Volumetric response of an ellipsoidal liquid inclusion: implications for cell mechanobiology

Elastic composites containing liquid inclusions exist widely in nature and in engineered systems. The volumetric response of liquid inclusions is important in many cases, such as an isolated cell embedded in an extracellular matrix or an oil pocket embedded within shale. In this study, we developed a model for describing the volumetric response of an ellipsoidal liquid inclusion. Specifically, we investigated the volumetric response of an ellipsoidal liquid inclusion embedded in a three-dimensional (3D) matrix through an analytical expression of the volumetric response. We performed parametric analysis and found that loading along the shortest axis can induce the most volume change, while loading along the longest axis can induce the least volume change. We also found that the volumetric response decreases with increasing Poisson ratio of the matrix. These results could be used to understand some cell behavior in a 3D matrix, for example, cell alignment under mechanical load.