  Surface tension governed by differential adhesion can drive fluid particle
mixtures to sort into separate regions, i.e., demix. Does the same phenomenon
occur in confluent biological tissues? We begin to answer this question for
epithelial monolayers with a combination of theory via a vertex model and
experiments on keratinocyte monolayers. Vertex models are distinct from
particle models in that the interactions between the cells are shape-based, as
opposed to distance-dependent. We investigate whether a disparity in cell shape
or size alone is sufficient to drive demixing in bidisperse vertex model fluid
mixtures. Surprisingly, we observe that both types of bidisperse systems
robustly mix on large lengthscales. On the other hand, shape disparity
generates slight demixing over a few cell diameters, a phenomenon we term
micro-demixing. This result can be understood by examining the differential
energy barriers for neighbor exchanges (T1 transitions). Experiments with
mixtures of wild-type and E-cadherin-deficient keratinocytes on a substrate are
consistent with the predicted phenomenon of micro-demixing, which biology may
exploit to create subtle patterning. The robustness of mixing at large scales,
however, suggests that despite some differences in cell shape and size,
progenitor cells can readily mix throughout a developing tissue until acquiring
means of recognizing cells of different types.
