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Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
D is the mass diffusivity (m 2 /s). μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/m·s) ρ is the density of the fluid (kg/m 3) Pe is the Peclet Number; Re is the Reynolds Number. The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is the Lewis number ...
Here, is the overall mass transfer coefficient, which could be determined by empirical correlations, is the surface area for mass transfer (particularly relevant in membrane-based separations), and ˙ is the mass flowrate of bulk fluid (e.g., mass flowrate of air in an application where water vapor is being separated from the air mixture). At ...
Where q” is the heat flux, is the thermal conductivity, is the heat transfer coefficient, and the subscripts and compare the surface and bulk values respectively. For mass transfer at an interface, we can equate Fick's law with Newton's law for convection, yielding:
This equation permits the prediction of an unknown transfer coefficient when one of the other coefficients is known. The analogy is valid for fully developed turbulent flow in conduits with Re > 10000, 0.7 < Pr < 160, and tubes where L/d > 60 (the same constraints as the Sieder–Tate correlation). The wider range of data can be correlated by ...
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction, or component) to another. Mass transfer occurs in many processes, such as absorption , evaporation , drying , precipitation , membrane filtration , and distillation .
D is the mass diffusivity, λ is the thermal conductivity, ρ is the density, D im is the mixture-averaged diffusion coefficient, c p is the specific heat capacity at constant pressure. In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition. [3] [4]