A droplet ofliquid A,ofradius r1, issuspended ina stream ofgasB.Wepostulate that there is a spherical stagnant gas film of radius r2 surrounding the droplet. The concentration of A in the gas phase isxA1atr=r1and xA2at the outer edge of the film, r=r2. Gas film r 1 r 2 a) By a shell balance, show that for steady-state diffusion r2NAr is constant within the gas film, and set the constant equal to r12NAr1, the value at the droplet surface. b) Show that the result in (a) lead the following equation for xA: ?1 2???1= − ???? 1−???2(??? ??) c) Integrate this equation between the limits r1 and r2 to get: ???1=???? ?2−?1(?2 ?1)ln(??2 ??1)
A droplet ofliquid A,ofradius r1, issuspended ina stream ofgasB.Wepostulate that there is a spherical stagnant gas film of radius r2 surrounding the droplet. The concentration of A in the gas phase isxA1atr=r1and xA2at the outer edge of the film, r=r2. Gas film r 1 r 2 a) By a shell balance, show that for steady-state diffusion r2NAr is constant within the gas film, and set the constant equal to r12NAr1, the value at the droplet surface. b) Show that the result in (a) lead the following equation for xA: ?1 2???1= − ???? 1−???2(??? ??) c) Integrate this equation between the limits r1 and r2 to get: ???1=???? ?2−?1(?2 ?1)ln(??2 ??1)
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Question
A droplet ofliquid A,ofradius r1, issuspended ina stream ofgasB.Wepostulate that
there is a spherical stagnant gas film of radius r2 surrounding the droplet. The concentration
of A in the gas phase isxA1atr=r1and xA2at the outer edge of the film, r=r2.
Gas film
r
1
r
2
a) By a shell balance, show that for steady-state diffusion r2NAr is constant within the gas
film, and set the constant equal to r12NAr1, the value at the droplet surface.
b) Show that the result in (a) lead the following equation for xA:
?1
2???1= − ????
1−???2(???
??)
c) Integrate this equation between the limits r1 and r2 to get:
???1=????
?2−?1(?2
?1)ln(??2
??1)
d)What is the limit of this equation when r2→∞?
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