# LTR: Convective Mass Transfer

Convective mass transfer refers to the transport of mass due to a moving fluid. Like heat convection, this typically refers to transport across phases, however, here solid-fluid transport is on equal footing with liquid-gas transport (rather than being the dominant example of convection). As with heat transport, it is clear that the rate of mass transfer will depend on the character of the fluid flow.

In analogy with Newton's "Law" of Cooling, we can write an expression for the molar flux due to convection as:

##### EQUATION:

$\displaystyle{N_a = \frac{M_a}{A} = k_c\Delta C_a}$

where $k_c$ is the convective mass transfer coefficient, $N_a$ is the molar flux of species $a$, $M_a$ is the molar flow of a, and A is the interphase area of contact.

##### NOTE:

We could write essentially the same expression based on mass concentrations, but will try to denote mass fluxes/flows with lower case letters. Also, for transport int he gas phase, we will often use partial pressures instead of molar concentrations.

As with heat transfer $k_c$ may also sometimes be referred to as a "film coefficient".

$k_c$ will depend on:

• the geometry of the phase boundaries (unlike heat transport, if we have gas-liquid transport this is a very difficult thing to calculate/measure!)
• the nature of the fluid (here the diffusivity)
• the nature of the flow (fluid mechanics!)
##### NOTE:

Again, determining the parameter, $k_c$, will often be the bulk of the work (or at least the only hard part) in a given convection problem.

##### OUTCOME:

Perform convective mass transfer calculations

##### EXAMPLE:

An aspirin sitting in your stomach has a solubility of 0.15 mol/L (so this is the concentration at the solid-liquid surface). Assuming that the concentration in the bulk of the stomach is zero and that the pill does not shrink, but stays a sphere with a 0.5cm diameter, calculate the molar flow into the stomach when the mass transfer coefficient is 0.1 m/s