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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.
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 ...
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.
B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m 2 s −1] C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s] u = speed [m s −1] In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur ...
This rate can be quantified through the calculation and application of mass transfer coefficients for an overall process. These mass transfer coefficients are typically published in terms of dimensionless numbers, often including Péclet numbers, Reynolds numbers, Sherwood numbers, and Schmidt numbers, among others. [2] [3] [4]
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:
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]
There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems. In the case of mass transfer, natural convection is caused by concentration gradients rather than temperature gradients. [2] = (,,) where