Modeling the interaction of biological cells with a solidifying interface

In this article, we develop a modified level set method for modeling the interaction of particles with a solidifying interface. The dynamic computation of the van der Waals and drag forces between the particles and the solidification front leads to a problem of multiple length scales, which we resolve using adaptive grid techniques. We present a variety of example problems to demonstrate the accuracy and utility of the method. We also use the model to interpret experimental results obtained using directional solidification in a cryomicroscope.