Heat and Mass Transfer in Binary Mixtures; A Computational Approach - Advances in Control and Automation of Water Systems - page 171

∂ k

( )

kj − − 1 k j =− ρ D r

R 2 R 1 l

∂ R

Here k --the concentration of the first component at the interface. [3-4] With the as-
sumption of homogeneity of parameters inside the bubble changes in the mass of each
component due to phase transformations can be written as

d 4

=

3/ 2

πρ π R 4 Rj

or

i i

dt 3

R

•

•
+==

ρρ , (5)

( )

/ /

R j , i 1, 2

i i i

3

Express the composition of a binary mixture in mole fractions of the component rela-
tive to the total amount of substance in liquid phase

n

1

N =

(6)

nn +

1 2

The number of moles i th component

n , which occupies the volume V , expressed in

terms of its density

n = ρ

V

i

µ

(7)

i

i

Substituting (7) in (6), we obtain

µ
µµ

k

( )

Nk = +−

2

(8)

( )

1

k 1 k

2 1

By law, Raul partial pressure [5] of the component above the solution is proportional
to its molar fraction in the liquid phase that is

( ) ( ) ( ) ( )

p = p TNk , p = p T 1 − Nk

(9) 1 S 1 v 1 R 2 S 2 v 1 R

Equations of state phases have the form:

( )

p = BT ρµ

/

/ , i = 1, 2

, (10)

i vi i

where B --gas constant,

T --the temperature of steam,

ρ --the density of the mixture

/

components in the vapor bubble

µ --molecular weight,

S p --saturation pressure. The

boundary conditions r = ∞ and on a moving boundary can be written as:

(11)

k = k k , = k T , = TT , = T

0 Rl 0 l v

r =∞ rR =

r =∞ rR =