Page 25 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

20

(56)

where a a = is the coefficient of temperature conductivity.
Cp'P
Equation (56) is called the Fourier-Kirehhoff equation or the
differential equation of conductivity in a moving medium. In this equation
besides temperature, variables are also velocity and density. That is why it must
be considered together with the equation of continuity and the Navier-Stokes
equations.

1.2.2. Diffusion lows

1.2.2.1. Diffusion in immovable medium
The mass transfer between gas and liquid phase in packed bed columns
is taking place by diffusion of the transferred component through the interface
between the two phases. That is why for understanding and calculating of this
process, the lows of diffusion have to be known. Diffusion is evening of the
concentration in a phase due to the movement of the molecules. The process
passes from higher to lower concentration. Its driving force is the concentration
gradient, or, strictly speaking, the gradient of the chemical potential. Because at
the conditions in packed columns the chemical potential gradient is dependent
mainly on the concentration gradient, later only the latter is considered as a
driving force of the diffusion processes.
The diffusion rate is defined as quantity of substance G transferred by
diffusion per unit of time f and unit of surface F. According to Fick's low this
. . , 3. dC
rate is proportional to the concentration gradient .
dx
(57)
Fdr dx

The coefficient of proportionality D is called diffusion coefficient, or
simple diffusivity. The minus sign takes into account that the diffusion process
passes against the concentration gradient, i.e. from higher to lower
concentration.