Page 446 - Modelling in Transport Phenomena A Conceptual Approach

426 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

9.21 Consider an industrial absorber in which gas bubbles (A) rise through a
liquid (B) column. Bubble diameters usually range from 0.2 to 0.6 cm while bubble
velocities range from 15 to 35cm/s (Astarita, 1967). Making use of Eq. (9.5139)
show that the range for the average mass transfer coefficient is

0.018 < (k,) < 0.047cm/ s

Hint: A reasonable estimate for DAB is cm2/ s.

9.22 Consider a gas film of thickness 6, composed of species A and B adjacent to a
flat catalyst particle in which gas A diffuses at steady-state through the film to the
catalyst surface (positive z-direction) where the isothermal first-order heteroge-
neous reaction A --f B occurs. As B leaves the surface it decomposes by isothermal
first-order heterogeneous reaction, B + A. The gas composition at z = 0, i.e., XA,
and XB,, is known.
a) Show that the equations representing the conservation of mass for species A
and B are given bv

b) Using the heterogeneous reaction rate expression at the surface of the catalyst,
conclude that
NA,=-NB, O<Z<S (4)
c) Since XA + XB = 1 everywhere in 0 < z 5 6, solution of the one of the consew
tion equations is sufficient to determine the concentration distribution within the
film. Show that the governing equation for the mole fraction of species B is

subject to the boundary conditions

at z=S xB=I+- NBZ
ck" (7)
where kS is the surface reaction rate constant.
d) Show that the solution of Eq. (5) is given by
XB = XB, cosh(A<) + 4sinh(A<)