Mushy zones are regions of intermixed liquid and solid which result from instability due to the build-up of solute during solidification of multispecies materials. A typical experiment consists of a uniformly-mixed binary alloy (salt water, for instance) at uniform "warm" temperature being placed upon a cold surface. In some cases, only a solid layer grows from the bottom of the tank. In other cases, a slowly advancing solid layer is capped by a rapidly advancing mushy layer. If the cold temperature is very cold, the solid layer initially grows quite rapidly as well. Common modelling assumptions include an infinite tank or negligible solute diffusion, but allowing for a finite tank and solute diffusion provides some very interesting results.