  We consider model order reduction for a free boundary problem of an osmotic
cell that is parameterized by material parameters as well as the initial shape
of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian
description of the model that is discretized by a mass-conservative finite
element scheme. Using reduced basis techniques and empirical interpolation, we
construct a parameterized reduced order model in which the mass conservation
property of the full-order model is exactly preserved. Numerical experiments
are provided that highlight the performance of the resulting reduced order
model.
