Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity

TL;DR

This paper analyzes how odd viscosity differences inside and outside a liquid domain in a membrane generate lateral lift forces, revealing nonreciprocal hydrodynamic responses due to active protein-induced odd viscosity contrasts.

Contribution

It provides an analytical framework for understanding hydrodynamic forces on active liquid domains with odd viscosity differences, highlighting the emergence of lateral lift.

Findings

Lateral lift arises only when in/out odd viscosities differ.

Odd viscosity contrast causes nonreciprocal hydrodynamic responses.

Analytical expressions for drag and lift forces are derived.

Abstract

We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion, and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the passive case without odd viscosity, the lateral lift arises in the active case only when the in/out odd viscosities are different. The in/out contrast in the odd viscosity leads to nonreciprocal hydrodynamic responses of an active liquid domain.