Mason-Weaver equation

The Mason–Weaver equation (named after Max Mason and Warren Weaver) describes the sedimentation and diffusion of solutes under a uniform force, usually a gravitational field. Assuming that the gravitational field is aligned in the z direction (Fig. 1), the Mason–Weaver equation may be written

where t is the time, c is the solute concentration (moles per unit length in the z-direction), and the parameters D, s, and g represent the solute diffusion constant, sedimentation coefficient and the (presumed constant) acceleration of gravity, respectively.

The Mason–Weaver equation is complemented by the boundary conditions

at the top and bottom of the cell, denoted as ${\displaystyle z_{a}}$ and ${\displaystyle z_{b}}$, respectively (Fig. 1). These boundary conditions correspond to the physical requirement that no solute pass through the top and bottom of the cell, i.e., that the flux there be zero. The cell is assumed to be rectangular and aligned with the Cartesian axes (Fig. 1), so that the net flux through the side walls is likewise zero. Hence, the total amount of solute in the cell

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