Mass Transfer Diffusion and Flow

The physical transport of mass is essential to many kinetic and d3mamic processes. For example, bubble growth in magma or beer requires mass transfer to bring the gas components to the bubbles radiogenic Ar in a mineral can be lost due to diffusion pollutants in rivers are transported by river flow and diluted by eddy diffusion. Although fluid flow is also important or more important in mass transfer, in this book, we will not deal with fluid flow much because it is the realm of fluid dynamics, not of kinetics. We will focus on diffusive mass transfer, and discuss fluid flow only in relation to diffusion. 

From the phenomenological flux equation, the diffusion equation may be derived. For a constant diffusivity, the diffusion equation for one-dimensional diffusion takes the following form (Equation 1-74)  

Given initial and boundary conditions, the concentration variation as a function of X and t can be solved from the diffusion equation. The above diffusion equation was given without derivation in Chapter 1. In this chapter, the diffusion equation is derived and solved. 

Diffusion does not proceed at a constant rate. The length of a diffusion profile, as characterized by the mid-diffusion distance, is not proportional to time. Rather, the mid-diffusion distance is proportional to the square root of time (Equation 1-79)  

Diffusion is ubiquitous in nature whenever there is heterogeneity, there is diffusion. In liquid and gas, flow or convection is often present, which might be the dominant means of mass transfer. However, inside solid phases (minerals and glass), diffusion is the only way of mass transfer. Diffusion often plays a major role in solid-state reactions, but in the presence of a fluid dissolution and recrystallization may dominate. 

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