Flow in a Chemical Potential Field: Diffusion

Abstract

Transport is measured by flux, which is defined as the net movement of matter in unit time through a plane of unit area normal to the gradient of potential. In the case of diffusion, molecules of specific components will travel down their concentration gradient, ∂c/∂x, until the gradient is removed or neutralized. During electrical conduction, mass, as well as charge, is transported in an electric field ∂ψ/∂x. In aqueous solutions, the mass and charges are derived from either electrolyte ions or the autoproteolysis of water, which yields protons and hydroxyl groups. In convection, or fluid flow, molecules are moved by a streaming process caused by an external force ∂P/∂x, for example, pressure from a pump, as in the cardiovascular system or gravitational forces generated in a centrifuge. Heat conduction, caused by a difference in temperature ∂T/∂x, is also the result of a net flow, not of the total number of particles, which remains constant in the system, but of the particles with a higher kinetic energy. Each of these transport phenomena has a named relation of the form given earlier by:

$$ {J_x} = - B\frac{{\partial A}}{{\partial x}} = - B{F_A} $$

(27.1)

These named relations are:

• 1. for diffusion, Fick’s law, and the constant is given as D, the diffusion constant;

• 2. for electrical conduction, Ohm’s law with the constant κ, the electrical conductivity;

• 3. for fluid movement, Poiseuille’s law, and the constant, C, is a hydraulic conductivity related to the viscosity;

• 4. for heat flow, Fourier’s law, and κ _τ is the thermal conductivity coefficient.