massetransport

Mass transport refers to the movement of mass within and between systems due to gradients of concentration, pressure, temperature, or chemical potential. In fluids, transport occurs via advection (bulk motion) and diffusion (molecular mixing).

Diffusion is described by Fick's laws: Fick's first law states that diffusive flux is proportional to the negative gradient of concentration; Fick's second law relates the change in concentration to the divergence of the diffusive flux. Diffusion dominates when advection is weak or for small scales.

Advection transports mass with the flow velocity; combined with diffusion leads to the advection–diffusion equation: ∂c/∂t + u·∇c = D∇²c + R, where c is concentration, u is velocity, D is diffusion coefficient, and R represents sources or sinks.

For charged species, transport is described by the Nernst-Planck equation, incorporating diffusion, electric migration, and convection; in porous media, Darcy's law governs fluid flow, and dispersion augments molecular diffusion.

Mass transport is governed by conservation laws and often couples with energy transport in reactive systems. Reaction-diffusion systems model chemical reactions with transport, capturing how reactions and movement influence concentration patterns.

Quantities like the Peclet number (Pe = uL/D) measure the relative importance of advection to diffusion; large Pe implies advection-dominated transport, while small Pe implies diffusion-dominated transport.

Applications span chemical engineering (separation, reactors), environmental engineering (groundwater contaminant transport), biology (nutrient flux in tissues), and materials science (diffusion in solids).