Convective Mass Transfer

Abstract

We already have encountered the mass transfer coefficient, defined in a manner analogous to the heat transfer coefficient. It is a parameter that is used to describe the ratio between the actual mass (or molar) flux of a species into or out of a flowing fluid and the driving force that causes that flux. For example, if a liquid flows over a solid surface that is dissolving in the liquid, one might write A c ∞ is the concentration of A in the liquid far from the solid surface. Here, c k is defined as the mass transfer coefficient in this situation, based on a concentration driving force. It is possible to define a mass transfer coefficient in the same situation using a mole fraction driving force. Given the geometry, the fluid and flow conditions, and the prevailing thermodynamic conditions, the molar flux must be the same, regardless of the type of driving force used. Thus, in this example, the two mass transfer coefficients are related to each other through x A c A k x k c ∆ = ∆ We define the mole fraction / A A x c c = , where c is the total molar concentration of the mixture. Thus, / A A x c c ∆ = ∆ . Substituting in the above result yields the connection between the two mass transfer coefficients. x c k ck = Mass transfer coefficients depend on the relevant physical properties of the fluid, the geometry used along with relevant dimensions, and the average velocity of the fluid if we are considering flow in an enclosed conduit, or the approach velocity if the flow is over an object. Dimensional analysis can be used to express this dependence in dimensionless form. The dimensionless version of the mass transfer coefficient is the Sherwood number Sh . c