equation of change for mass transport

8/20/2019 Equation of Change for Mass Transport

http://slidepdf.com/reader/full/equation-of-change-for-mass-transport 1/6

EQUATION OF CHANGEFOR MASS TRANSPORT



THE EQUATION OF CONTINUITY FOMULTICOMPONENT MIXTURE

■ Apply the law of cone!"at#on of $a to each pec#e % #n a $#&t

N/ 0■ Con#1e! a yte$ # a "ol'$e ele$ent 2& 2y 23 4&e1 #n a pac

the 6'#1 $#&t'!e # 6ow#n5 )!efe! 45'!e -0+7+/0

■ 8#th#n th# $#&t'!e( !eact#on a$on5 the "a!#o' che$#cal pec#e

■ 8e 'e the y$9ol r a to #n1#cate the !ate at wh#ch pec#e % #

)$a:"ol'$e0t#$e/0

■ Ma 9alance;

< rate of increase of mass of α in the volume element

< rate of addition of mass of α across face at x

< rate of removal of mass of α across face at x + ∆x

■



■ The co$9#ne1 $a 6'& #ncl'1e 9oth the $olec'la! 6'& an1 con

■ 8!#tten 1own the ent#!e $a 9alance an1 1#"#1e 9y 2& 2y 23( lthe "ol'$e ele$ent 1ec!eae to 3e!o(

= - + α = 1,2,3,…, N (19.1-5)

■ Th# # the e>'at#on of cont#n'#ty fo! pec#e % #n a $'lt#$co$$#&t'!e0

■ It 1ec!#9e the chan5e #n $a concent!at#on of pec#e % w#thpo#nt #n pace 9y the 1#ff'#on an1 con"ect#on of %( a well !eact#on that p!o1'ce o! con'$e %0

■ The >'ant#t#e ( ( a!e the Ca!te#an co$ponent of the $a 6'

"α

5#"en #n E>0)?/ of Ta9le +@07+0

■ E>'at#on +B0+7 $ay 9e w!#tten #n "ecto! notat#on a

* % * +(,(-(.( N )+B0+7D/

■ O! '#n5 E>0 )/ #n Ta9le +@07+ to w!#te the E>0 )+B0+7@/0

■ E>'at#on of cont#n'#ty fo! the $#&t'!e( * )+B0+

< #1ent#cal to e>'at#on of cont#n'#ty fo! a p'!e 6'#1 5#"en #n E>0-0

■



■ To o9ta#n E>0 +B0+7( E>0 )G/ of Ta9le +@07+ ha1 to 9e 'e10 y law of con

!% *

■ F#nally we o9ta#n )fo! 6'#1 $#&t!'!e of contant $a 1en#ty/ )+B0+7B

■ The e>'at#on of cont#n'#ty fo! pec#e % #n $ola! >'ant#t#e #

% * +(,(-(.( N )+B0+7+/

■ * $ola! !ate of p!o1'ct#on of % pe! 'n#t "ol'$e0 Th# e>'at#on can 9e !e)J/ #n Ta9le +@07+ to 5et e>'at#on +B0+7++0

■ A11#n5 all N e>'at#on #n E>0+B0+7+ o! ++( the e>'at#on 9eco$e

* )+B0+7+,/

7 fo! the e>'at#on of cont#n'#ty of the $#&t'!e0 E>0 )M/ #n Ta9le +@07+0

■ The che$#cal !eact#on te!$ 1oe not 1!op o't 9eca'e the n'$9e

necea!#ly cone!"e1 #n a che$#cal !eact#on0 F#nally we note that)+B0+7+-/

7 fo! a 6'#1 $#&t'!e of contant $ola! 1en#ty c0

■ E>0)+B0+7+/ an1 )+B0+7+/ e&p!e the a$e phy#cal content( 9't w!#ttnotat#on; )Ma >'ant#t#e/ an1 )Mola! >'ant#t#e/0

■



#na!y yte$ w#th Contant D AB

■ Ine!t#n5 F#c Law f!o$ E>0 )A/ of Ta9le +@07, #nto E>0 +B0+7+;

)+B0+7+D/

■ ?ec!#9e the 1#K'#on #n 1#l'te l#>'#1 ol't#on at contant T an1

■ Ine!t#n5 F#c Law f!o$ E>0 )/ of Ta9le +@07,( the E>0 )+B0+7+/

)+B0+7+@/

■ Uef'l fo! low71en#ty 5ae at contant te$pe!at'!e an1 p!e'!

■

#na!y yte$ w#th Contant cD AB



■ If no che$#cal !eact#on( the te!$ of che$#cal p!o1'ct#on a!e all 3

■ If " * ( an1 # contant #n E>0 +B0+7+D( o! " * an1 c # con+@( then the e>'at#on 9eco$e

)+B0+7+/

■ Calle1 F#c econ1 law of 1#K'#on0

■ Ue1 fo! 1#K'#on #n ol#1 o! tat#ona!y l#>'#1 )" * #n E>0 e>'#$ola! co'nte!71#K'#on #n 5ae )" * #n E>0 +B0+7+@/0 It $e$ola! 6'& w#th !epect to tat#ona!y coo!1#nate # 3e!o( o! e"e!$o"e #n the po#t#"e 371#!ect#on( the!e # a $ole of that $o"e

371#!ect#on0

■ Ta9le 7+ ++ #n te!$ of % fo! E>0 +B0+7+ an1 +B0+7+D fo! con

■

#na!y yte$ w#th e!o Jeloc#ty

equation of change for mass transport

Documents