A viscoelastic theory for ultrasound-induced intracellular streaming

Abstract

Ultrasound is increasingly used to control biological cells, but its multiple physical effects, including radiation force, streaming, heating, and cavitation, require theoretical frameworks that can quantify their relative strengths. Here we develop a semi-analytical model to predict flow patterns and energy distributions of ultrasound-induced intracellular streaming. Cells are modeled as viscoelastic droplets immersed in a fluid with different viscoelastic properties. For this geometry, the momentum equation with an Oldroyd-B constitutive law is solved using a perturbation expansion commonly applied in acoustofluidics. The resulting equations for the different orders of the expansion are solved using partial wave expansion and explicit integration. We investigate our model for a range of parameters which is relevant both for synthetic polymer and for protein solutions. We find a series of flow reversals that we can connect to the distribution of energy into the different modes. We also consider density and compressibility contrasts, which shift these transitions and introduce new ones. Finally, we discuss the potential biological relevance of our mathematical results for cellular sensing and signaling.