences. One of

these is well established and concerns the decrease of

CHF on poorly wetted heaters (see Fig. 3 of Part I), as

found by Costello and Frea [13] almost contemporane-

ously to the works of Kutateladze and Zuber. This does

not violate the ‘‘limit’’, and therefore is not directly

detracting; it does provide, however, a prelude of the

difficulty by the need to introduce a regime transition

that is sharp and not understood. The other two kinds

of detraction are directly challenging to the limit, but,

supported by scant and/or uncertain data, their in-

fluence has remained largely isolated. One of these

pertains to the ability of Eq. (1) to cope with subat-

mospheric ambient pressures and the other with devia-

tions from the predicted trend under fractional and

microgravities.

Extensive work on the subatmospheric boiling was

performed in Russia [14–18]. Labulsov et al. reported

CHF of water and ethanol boiling on a disk heater of 32

mm in diameter [16]. Samokhin and Yagov obtained

CHF in boiling of organic liquids on a larger disk (64

mm in diameter) [18]. Avksentyuk and Mesrakesshvili

performed subatmospheric boiling experiments with

benzen and water [17]. All these data show a trend of

CHF deviating from predictions of the Kutateladze

correlation with the decreasing pressure. In experimentswith water, this difference becomes as much as 3–4 times

as the ambient pressure is decreased below 6 kPa [19].

The subatmospheric experimental data should however

be treated with caution with respect to the applicability

of the Kutateladze–Zuber theory to their conditions.

The effect of gravitational acceleration is important

for space applications and has been investigated more

broadly. Straub et al. performed boiling experiments in

parabolic aircraft flights using a rectangular plate of

40 Â 20 mm both in horizontal and vertical orientations

[20]. They noted that at reduced gravity observed re-

ductions in CHF are slower than the 1

4

-power prediction

by Kutateladze–Zuber equation, Eq. (3). More recent

results from experiments conducted in parabolic aircraft

flights yielded a CHF reduction by 60%, as compared to

the approximately 94% predicted by the Kutateladze–

Zuber equation for the 10À5 g in these experiments [21].

In a follow-on work, Oka et al. reported that for 10À5 g ,

CHF in water is more than 50% of that at normal

gravity [22]. These results are challenged by other CHF

data obtained by Shatto and Peterson [23], also in par-

abolic flights, using a cylindrical cartridge heater (9.4

mm in diameter) immersed in water. Specifically, at re-

duced pressures and microgravity (0.0005 g to 0.044 g )

Nomenclature

C p coefficient of heat capacity, J/kg K

g gravitational acceleration, m/s2

H lv latent heat of evaporation, J/kg

k thermal conductivity, W/m KKu Kutateladze number

l distance between nucleation sites, cm

L heater size, m

N nucleation site density, cmÀ2

q heat flux, kW/m2

t time, s

T temperature, °C

U velocity, m/s

Greek symbols

d capillary length, or thickness, m

q density, kg/m3

r coefficient of surface tension, N/m

DT temperature difference, K

Subscripts and superscripts

cr critical

K–Z Kutateladze–Zuber

‘ liquid

s saturation

v gas, vapor

w wall, heater

Ã dimensionless

794 T.G. Theofanous et al. / Experimental Thermal and Fluid Science 26 (2002) 793–810



they obtained CHF smaller than the Kutateladze–Zuber

predictions. The authors [23] concluded that even for

gravity as low as 10À3 g boiling crisis is governed by the

Taylor–Helmholz instability mechanism on vapor jet

emanating from the heater’s surface.

However intuitively appealing as the ‘‘hydrodynamic-

limit’’ idea may be, quantitatively it turns out to be verypuzzling. Take for example water boiling at atmospheric

pressure. From Eq. (1) we have U cr $ 0:9 m/s, so that

qcr $ 1:2 MW/m2, and with q‘=qv $ 1600, the needed

liquid supply is found to be only $0.6 mm/s. This means

that in order to interfere with such a minuscule rate of

supply, the vapor, in counterflow, has to ‘‘lift’’ essen-

tially all the liquid up against gravity to the point of

barely allowing it to touch the heater surface. A condi-

tion known as flooding, this would require more than an

order of magnitude greater velocities (and heat fluxes).

That this is so can be seen readily from Kutateladze’s

own flooding criterion, Ku ¼ 3:2 [24], and also from

balancing the drag force on a capillary drop (d $ d)

suspended against gravity. This being as straightforward

as it is basic, the other puzzle is: How could it have gone

unattended for so long?

Could it be that the effect of this ‘‘limitation’’ is in-

direct? That is, could it be that this apparent ‘‘break of

stability’’ in external (macro) hydrodynamics triggers an

‘‘inner’’ sequence of events that lead to dryouts? But

then for Eq. (1) to still work, this inner sequence must be

universal; that is, it should not introduce any other pa-

rameters. Or, could it be that Eq. (1) is simply a reduced

form (note the absence of viscosity) of some ‘‘inner’’

(micro)hydrodynamics problem that defines the onset of dryout in the limit of very well-wetting conditions? Or,

finally, could it be that (macro)hydrodynamics control is

so far out (as our estimates above indicate), that burn-

out is always controlled by heater-surface properties,

and that experimentally observed burnouts have been

fortuitously connected to such a ‘‘limit’’? With the re-

sults of our BETA experiment, we can now begin to

develop definitive answers to these questions.

The paper is organized as follows. In Section 2, we

begin with the overall behavior as manifest by the CHFs

measured. The principal parameter is heater-surface

aging, which, as discussed in Part I, is a feature not

captured by static or receding contact angle measure-

ments. A key point is that at each burnout condition we

now also have the nucleation pattern, and hence the

nucleation site density. We find these to exhibit a strong

positive correlation, and this is discussed relative to

current models and beliefs on the matter. The discussion

in Section 2 also includes all relevant previous work on

integral CHF measurements, as well as what is available

on the CHF behavior of very thin heaters. Our next step,

in Section 3, is to delve into the details of inception and

growth of the dryout spots, as eventually they become

responsible for burnout. We identify reversible and ir-

reversible dry spots and provide quantitative measures of

their temporal and spatial characteristics. Although

previous information on such matters is essentially

nonexistent, our discussion includes previous notewor-

thy attempts as pertinent for perspective and credit. A

complementary view of, and context for the so-charac-

terized dryout behaviors is provided in Section 4. Aidedby X-ray radiography, we are able to translate the ther-

mometric records into the detailed flow regime, and the

revelation of a scale separation phenomenon as a general

organizing principle of saturated high-flux boiling. On

this bases, we then proceed to define the key physics of

burnout. Examined in this light we find all previously

postulated thermal (heater)-control models to be inap-

propriate. The focus achieved by this definition of key

physics is suggestive of the kind of theoretical work

needed for further development of understanding, and of

the kinds of experiments that could best contribute to

such efforts. We close with a succinct listing on the major

conclusions in Section 5.

2. Critical heat flux

A total of 25 burnouts tests were conducted with

BETA heaters (see Part I) as summarized in Table 1.

The table also includes three representative burnout

events (C1, C2, and C3) obtained with a thick copper

heater fitted in the BETA test vessel. From the table we

can see that the BETA heaters ranged in thickness from

140 to 1000 nm, which, as expected, had no particular

influence. We also varied the water quality and mode of power delivery with apparently no strong direct effects.

On the other hand, a major variability was introduced

by heater aging, which, as explained in Part I, entailed

no significant change in static or receding contact an-

gles, nor in the macroscopic appearance of the heater

surface (mirror shine). A further variability was intro-

duced by extended exposure to boiling, and the atten-

dant cumulation of microscopic impurities (thereby

observing an indirect influence of water quality) as re-

vealed by SEM and AFM imaging (see Part I). Such

heaters were classified as ‘‘heavily aged’’.

Arranged in ascending order as in Fig. 1, these results

indicate an essentially continuous variation over a wide

range of burnout performance, from $50% to $140% of

the hydrodynamic ‘‘limit’’, and this leads to two im-

portant questions. One, having decisively violated the

quantitative Kutateladze–Zuber limit, now we must ask

whether there is any role left for the ‘‘external’’ hydro-

dynamics. In particular, could it be that a limit still

exists but it is simply at a higher heat flux level? Two,

viewed coherently as a single regime of heater-surface

control, is it reasonable to expect that the observed

variation could be related to measurable liquid/surface

properties and related mechanisms. We take up these

T.G. Theofanous et al. / Experimental Thermal and Fluid Science 26 (2002) 793–810 795



questions in detail in the next two sections. In the re-

mainder of this section, we can prepare the way by

pointing to an immediate result –– the strong correlation

of CHFs measured to nucleation site densities. In ad-

dition, this is a good place to discuss other relevant

work, on integral burnout performance, including the

previously identified (special) effect of heater thermal

capacity.

From all tests for which we have IR records at, or

very near burnout, we could extract nucleation side

densities, as discussed in Part I, and the results are

shown in Fig. 2. Despite the considerable scatter, a

strong positive correlation is evident. This contradicts

the models of Kolev [25] and Ha and No [26], which,

based on the Wang and Dhir [27] data on nucleation site

density, predict instead a strongly negative correlation.

There are two possible ways to interpret this experi-

mentally found correlation. One, implying an indirect

effect, we could think that what makes the surface re-

sistant to burnout makes it also more amenable to nu-

cleation. Two, supposing a direct effect, we can think of

Table 1

BETA burnout experiments

Experiment Heater thickness

(nm)

Heater aging Water quality Power supply CHF (kW/m2) qcr=qK – Z

F1 1000 Fresh HPLC DC, SS 925 0.77


F3 270 Fresh DI DC, SS 850 0.71

F4 500 Fresh HPLC DC, SS 800 0.67F5 500 Fresh HPLC DC, T 700 0.58

F6 500 Fresh HPLC DC, T 950 0.79



F9 140 Fresh DI AC/60 Hz, sin 670 0.56



F12 140 Fresh DI AC/30 Hz, square 750 0.63

A1 500 Aged HPLC DC, SS 1200 1.00

A2 300 Aged HPLC DC, T 1220 1.02

A3 270 Heavily aged HPLC DC, SS 1517 1.26

A4 500 Heavily aged HPLC DC, SS 1530 1.28

A5 270 Aged DI DC, SS 1156 0.96

A6 270 Heavily aged DI DC, SS 1380 1.15A7 500 Heavily aged HPLC DC, T 1610 1.34

A8 450 Aged HPLC DC, SS 1020 0.85

A9 500 Aged HPLC DC, SS 1000 0.83

A10 270 Aged DI DC, SS 938 0.78

A11 140 Aged DI AC/60 Hz, sin 1159 0.97

A12 140 Aged DI AC/60 Hz, sin 1062 0.88

A13 140 Aged DI AC/1000 Hz,

square

1185 0.99

C1 Copper block Heavily aged HPLC DC, SS 1640 1.37

C2 Copper block Heavily aged HPLC DC, SS 1710 1.43

C3a Copper block Heavily aged HPLC DC, SS 1630 1.36

qK – Z ¼ 1200 kW/m2; AC: alternating current; DC: direct current; SS: Steady State; T: Transient; HPLC: high-purity water used in liquid chro-

matography; DI: de-ionized, clean water.a

In C3, the test section subdivided into eight, 10 Â 10 mm cells.

Fig. 1. Results of the BETA experiment: (}) nanofilm heaters; (N)

thick copper heater with surface modification as noted; (j) thick

copper heater with test section volume subdivided into eight, 10Â 10

mm cells. As shown both extremes are highly reproducible.

qK – Z ¼ 1200 MW/m2. Results of the three AC tests (F9, F10 and F11)

are not shown.




increasing nucleation with attendant smaller in size nu-

cleation-affected heater areas, and thus an easier resup-

ply of the microlayer in the most vulnerable central

region (see also Sections 3 and 4). In any case, the ob-

served behavior is inconsistent with a ‘‘repulsion’’ or

other external hydrodynamics control idea, as in our

uniform-flux experiments this (vapor flow) repulsion

does not depend on nucleation site density (see also

Section 4).

2.1. Discussion

Previous experiments on pool boiling crisis wereconducted on both horizontal and vertical surfaces,

using heaters of various sizes and shapes (plates, strips,

discs, cylinders, spheres, and wires) –– see, for example,

the reviews of Katto [28,29]. There is almost no atten-

tion paid to the effect of these features on the flow re-

gimes, and with just a few exceptions to be noted below,

nor to the applicability of the Kutateladze–Zuber result.

This has generated confusion not only on the experi-

mental validation of the hydrodynamic theory, but also,

it led to erroneous interpretations of flow structures, and

thus to inappropriate ‘‘models’’. Clarifications of these

matters is necessary if we are to decisively address the

mechanism of burnout in light of all experimental evi-

dence, including the present as well as all previous rel-

evant work.

The commonality of the Kutateladze and Zuber

ideas, expressing the external hydrodynamics control,

boils down to scaling a critical vapor velocity in terms of

the relevant fluid properties –– densities and surface ten-

sion –– and the body force field. There is no external

length scale, and this implies a limitation to horizontal

infinite flat plates. For both there is an ‘‘internal’’ length

scale, the capillary length, and this provides an ap-

proximate measure of the dimensions above which the

plate can be considered infinite –– say of the order of 10

capillary lengths. For water at 1 atmosphere, this means

a length scale of $25 mm. But there are also some basic

differences in the two ways of thinking that have to be

kept in mind in addressing issues of geometry, satisfying

respectively self-similarity.

Zuber’s postulated Rayleigh–Taylor controlled coun-ter-current flow is macroscopic, and it is easy to see that

self-similarity for it requires strict absence of external

length scales able to introduce departures from (on the

average) one-dimensional (1D) behavior [6]. In turn, this

requires that the liquid pool contains no bypass regions

(its cross-section is fully coincident with the heater’s

cross-section), and that it is of small aspect ratio (height

divided by the smallest lateral dimension). Costello et al.

[30] understood all these requirements and their exper-

iments (conforming to them) with a 50 Â 150 mm2

heater yielded a CHF of 1.1 MW/m2, almost in exact

agreement with Eq. (3). Also, Lienhard and Dhir un-

derstood this, as they pursued small length and other-

shape affects within the hydrodynamic context [8,9]. On

the other hand, Gaertner’s [31] experiment conducted

with a 5 cm in diameter disc placed at the bottom of a

deep (20 cm) and wide (14 cm) liquid pool fails to meet

these requirements. Yet, the observed flow regime, a

periodic formation, hovering, and departure of a vapor

‘‘mushroom’’ bubble, which is a direct consequence of

the particular, recirculation inducing, pool geometry,

had a prevailing influence, both in ‘‘re-deriving’’ the

general Kutateladze–Zuber result [28], as well as in in-

spiring several heater-surface-centered (thermal) models

[11,32,33]. Further, these models make use of a microjet-pierced liquid ‘‘macrolayer’’ at the base of the mushroom

bubble, presumably ‘‘seen’’ by Gaertner, but evident

nowhere in his paper. Gaertner [31] measured CHFs of

up to 1.55 MW/m2 (135% of the Kutateladze–Zuber

value) and he took this to be supportive of the hydro-

dynamic limit.

Kutateladze’s idea of ‘‘repulsion’’ is more vaguely

stated, and thus it allows a somewhat greater flexibility

in satisfying self-similarity. It appears that he is focused

in a boundary layer, right next to the heater surface, and

he thinks of a hydrodynamic transition occurring within

this layer. Following his experiments with Gogonin [5],

they assert that a width of even 2 capillary lengths ( $2

mm in their ethanol experiments) is sufficient to elimi-

nate the effect of an external length scale. Their water

pool was deep ($15 cm) and much wider than their

heater (10 cm). These experiments yielded the Ku ¼0:145 result (as in Eq. (3)). Excellent agreement with Eq.

(3) was also reported by Kutateladze and Malenkov in

later water boiling experiments [34]. Unfortunately, no

mention of the flow regimes observed was made in these

papers, but Kutateladze had no doubt that the two-

phase flow above the heater was dispersed and highly

chaotic (i.e., he disagreed with Zuber’s picture of a

Fig. 2. Relation between CHF and nucleation site density measured

just prior to burnout.




relatively regular array of vapor jets). What remains

unclear is the extent of interplay between the external

hydrodynamics and the transition within the boundary

layer that was the focus of Kutateladze’s interest. In this

interpretation both Gaertner’s and Kutateladze’s own

experiments are open to question of such ‘‘external’’

influences. Remarkably, all other previous experimentsare even further removed from these self-similarity

requirements.

As indicated in Table 1 (and Fig. 1) the highest CHF

level reached in this work, 1.6–1.7 MW/m2, was both

on nanofilm as well as on thick copper heaters. This

is remarkable from a couple of different standpoints

and needs further elaboration. First is the effect(s) of

heater-surface properties already mentioned. Previous

knowledge is based mainly on the work of Hahne and

Diesselhorst [35] and of Liaw and Dhir [36], who ex-

pressed this effect in terms of surface wettability, as

measured by the static contact angle. The latter con-

ducted transition boiling experiments with water and

freon-113 on copper heaters, 63 Â 103 mm2, placed ver-

tically in a pool of liquid being boiled. Freon wets the

copper surface well. For water contact angles obtained

were in the range 18–107°. At 18°, the peak heat flux

measured was near (97%) the ‘‘hydrodynamic’’ limit,

while for higher contact angles the decreasing trend was

as illustrated in Fig. 3 of Part I. This is to be compared

with Fig. 1; all nanofilm heater data being at the same

static contact angle of $65°. Moreover, the highest level

reached with such heaters appears to coincide with the

CHFs measured on the thick copper heater whose sur-

face was treated (as described in Part I) to a highlysmooth and wetting finish –– a contact angle of under 15°.

Second is the effect of heater heat capacity. Previous

knowledge is based mainly on the work of Bergles and

co-workers [37,38], who following sporadic work such as

that of Tachibana et al. [39], Guglielmini and Nannei

[40], expressed the effect in terms of the quantity

DÃ $ dwðk wqwC p ;wÞ1=2, where the wall (heater) thickness

dw, is combined with the quantity containing the wall

thermal properties (conductivity k w, density qw, and

heat capacity C p ;w). They experimented with horizon-

tally suspended, vertically positioned, ribbon heaters (5

mm height by 50 mm length) of various thicknesses,

down to 10 lm, and constitution (copper, steel, mo-

lybdenum, etc.). Carvalho and Bergles [37] correlated

the data, including other data with both plates and

cylinders, independently of orientation (vertical, hori-

zontal), and the result is a gradual diminishing of CHF

from the ‘‘hydrodynamic-limit’’ value for DÃ $ 10, down

to $10% for DÃ $ 5 Â 10À3. The DÃ for our nanofilm

heaters is 10À3, or 0.24 if based on the glass substrate

thickness and properties, and according to the correla-

tion, our CHFs should be limited to $50% and below

10% of the hydrodynamic limit respectively. Instead, our

data show an exceedence to 140%.

3. Characterization of burnout

In Part I (Section 4.3) we identified hot spots that

appear within bubble bases as dry spots. Typically, a dry

spot temperature reaches a maximum, and then it drops

during an apparent rewetting event. We call these ‘‘re-

versible’’ dry spots. At higher heat fluxes, the number of such dry spots increases and so does their lifetime span.

Ultimately, when the CHF level is reached, one or more

of these dry spots take off in a thermal runaway,

growing in size, that quickly lead to heater failure–the

burnout. These are our ‘‘irreversible’’ dry spots. Clearly,

it is this transition from reversible to irreversible dry

spots that contains a major portion of the key physics,

and hence the quantitative definition of the burnout

process. This is the subject of this section. The remain-

der of the key physics is concerned with the hydrody-

namic context in which these dry spot dynamics take

place, that is, the mode of interaction with the external

(to the microlayer) hydrodynamics, and this is the sub-

ject of the next section. We begin with an overview of

previous relevant work found in the literature.

The essentially impossible task of directly observing

dry areas by photographic means was pursued early on

by several well-known investigators [10,31,41,42]. While

nothing concrete could be documented, interpretations

of such visualizations have remained influential (to this

day) in the conceptual perception and modelling of the

dryout phenomenon. In particular, this includes a peri-

odic ‘‘mushroom’’ bubble, fed by a steady, dense micro-

jet system on a liquid macrolayer at its base [11,32] –– a

regime which is negated by the findings of the presentwork.

Instrumentation for direct detection of dry areas was

introduced by Van Ouwerkerk [43]. The heater was a

transparent, vapor-deposited gold film, on a glass sub-

strate, and dry areas could be distinguished from wet

ones on the basis of total reflection of (white) light

shown in from below. Experiments were conducted

with n-heptane, on a 90 Â 90 mm2 heater, within an ap-

parently two-dimentional (2D) test section geometry

(200 Â 200 mm2). He reported observations of dry areas

formed beneath bubbles. At the atmospheric pressure,

burnout was found to occur at heat flux of 195 kW/

m2 –– that is $75% of the Kutateladze–Zuber prediction

(253 kW/m2) for n-heptane. This result is consistent with

CHF obtained in BETA experiments on fresh nanofilm

heaters. Van Ouwerkerk argued that dryout occurs

when a dry area is larger than a critical size.

Apparently unaware of Van Ouwerkerk’s work

Nishio et al. [44] resurrected the total reflection tech-

nique some 25 years later. For a substrate they used a

single sapphire crystal, 5 mm thick, and a transparent

electro-conductive film as the heater. The fluid boiled

was a refrigerant, R113. They used a high-speed video

camera to image a heater area of 9 Â 12 mm2 from




below through a silicon oil bath. Information about the

heater’s surface characteristics and wettability by R113

is not given in the paper [44]. At low heat fluxes, round

dry areas were found in the bubble bases. As heat flux

increases, the primary dry areas coalesce and cover 40%

of the heater surface. Near CHF the wetted area was

found to exist as a network of wriggling continuouscanals of liquid. This behavior was not borne out by the

infrared thermometry results in BETA.

3.1. General observations of burnout in BETA

In running a test to burnout in BETA, we can observe

the complete heater thermal response in real time, and

as noted above, we have a qualitative warning of an

impending crisis by the number and lifetimes of the

reversible dry spots. Still, a crisis event occurs cata-

strophically in a time frame of less than a second, and

initially it proved difficult to capture by manually trig-

gering the ‘‘recoord’’ of the camera, which at 1000

frames/s allowed only 1 s of record time. Perhaps more

importantly, this forward-recoord trigger precluded cap-

turing the all-too-important sequence of events leading

up to burnout. The situation was remedied by devel-

oping back-trigger capability for our IR camera, and

expanding data transfer and storage to allow a total of

4000 full frames (4 s at 1000 frames/s). A total of four

runs, the F1, F2, A1, and A2 have been recorded in this

fashion so far, and these are the data discussed in this

section. We begin with overall qualitative observations

on representative thermometric images, shown in Figs.

3–6 for these four burnouts, respectively.In these figures, superposed to the two kinds of nu-

cleation patterns (for fresh and aged heaters) discussed

in Part I, we can see the dry areas as bright spots, that

appear and disappear, or grow, and eventually merge, to

the macroscopic patterns that cause failure (in the last

frame of each sequence). Significantly, the growth oc-

curs simultaneously in more than one of the hot spots,

and this is most evident in Fig. 3. On the other hand, as

seen in Fig. 4 (fourth frame) an initial attempt of as

many as five spots to grow and merge is forestalled byFig. 3. Burnout of a fresh heater (F1) at 925 kW/m 2.

Fig. 4. Burnout of a fresh heater (F2) at 950 kW/m2. Sample of nine

frames of IR image from a 4 s record. To illustrate chaotic nature and

variability we chose the frames not to be sequential.

Fig. 5. Burnout of an aged heater (A1) at 1200 kW/m2.




an apparent rewetting event that lent way to a normal

nucleation pattern in subsequent frames. The same is

also seen in the second frame of Fig. 6, although in this

case, one of the hot spots appears to have survived. In

general, the final transition to unstable behavior in aged

heaters appears more abrupt and from a much smaller

population (site density) of reversible dry spots, as

compared to fresh heaters. While this is consistent with

the difference in respective power levels, it is such

quantitative behavior that can provide the clues for, and

testing of ideas as to the mechanism of incipient insta-

bility. An initial sampling of the quantitative features

available in such thermometric records is provided fur-

ther below. Based on the qualitative information just

presented a number of important conclusions regarding

previous models of dryout-induced crisis can be reached

immediately.Specifically, this refers to the vapor-stem model of

Dhir and Liaw [32], and the hot-spot model of Unal

et al. [33]. The former envisions a static pattern of steam

microjets, extending from their base, and a respective

dry patch on the heater wall, through a macrolayer –– a

liquid film of a few hundred microns in thickness. Ac-

cording to this model the approach to CHF is accom-

panied by an increase in population of these small ($500

lm) dry patches, and crisis occurs when they are found

to be so dense as to merge at their bases. This turns out

at a dry patch occupancy of around 50%. Surface wet-

tability is taken into account by the contact angle at the

base of the jet in combination with its effect on nucle-

ation site density. None of these features are confirmed

by the BETA experiments. The Unal et al. [33] idea of

dryout, on the other hand, hypothesizes that boiling

crisis involves heater surface superheating to the Le-

idenfrost temperature, and took radial conduction in the

heater’s body as a principal mechanism modulating the

approach to criticality. In implementation they super-

posed this to a combination of the Dhir–Liaw [32] and

Haramura–Katto [11] models. For thick copper heaters

they find that crisis requires the formation of dry pat-

ches as large as 5 cm in diameter (compare this to Dhir’s

submillimeter stem bases). Further they find that thin,

poorly conducting heaters should be very susceptible to

burnout. In addition to being open to the same criticism

as are its base models, this heater ‘‘conductivity’’ effect is

utterly in conflict with the BETA experiments where

CHF as high as 1.6 MW/m2 were found. It should be

noted that both the Dhir–Liaw and Unal et al. ap-proaches to explaining the crisis were apparently based

on visual observations made by Gaertner [31]; however,

none of these features can be found documented in his

paper. From our own experience, even under conditions

of much lower nucleation density, visualizations such as

those reported by Gaertner are not possible.

3.2. Quantitative features of reversible dry spots

As noted already, dry spots develop always at the

center of bubble-cooled areas. Two kinds of behavior

could be identified. One pertains to newly formed bub-

bles at a highly superheated region of the wall (and

adjacent liquid) –– a situation that is mostly relevant to

fresh heaters. The other pertains to bubbles emanating

continuously from fixed nucleation sites, thus main-

taining a relatively low superheat that fluctuates regu-

larly in time –– a situation found both on aged as well as

on fresh heaters. In Part I, we called this ‘‘irregular’’ and

‘‘regular’’ bubbles respectively. In Section 4.3 of Part I,

we also elaborated on how we detect the initial forma-

tion of dry spots, as they evolve through cooling–heat-

ing cycles in the middle of (some of the) bubble-cooled

areas. Here, we would like to provide sample data on the

heating–cooling cycles and the sizes that characterize thereversible dry spots themselves. As discussed in Part I,

an appropriate demarcation of ‘‘dry’’ state on a BETA

heater is an IR temperature measurement in excess of

$170 °C, and this is the criterion utilized in the data

reductions below. Also, we should be reminded at this

point that temperatures above $200 °C are only indi-

cative, because they involve extrapolation of the cali-

bration curve used for all runs reported here.

A typical appearance and disappearance of a revers-

ible dry spot at 800 kW/m2 (from the F1 series of tests) is

shown in Fig. 7. In the same figure we can also see the

digitized temperature transient at the center of the hot

spot. From records such as this, one can deduce the

relevant length and time scales –– in this case ‘‘mm’’ and

‘‘hundreds of ms’’ respectively. A most remarkable

feature in this case is that the temperature at the center

keeps on increasing, while the size of the hot spot seems

to shrink (between 50 and 150 ms). In still greater detail,

we can extract 2D digital records such as the one shown

in Fig. 8. This case too is from a reversible dry spot that

appeared at a heat flux, very close (within 50 kW/m 2) to

the one that caused burnout of this heater. Again, we

can see similar length and time scales, but in addition,

we now also have a quantitative depiction of the tre-

Fig. 6. Burnout of an aged heater (A2) at 1220 kW/m2.




mendously steep temperature gradients (6000 K/mm) in

the region between the hot spot and the surrounding

‘‘cool’’ area. Even with our extremely thin and poorly

conducting heater-substrate assembly, at such tempera-

ture gradients, conduction cannot be completely ne-

glected, and a significant amount of additional work (in

data analysis) is needed in order to extract all that is

possible from such a detailed diagnostics. Remarkable

in this figure is the profile at 134 ms –– it shows simul-

taneous heatup (and dryout) at the center, and coolingin a surrounding (ring) area (a contact line moving

outwards).

Reversible dry spots are of immense interest, because

it is through them that the burnout runaway, that is the

irreversible dry spots, arise. Thus, we are especially in-

terested in reversible dry spot behavior very near and

during burnout, and this will be the focus of the rest of

our discussion in this subsection.

Typically, we found reversible dry spots to grow to a

size of 1–4 mm, the larger sizes favored by fresh heaters

and irregular bubbles. Corresponding lifetimes were

found to range from 60 to 600 ms. Representative data

are summarized in Fig. 9. Note that the character, in this

respect, of every heater is starkly different. Of these four

runs, it appears that F2 found itself at a final power level

that was particularly close to the transition to unstable

behavior, and thus it provided, by comparison to the

other runs, a much wider ‘‘action’’, and thus data, on

reversible dry spots (see Fig. 4). As we can see in Fig. 9,

these data show that sizes and lifetimes are correlated in

a manner that can be understood intuitively –– the bigger

spots live longer. On the other hand, the scatter ob-

served, especially for the smallest spots, can be under-

stood by recognizing the significant role of radial

Fig. 7. Illustration of the dynamics of a reversible dryspot on a fresh heater (F1), at 800 kW/m 2. The figures show an area of 6 mm Â 6 mm of the

heater. The temperature scales are shown to the right of each image. The temperature transient shown on the extreme right is for the center spot of

the images pictured, including intermediate frames not shown on the left.

Fig. 8. Evolution of the temperature field around a nucleation site that

becomes the origin of a dry spot in test F2.




conduction in dissipating a portion of the thermal en-

ergy generated within the dry area. For example, for a

well-supplied (evaporating) meniscus around a 0.7 mm

in diameter dry spot, a heat flux of up to 1 MW/m2 can

be dissipated before the center exceeds 250 °C.

A further detail of behavior is available by looking at

the growth–collapse dynamics of the dry spots, as il-

lustrated in Figs. 10 and 11. In these figures, the time

and dry spot diameter have been normalized by the

lifetime (t total) and maximum diameter (d maxds ) of each dry

spot respectively. Two kinds of behavior have been

discerned. One (let us say Type 1) as depicted in Fig. 10,involves a very rapid growth to the maximum size,

within a time frame of $1=10th of the lifetime, and then

a gradual, pretty monotonic collapse. The other (Type

2), shown in Fig. 11, exhibits a ‘‘hesitant’’ or interrup-

tive growth, through a complex series of steps, over a

time frame that can extend up to $1=2 of the lifetime,

and then a gradual collapse, the tail end of which (last

$40%) appears to be quite more precipitous in com-

parison to the collapses seen in Fig. 10. Still another,

complementary perspective can be obtained from Fig.

12, showing the fractional growth time (t grow=t total) of

the dry spots analyzed against their maximum diameter.

We can see that Type 1 and Type 2 dry spots are dis-

tinguished by their large and small sizes respectively.

This method of presentation ––

dry spot diameter nor-malized by the mean distance between nucleation sites,

lns $ ffiffiffiffiffiffiffiffiffi

1= N p

’ 3:45 mm in this run –– also shows that the

size of dry spots is some fraction of this mean distance,

while being bounded by it from above. Along these lines

Fig. 9. Relation between size of reversible dry spots and their lifetime

span.

Fig. 10. Growth and collapse of three reversible Type 1 dry spots in

test F2.

Fig. 11. Growth and collapse of three reversible Type 2 dry spots in

test F2.

Fig. 12. Fractional expansion time versus maximum dry spot size

normalized by lns ’ 3:45 mm (Test F2).




and in more local detail, we show in Fig. 13 the maxi-

mum size of dry spots in relation to the mean distance

from neighboring nucleation sites, specific to each spot

(lns). Now, we have an even more clear hint that the

growth of dry spots is interfered with by the neighbor-

ing, bubble-cooled areas.

3.3. Irreversible dry spots

A typical irreversible dry spot is shown in Fig. 14.

Key ingredients of the behavior are a growth velocity

scale of millimeters per second, a short/fast cooling

event just prior to the thermal runaway, and a heatup

rate quite close to that estimated for adiabatic condi-

tions. Each of these is taken up in turn in the following.

The evolution of the dry area (in the four runs being

discussed) with time is shown in Figs. 15 and 16, for the

fresh and aged heaters respectively. As noted above, for

these four runs, we have sufficient record time to follow

the reversible dry spots as well, over the time frame of seconds prior to burnout. We can see that the reversible

dry spot areas fluctuate at rather low levels ($10 mm2 or

$1% of the heater area), and that the growth associated

with the onset of instability is quite catastrophic. Failure

occurs at a dry area fraction of $10%. As noted above,

all indications are that power in run F2 was the closest

to the true critical power, and as a manifestation of this

Fig. 13. Relation between the maximum size of reversible dry spots and

a characteristic distance (lns) between neighboring active sites (see

text). The bounding line indicates the maximum possible size of the dry

spot being constrained by the neighboring bubble-cooled areas.

Fig. 15. Evolution of dry areas as burnout is reached in Tests F1 and

F2.

Fig. 14. Illustration of the dynamics a dryspot in the process of burning out. The figures show an area of 6 mm Â 6 mm of the heater. The dryspot

propagation speed is $5 mm/s for the first 200 ms and slows down to $1.5 mm/s in the later stage. The graph in the right shows the temperature

transient for the initial heatup phase of the dryspot when contribution of the radial conduction is not negligible. The dashed line indicates the

adiabatic heatup rate.




we see again here the greatly expanded reversible dry

spot ‘‘activity’’ on a time scale of seconds.

On the short cooling transient that seems to always

precede dryout, additionally to Fig. 14, we provide Fig.

17, pertaining to an ‘‘irregular’’ bubble, and Figs. 18 and

19, which are regular bubbles on a fresh and aged hea-

ter, respectively. In Fig. 17, the plateau of $150 °C in-

dicates a highly superheated liquid layer immediately in

contact with the heater. This is the kind of ‘‘space’’ seen

in between bubble-cooled areas in images such as those

of Figs. 3 and 4. Referring to Fig. 17, the rapid cool-

down at $120 ms corresponds to a nucleation event seen

by the appearance and growth of a bubble-cooled area

(2–4 mm in diameter) in the IR image. This cooldown

(of the center) is interrupted sharply, within a matter of

a few milliseconds, to yield a rapid, nearly adiabatic

heatup, a behavior quite similar to that already seen for

an irreversible dry spot in run F1 (Fig. 14). Such a

turnaround from a cooldown, to a monotonic heatup, is

also evident in Figs. 18 and 19, although now in a milder

form, as appropriate to the lower superheats seen under

‘‘regular’’ bubbles. In more detail, in Fig. 18, we see a

couple of previous attempts to run away, at $5 and

60 ms, but these were interrupted shortly by rewetting

events. Another manifestation of complexity is the more

elaborate interplay between heatup and attempted rew-

ets, as illustrated in Fig. 20. From the complete images

we could see in this case dry spot dynamics to be affected

by nearby nucleation events. This dry spot too eventu-

ally becomes completely unstable and is on its way to

burnout.

Fig. 16. Evolution of dry areas as burnout is reached in Tests A1 and

A2.

Fig. 17. Temperature at the location of dry spot origin. Test F2 at

q ¼ 950 kW/m2.

Fig. 18. Temperature at the location of a dry spot origin. Test F2 at

950 kW/m2.

Fig. 19. Temperature at the location of a dry spot origin. Test A1 at

1200 kW/m2.




Remarkably, in none of the irreversible dry spots

observed did the heatup rate quite match that calculated

for an adiabatic condition, as one would expect for a

large ( D > 2 mm) dry spot. For example, while the ini-

tial heatup rate in Fig. 14 ($1400 K/s) is consistent with

an energy balance that accounts for radial conduction

through the glass substrate as the only loss mechanism,

later on it is seen to ‘‘fall off’’ (rather than approach) the

adiabatic heatup rate also shown in the figure ($2400 K/

s). Similarly, the heatup rates in Figs. 17–19, 2500, 1750

and 2233 K/s respectively, are lower than the adiabatic

values of 3166, 3166 and 4000 K/s. We have tried to bemeticulous about the thermophysical properties of the

glass utilized in these calculations, but the values used

for heat capacity could not be positively confirmed.

Similarly, we took extra pains to confirm the thermal

power delivered to our heater under both wet and dry

conditions, also taking into account the resistivity vari-

ation with temperature (see Part I). On the other hand,

we note that all thermal runaways show a smooth

monotonic increase, unlike the fluctuating behavior due

to losses to the fluid above seen in all other situations

preceding the thermal runaway (see Figs. 17–19). A

number of possible, but ‘‘exotic’’ mechanisms for losses

beyond film boiling come to mind, so this matter de-

serves further investigation.

In conclusion, these direct observations of the burn-

out process in BETA suggest that dryout is a sharply

defined critical phenomenon, with highly localized, but

not singularly so, incipience, and very rapid (runaway)

character. One key context of this incipience is a highly

dynamic appearance and collapse of (reversible) dry

spots, which are highly localized too, affecting less than

1% of the area. The other context is the microlayers that

feed the so-formed contact lines (microhydrodynamics),

and the interaction of these microlayers with the exter-

nal hydrodynamics –– the two-phase counter-current

flow on top of the heater. This is the subject of the next

section.

Views of burnout that are generally consistent with

the ‘‘critical’’ character of the phenomena identified/

quantified above, have been previously postulated by

Reyes and Wayner [45] and Sefiane et al. [46]. Reyes andWayner looked at the forces around a static contact line,

and tried to relate the onset of instability to a ‘‘critical’’

temperature. The BETA experiments show that burnout

on a heater may be initiated in the bubble bases with

local surface superheats varying from 20 to 60 K. This

contradicts the Reyes–Wayner concept that relates

burnout to a heater-surface-average critical superheat

($30 K for water). Sefiane and co-workers, on the other

hand, again focused on the stability of contact lines,

assigned a principal role on the vapor recoil as a de-

stabilizing mechanism as first introduced in the work of

Palmer [47] for liquid evaporation at reduced pressure.

Application of this mechanism to boiling crisis has

however been only discussed in qualitative terms. It is

interesting to note that for conditions of interest (water,

atmospheric pressure) the recoil pressure [D P ’ ðq= H lgÞ2=qv], being the driving force for the recoil insta-

bility, is about 0.25 Pa, while the stabilizing force due to

surface tension ($r=d) on a thin layer (d) is several order

of magnitudes larger.

4. Flow regimes

At a heat flux of 1 MW/m2 the superficial vapor

velocity is $1 m/s and the flow is well past the point

where a bubbly regime can be sustained. According to

Kutateladze [24], this kind of transition occurs at

Ku ¼ 0:3

ffiffiffiffiffiqv

q‘

r $ 10À2 ð4Þ

that is, at a heat flux of $100 kW/m2. At such relatively

high velocities then, the vapor flow is accommodated by

‘‘expanding’’ the two-phase region sufficiently to allow

an increasing amount of disengagement from the liquid

in the pool. In a 1D geometry this occurs by the co-

alescence into larger bubbles, and ultimately by the

formation of temporary vapor channels, that impart a

‘‘churning’’ or ‘‘chugging’’ quality to it. In this regime,

typically the void fractions reach, on a time-averaged

basis, to above $40%, and vary slowly with vapor flow.

The characteristic scales of such a flow pattern are much

greater than that of the capillary length, and the detailed

behavior now depends very much on the geometry and

dimensions of the flow domain. However, the key

character of the flow is ‘‘churning’’, in any case, over a

range of vapor velocities up to an order of magnitude

greater (see Section 1), and this we believe we captured

Fig. 20. Temperature at the location of a dry spot origin. Test F2 at

950 kW/m2.




in our BETA test section, by operating with low aspect

ratio (height to the smaller lateral dimension) liquid

pools.

As illustrated in Figs. 21 and 22, the above-described

basic considerations are fully borne out by the behaviors

found in BETA. Note, in particular, the ‘‘large’’ internal

scales, and the chaotic character of the liquid–vapordistribution revealed by the radiographs. Also note that

the void fraction averaged over the main portion of the

pool is $40%, as expected. The underlying churning was

also recorded in the high-speed videos, and it was quite

evident too in visual observations. While some dynam-

ics-induced dispersal to liquid droplets could be seen at

the top, as evidenced by the radiographs too, even at the

highest flux levels reached the amount of carryover was

negligible.

More specifically now, as we can see in these radio-

graphy, the bottom of the pool, adjacent and all across

the heater, is occupied by a very high void fraction re-

gion ––

like a vapor ‘‘blanket’’. In Fig. 21, we see that

within 1 mm of the heater surface the cross-sectional-

average void fraction reaches $80–90%. This indicates a

most remarkable separation of the external (macro)hy-

drodynamics from the heater, which to remain cooled,

as evidenced by the IR images in Figs. 3–6, must be

continuously covered by liquid. Thus, we can envision a

continuous liquid supply –– note that the blanket is not

Fig. 21. Radiographic image of the boiling liquid pool at 1000 kW/m 2 on an aged nanofilm heater (A7). On the right is the void fraction scale. The

straight black line at the bottom is the image of the heater/glass assembly. The graphs show the deduced cross-sectional-average void fraction as a

function of distance from the heater.

Fig. 22. Radiographic image of the void fraction distribution at 1100

and 1200 kW/m2 on an aged heater (A7). On the right are void fraction

scales.




100% vapor –– and an attendant action at the microhy-

drodynamic level, as this liquid spreads upon an ex-

tended microlayer, while nucleation events within it

participate in the spreading process, expelling any excess

to the region above.

That this ‘‘separation’’ is organic is further evidenced

by contrasting the chaotic macrohydrodynamics above,to the order, uniformity, and regularity of the micro-

hydrodynamics on the heater, as seen in the IR mov-

ies –– and only partly evident in the selected frames

shown in Figs. 3–6. We can thus refer to a ‘‘scales sep-

aration’’ phenomenon, in high heat flux, saturated pool

boiling. One implication is that the heater and the ex-

tended liquid microlayer on it operate autonomously,

that is, without any significant influence of the external

hydrodynamics. A subsequent implication is that since

the presence of the liquid pool is only incidental, the

burnout phenomenon can be studied in isolation by

focusing on the heater-microlayer system alone. This is

beneficial in eliminating the obscuring (and superfluous)

external hydrodynamics, allowing direct visual access

from above as well (Configuration B in Fig. 4 of Part I)

and an even better understanding of the microhydro-

dynamics through control of the liquid supply.

In conjunction with the above-identified scale sepa-

ration, we can now examine the IR records towards

understanding the flow regimes that govern microhy-

drodynamics. Ignoring transient effects (the time con-

stant of a 5 lm thick microlayer, heated on one side,

vaporizing on the other, is 0.5 ms) the temperature of

every pixel on the IR record can be converted to a mi-crolayer thickness (d) by d ¼ k ‘ðT w À T sÞ=q, where T wand T s are the heater and saturation temperatures re-

spectively. Sample results for a fresh and a heavily aged

heater are shown in Figs. 23 and 24 respectively. The

picture is one of an ‘‘extended’’ microlayer punctuated

by steep depressions (‘‘craters’’), where thicknesses reach

down to a few microns. Sequential arrangements of

frames such as these allow one to visualize the full dy-

namic pattern of the microhydrodynamics. The average

thickness of the microlayer in an aged heater is in the

range from 10 to 15 lm, while for fresh heaters this

range changes to 20–30 lm near-CHF conditions. The

thicker film (30 lm) corresponds to surface superheats

of up to 55 K. Such a high superheat is present in the

nucleation-free areas of fresh heater just prior to the dry

spot formation. In the region between bubble sites, heat

is removed from the heater surface to evaporating

Fig. 23. Map of microlayer thickness on a fresh heater (test F1) near burnout at q ¼ 850 kW/m2. The thickness map presented is pixel

(250 lm Â 250 lm) –– averaged and with an accuracy of Æ5% (relative) due to time response of the glass heater.




interface by means of heat conduction through the liq-

uid film. The dynamics and stability of this liquid layer

are likely to be governed by the distance between the

neighboring nucleation sites. This explains the effect that

nucleation patterns have on the burnout.

Clearly, ‘‘rupture’’ of the liquid film under certain

conditions and subsequent dry spot spreading produces

boiling crisis. What is at play here is a complex set of

hydrodynamic phenomena coupled to capillarity, in-

cluding: long-range forces at the nucleation at the nu-

cleation-site-tips of the microlayer, viscous flow

supplying the microlayer from the surrounding thicker

regions, surface tension forces due to the curvature at

the tip. All these combine with the nucleation site den-

sity which supplies an ‘‘external’’ length scale, to medi-

ate conditions for which the supply (flow into the

depression) is not large enough to make up the demand

due to evaporation.

Digitized records, such as those shown in Figs. 23 and

24 provide the basis for more detailed quantitative

analysis, including possible corrections due to transient

and lateral conduction effects, as well as for guiding and

testing predictive models of the relevant processes. All in

all, we have here the ‘‘fingerprints’’ of boiling, all the

way into burnout, and a scale separation phenomenon

as a general organizing principle for saturated, high heat

flux boiling, that allows proper focusing on the micro-

hydrodynamics as the sole control of boiling crisis.

5. Concluding remarks

• This work addresses boiling heat transfer –– a subject

that despite its outstanding technological importance,

and indeed a most rich fluid-physics content, has re-

mained deeply misunderstood. We focused on boiling

crisis, a phenomenon that leads to ‘‘burnout’’, that is

the physical destruction of the heat-generating body,

once a certain value of heat flux is exceeded. Recog-

nizing that boiling is the most efficient mode of heat

transfer, this ‘‘limits to coolability’’ question is really

of profound character, both in the practical as well as

the scientific contexts.

• In this work we have found a new way to focus the

question, and this we believe creates new opportuni-

ties for rapid progress toward basic understanding,

and consequently toward prediction as needed for de-

sign. This is important for balancing construction/

Fig. 24. Map of microlayer thickness on a heavily aged heater (test A4) near burnout at q ¼ 1500 kW/m2. The thickness map presented is pixel

(250 lm Â 250 lm) –– averaged and with an accuracy of Æ5% (relative) due to time response of the glass heater.




operation costs of engineering equipment against re-

liability/safety concerns. This is important, too, for

creating ‘‘designer’’ surfaces for specialized cooling

demands (microelectronics, refrigeration, etc.). Fi-

nally, this is (perhaps most crucially) important in

cases that prohibit trial-and-error approaches, such

as needed in certain space and nuclear applications.• The experimental approach developed and employed

in the present work was found to be crucial for the

understanding of the boiling crisis phenomenon.

The first key element of the experimental approach

is the ability to see the whole patterns of heat transfer

and fluid flow, and to obtain quantitative informa-

tion about what happens on the heater-surface prior

and during the burnout. This was achieved by means

of high-speed, high-resolution infrared thermometry

on a nanoscale heater, and X-ray radiographic imag-

ing of the boiling liquid volume. The other key element

is the ability to control and characterize experimental

conditions, through the use of high-purity water, the

contamination-free test section, a protocol for heater

aging, and the heater’s pre- and post-test microscopic

and nanoscopic examination.

• At high heat fluxes, both reversible and irreversible

dry spots were observed. The BETA experimental

data indicates that the dry spot growth is constrained

and guided by neighboring active nucleation sites.

Furthermore, the data obtained in burnout experi-

ments show a direct correlation between CHF and

nucleation site density. Nucleation site density in turn

was found to increase with the degree of heater aging.

This finding indicates a potential to improve the hea-ter performance through controlled surface oxidation

and microstructuring.

• The BETA infrared images show an increasing order

and regularity of the thermal pattern as the heat flux

increases. This contrasts with an increasingly chaotic

behavior of the two-phase flow dynamics above the

heater as evidenced by the X-ray images of the boil-

ing zone. Thus we can conclude that boiling heat

transfer is independent of the complex two-phase

flow hydrodynamics above the heater, and in partic-

ular that the previous hydrodynamic theory of boil-

ing crisis is not appropriate.

• This separation of scales creates a focus of inquiry for

the dynamics of microlayer sitting and vaporizing on

the heater surface as an autonomous system. This in

turn means that such an extended microlayer, and its

rupture, can be studied in its own, by direct observa-

tion, both from above, as well as by high-speed infra-

red thermometry from below.

• We believe the same organizing principle, that is the

scale separation, will be present at least under the

weak convection conditions most interesting for

space applications. Now, for both pool and convec-

tion boiling, the research must focus on the role of

heater-surface and liquid properties, as those alone

determine coolability limit, at 1 g , and we have strong

reasons to believe that this is true also for fractional

gravities (Moon, Mars) as well.

Acknowledgements

The multifaceted, long-range approach described in

this paper became possible thanks to the cooperative

support through NASA grant NAG3-2119 Office of Bio-

logical and Physical Research, US Nuclear Regulatory

Commission Contract NRC-04-98-051, and Lawrence

Livermore National Laboratory Contract B502686. We

are grateful to Dr. T. King (NRC), Dr. J. McQuillan

(NASA), and Dr. S. Dimolitsas (LLNL) for their en-

couragement and cooperation. We appreciate the help

of Mr. M. Vanderbroek (UCSB) in vapor-depositing

the nanofilm heaters and Dr. A. Adams (SBFP) in

technical support for the infrared camera. The authors

are thankful to the technical support for this work

provided by Mr. T. Salmassi and Dr. K. Gasljevic at

UCSB/CRSS on the design and construction of the

BETA test section, power supply, and X-ray operation.

The work made use of the MRL Central Facilities

supported by the National Science Foundation under

award DMR96-32716.

References

[1] S.S. Kutateladze, On the transition to film boiling under naturalconvection, Kotloturbostrenie 3 (1948) 10.

[2] S.S. Kutateladze, Hydrodynamic model of heat transfer crisis in

free-convection boiling, J. Tech. Phys. 20 (11) (1950) 1389–1392.

[3] S.S. Kutateladze, Hydrodynamic theory of boiling regime transi-

tion in free convection, Bull. Acad. Sci., USSR 4 (1951) 529–536.

[4] S.S. Kutateladze, I.G. Malenkov, Experimental investigation of

the analogy between the process of boiling and bubbling, J. Appl.

Mech. Tech. Phys. 7 (2) (1966) 97–99.

[5] I.I. Gogonin, S.S. Kutateladze, Critical heat flux as a function of

heater size for a liquid boiling in a large enclosure, J. Eng. Phys. 33

(5) (1977) 1286–1289.

[6] N. Zuber, On the stability of boiling heat transfer, ASME J. Heat

Transfer 80 (2) (1958) 711–720.

[7] N. Zuber, Hydrodynamic aspects of boiling heat transfer. Ph.D.

Thesis, UCLA, 1959 (also USAEC Rep. AECU-4439).[8] J.H. Lienhard, V.K. Dhir, Hydrodynamic prediction of peak

pool-boiling heat fluxes from finite bodies, Trans. ASME, J. Heat

Transfer 95 (2) (1973) 153–158.

[9] J.H. Lienhard, V.K. Dhir, D.M. Riherd, Peak pool boiling heat

flux measurement on finite horizontal flat plates, Trans. ASME,

J. Heat Transfer 95 (4) (1973) 477–482.

[10] Y. Katto, S. Yokoya, Principal mechanism of boiling crisis in pool

boiling, Int. J. Heat Mass Transfer 11 (6) (1968) 993–1002.

[11] Y. Haramura, Y. Katto, A new hydrodynamic model of critical

heat flux applicable widely to both pool and forced convection

boiling on submerged bodies in saturated liquids, Int. J. Heat

Mass Transfer 26 (3) (1983) 389–399.

[12] V.K. Dhir, Boiling heat transfer, Annu. Rev. Fluid Mech. 30

(1998) 365–401.




[13] C.P. Costello, W.J. Frea, A salient non-hydrodynamic effect in

pool boiling burnout of small semi-cylinder heater, Chem. Eng.

Prog. Symp. Ser. 61 (1965) 258–268.

[14] E.A. Kazakova, Effect of pressure on first crisis in water boiling

on a horizontal plate, in: S.S. Kutateladze (Ed.), Issues in heat

transfer under phase change, GEI, Moscow, 1953, pp. 92–101.

[15] S.S. Kutateladze, N.N. Mamontova, Investigation of critical heat

fluxes with pool boiling of liquids under reduced pressure con-

ditions, Inzenerno-Fizicheski J. 12 (3) (1967) 181–186.

[16] D.A. Labulsov, V.V. Yagov, A.K. Gorodov, Critical heat fluxes

in boiling at low pressure region, in: Proceedings of the 6th

International Heat Transfer Conference, vol. 1, 1978, pp. 221–225.

[17] B.P. Avksentyuk, Z.S. Mesrakesshivili, The effect of subcooling

on critical heat fluxes with liquid boiling in the region of sub-

atmospheric pressures, in: Boiling and Condensation, Novosi-

birsk, Institute of Thermal Physics, USSR Academy of Sciences,

1986, pp. 46–51.

[18] G.I. Samokhin, V.V. Yagov, Heat transfer and critical fluxes with

liquids boiling in the region of low reduced pressures, Thermal

Eng. 35 (1988) 115–118.

[19] V.V. Yagov, A physical model and calculation formula for critical

heat fluxes with nucleate pool boiling of liquids, J. Thermal Eng.

35 (6) (1988) 333–339.

[20] J. Straub, M. Zell, B. Vogel, Pool boiling in reduced gravity field,

in: Proceedings of the 9th International Heat Transfer Conference,

Jerusalem, Israel, vol. 1, Hemisphere, NY, 1990, pp. 91–112.

[21] Y. Abe, T. Oka, Y. Mori, A. Nagashima, Pool boiling of a non-

azeotropic mixture under microgravity, Int. J. Heat Mass Transfer

37 (1994) 2405–2413.

[22] T. Oka, Y. Abe, Y.H. Mori, A. Nagashima, Pool boiling of

n-pentane, CFC-113, and water under reduced gravity: parabolic

flight experiments with a transparent heater, Trans. ASME J.

Heat Transfer 117 (2) (1995) 408–417.

[23] D.P.Shatto, G.P. Peterson, Pool boilingcritical heatflux in reduced

gravity, Trans. ASME J. Heat Transfer 121 (1999) 865–873.

[24] S.S. Kutateladze, Elements of the hydrodynamics of gas–liquid

systems, Fluid Mech. –– Soviet Res. 1 (4) (1972) 29–68.

[25] N.I. Kolev, How accurately can we predict nucleate boiling, Exp.Thermal Fluid Sci. 10 (1995) 370–378.

[26] S.J. Ha, H.C. No, A dry-spot model of critical heat flux applicable

to both pool boiling and subcooled forced convection boiling, Int.

J. Heat Mass Transfer 43 (2) (2000) 241–250.

[27] C.H. Wang, V.K. Dhir, Effect of surface wettability on active

nucleation site density during pool boiling of water on a vertical

surface, J. Heat Transfer 115 (3) (1993) 659–669.

[28] Y. Katto, Critical heat flux in pool boiling, in: V.K. Dhir, A.E.

Bergles (Eds.), Proceedings of Engineering Foundation Confer-

ence on ‘‘Pool and External Flow Boiling’’, ASME, New York,

1992, pp. 151–164.

[29] Y. Katto, Critical heat flux, Int. J. Multiphase Flow 20 (suppl.)

(1994) 53–90.

[30] C.P. Costello, C.O. Bock, C.C. Nichols, A study of induced

convective effects on pool boiling burnout, CEP Symp. 61 (59)(1966) 271–280.

[31] R.F. Gaertner, Photographic study of nucleate pool boiling on a

horizontal surface, J. Heat Transfer 87 (1965) 17–29.

[32] V.K. Dhir, S.P. Liaw, Framework for a unified model for nucleate

and transition pool boiling, J. Heat Transfer 111 (1989) 739–745.

[33] C. Unal, P. Sadasivan, R. Nelson, On the hot-spot-controlled

critical heat flux mechanism in pool boiling of saturated fluids, in:

V.K. Dhir, A.E. Bergles (Eds.), Proceedings of Engineering

Foundation Conference on ‘‘Pool and External Flow Boiling’’,

ASME, New York, 1992, pp. 193–201.

[34] S.S. Kutateladze, I.G. Malenkov, Hydrodynamic analogy be-

tween heat transfer and nucleate boiling crisis in boiling and

bubbling, Exp. data. Heat Transfer –– Soviet Res. 16 (4) (1984) 1–

46.

[35] E. Hahne, T. Diesselhorst, Hydrodynamic and surface effects on

the peak heat flux in pool boiling, in: Proceedings of the 6th

International Heat Transfer Conference, Toronto, vol. 1, 1978,

pp. 209–219.

[36] S.P. Liaw, V.K. Dhir, Effect of surface wettability on transition

boiling heat transfer from a vertical surface, in: Proceedings of the

8th International Heat Transfer Conference, San Fransisco, vol. 4,

1986, pp. 2031–2036.

[37] R.D.M. Carvalho, A.E. Bergles, The effects of the heater thermal

conductance/capacitance on the pool boiling critical heat flux, in:

V.K. Dhir, A.E. Bergles (Eds.), Proceedings of Engineering

Foundation Conference on ‘‘Pool and External Flow Boiling’’,

ASME, New York, 1992, pp. 203–211.

[38] I. Golobic, A.E. Bergles, Effects of heater-side factors on the

saturated pool boiling critical heat flux, Exp. Thermal Fluid Sci.

15 (1) (1997) 43–51.

[39] F. Tachibana, M. Akiyama, H. Kawamura, Non-hydrodynamic

aspects of pool boiling burnout, J. Nucl. Sci. Tech. 4 (1967) 121–

130.

[40] G. Guglielmini, E. Nannei, On the effect of heating wall thickness

on pool boiling burnout, Int. J. Heat Mass Transfer 19 (9) (1976)

1073–1075.

[41] R.F. Gaertner, J.W. Westwater, Population of active sites in

nucleate boiling heat transfer, Chem. Eng. Prof. Symp. Ser. 56

(30) (1960) 39–48.

[42] D.B. Kirby, J.W. Westwater, Bubble and vapor behavior on a

heated horizontal plate during pool boiling near burnout, Chem.Eng. Prog. Symp. Ser. 61 (57) (1965) 238–248.

[43] H.J. Van Ouwerkerk, Burnout in pool boiling. The stability of

boiling mechanisms, Int. J. Heat Mass Transfer 15 (1) (1972) 25–

34.

[44] S. Nishio, T. Gotoh, N. Nagai, Observation of boiling structures

in high heat-flux boiling, Int. J. Heat Mass Transfer 41 (1999)

3191–3201.

[45] R. Reyes, P.C. Wayner, An adsoprtion model for the superheat at

the critical heat flux, Trans. ASME J. Heat Transfer 117 (3) (1995)

779–782.

[46] K. Sefiane, D. Benielli, A. Steinchen, A new mechanism for

pool boiling crisis, recoil instability and contact angle influence,

J. Colloids Surf. A: Physicochem. Eng. Aspects 142 (1998) 361–

373;

Also A. Steinchen, K. Sefiane, Stability analysis of the pool-boiling crisis, J. Phys.: Condens. Matter 8 (47) (1996) 9565–9568.

[47] H.J. Palmer, The hydrodynamic stability of rapidly evaporating

liquids at reduced pressure, J. Fluid Mech. 75 (3) (1976) 487–511.


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