Mass transfer coefficient

The mass transfer coefficient (another notation , also in American-speaking countries ) is a measure of the volume flow transferred per area. It depends on the exchange area, the concentration gradient and the mass flow . ${\displaystyle \beta }$ ${\displaystyle \beta _{\mathrm {c} }}$ ${\displaystyle k_{\mathrm {c} }}$

definition

The mass transfer coefficient is a diffusion rate constant that can be calculated from the mass flow rate, the mass transfer area and the concentration difference as the driving force ${\displaystyle \beta }$

${\displaystyle \beta ={\frac {{\dot {n}}_{\mathrm {A} }}{A\Delta c_{\mathrm {A} }}}}$

With:

• ${\displaystyle {\dot {n}}_{\mathrm {A} }}$: Mole flow rate in mol / s
• ${\displaystyle A}$: effective mass transfer area in m ²
• ${\displaystyle \Delta c_{\mathrm {A} }}$: Concentration difference in mol / m ³ .

The unit of corresponds to a volume flow through a surface element or shortened . ${\displaystyle \beta }$ ${\displaystyle \mathrm {m^{3}/(s\cdot m^{2})} }$ ${\displaystyle \mathrm {m/s} }$

More forms of expression

Mean mass transfer coefficient

For a flat plate (normal to the axis), the change in the concentration profile in the thin boundary layer near the wall is large in relation to the other coordinate axes. Then it is sufficient to consider the diffusion in the direction and the result is an average mass transfer coefficient ${\displaystyle y}$ ${\displaystyle y}$

${\displaystyle \beta _{\mathrm {m} }={\frac {1}{L}}\int _{0}^{L}\beta _{\mathrm {lokal} }\mathrm {d} x}$

along the characteristic length . In the case of thin boundary layers, this argumentation can also be transferred to other geometries. ${\displaystyle L}$

Ratio of actual to diffusive mass transfer

A measure of the actual mass transfer in relation to the purely diffusive mass transfer is expressed by the Sherwood number . This is defined as follows ${\displaystyle {\mathit {Sh}}}$

${\displaystyle {\mathit {Sh}}={\frac {\beta L}{D}}}$

With:

• ${\displaystyle L}$: characteristic length
• ${\displaystyle D}$: Diffusion coefficient

See also

• Volume-related mass transfer coefficient

Individual evidence

1. ↑ ^{a b} H. D. Baehr and K. Stephan: Heat and mass transfer . Springer, Heidelberg 2010, ISBN 978-3-642-05500-3 .
2. ↑ JD Seader, Ernest J. Henley: Separation Process Principles . Wiley, New York, ISBN 0-471-58626-9 .
3. ^ J. Mulder: Basic Principles of Membrane Technology . Springer, 1996, ISBN 978-0792342472 .