A droplet of liquid A of radius r₁ is suspended in a stream of gas B shown below. Gas film We postulate that there is a spherical, stagnant film of radius r2 surrounding the droplet. The concentration of A in the gas phase is XA₁ at r = r₁ and XA2 at the outer edge of the film r = r (a) Use conservation of mass to show that the flux of species A in the gas film is: 1 d r² dr :(r² NA,r): 0 = Is the flux constant throughout the film? Why or why not? (Think about geometry.) (b) Use the expression for the molar flux NA,r (including convection and diffusive terms) show that the concentration profile in the film satisfies the following differential equation: d 1- (r² d - [In(1 − x₁)]) = State the boundary conditions. Do not attempt to solve the ODE. r² dr dr = 0
A droplet of liquid A of radius r₁ is suspended in a stream of gas B shown below. Gas film We postulate that there is a spherical, stagnant film of radius r2 surrounding the droplet. The concentration of A in the gas phase is XA₁ at r = r₁ and XA2 at the outer edge of the film r = r (a) Use conservation of mass to show that the flux of species A in the gas film is: 1 d r² dr :(r² NA,r): 0 = Is the flux constant throughout the film? Why or why not? (Think about geometry.) (b) Use the expression for the molar flux NA,r (including convection and diffusive terms) show that the concentration profile in the film satisfies the following differential equation: d 1- (r² d - [In(1 − x₁)]) = State the boundary conditions. Do not attempt to solve the ODE. r² dr dr = 0
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
Related questions
Question
![A droplet of liquid A of radius r₁ is suspended in a stream of gas B shown below.
Gas film
We postulate that there is a spherical, stagnant film of radius 1₂ surrounding the droplet. The
concentration of A in the gas phase is XA₁ at r = ₁ and XÃ2 at the outer edge of the film r = r₂.
(a) Use conservation of mass to show that the flux of species A in the gas film is:
1 d
r² dr
(r² N₁,r) = 0
Is the flux constant throughout the film? Why or why not? (Think about geometry.)
(b) Use the expression for the molar flux NA,r (including convection and diffusive terms) to
show that the concentration profile in the film satisfies the following differential
equation:
1 d
(r² = [In(1-x₂)]):
dr
State the boundary conditions. Do not attempt to solve the ODE.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb1cc6be-d758-43b5-95ea-09c15572ab6a%2F16b186ae-c349-487b-8c1a-8f6727091913%2Fcugncj_processed.png&w=3840&q=75)
Transcribed Image Text:A droplet of liquid A of radius r₁ is suspended in a stream of gas B shown below.
Gas film
We postulate that there is a spherical, stagnant film of radius 1₂ surrounding the droplet. The
concentration of A in the gas phase is XA₁ at r = ₁ and XÃ2 at the outer edge of the film r = r₂.
(a) Use conservation of mass to show that the flux of species A in the gas film is:
1 d
r² dr
(r² N₁,r) = 0
Is the flux constant throughout the film? Why or why not? (Think about geometry.)
(b) Use the expression for the molar flux NA,r (including convection and diffusive terms) to
show that the concentration profile in the film satisfies the following differential
equation:
1 d
(r² = [In(1-x₂)]):
dr
State the boundary conditions. Do not attempt to solve the ODE.
=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 12 images
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The