Biochemical Engineering Fundamentals Part 1 - Bailey J., Ollis D. 1989

Transport Processes in Biotechnological Systems
Mass Transfer Involving Freely Rising and Freely Falling Bodies

The mass transfer rate between different Zones of the system is governed by equations describing the conservation of mass for the entire system as well as its individual components (such as oxygen), along with momentum balance. When these equations are expressed in terms of dimensionless variables representing changes in distances, velocities, and concentrations—and when the density difference between the two contacting phases serves as the primary driving force for The transport of a liquid or gaseous component—the resulting equations yield three dimensionless parameters (similarity criteria) known as the Grashof, Sherwood, and Schmidt numbers. In the context of mass transfer, these numbers are defined as follows:

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Here, D represents the characteristic dimension and μl is the viscosity of the continuous phase. It can be expected that for convective motion, the expressions for Mass transfer coefficients will incorporate only these three similarity criteria.



Last update: 06/08/2026

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