Sneha Krishnan | Searcharxiv

arXiv2026

Force Dipole Interactions in Membranes with Odd Viscosity

We develop a hydrodynamic framework for the interactions and collective dynamics of force dipoles embedded in a compressible fluid membrane supported by a shallow viscous subphase. Starting from the generalized two-dimensional Stokes equations with shear, dilatational, and odd (Hall) viscosities, we derive an exact real-space Green tensor using Hankel transforms. The resulting tensor is characterized by three hydrodynamic screening scales associated with shear, compressional, and odd-viscous modes, and smoothly reduces to the standard limiting cases of incompressible membranes and compressible parity-symmetric membranes, while also capturing the chiral response generated by odd viscosity. Using this Green tensor we obtain the velocity and vorticity fields generated by a force dipole and formulate the dynamical system governing interacting dipoles. The analysis reveals several distinct dynamical regimes and identifies observables that isolate the antisymmetric odd-viscous contribution to dipole interactions, including transverse drift and chiral relative motion.

cond-mat.soft↗

arXiv2025

Hamiltonian Active Particles in Incompressible Fluid Membranes

Active proteins and membrane-bound motors exert force dipole flows along fluid interfaces and lipid bilayers. We develop a Hamiltonian framework for the interactions of pusher and puller dipoles embedded in an \emph{incompressible} two-dimensional membrane supported by a shallow viscous subphase. Beginning from the Brinkman-regularized Stokes equations of the membrane-subphase system, we construct the near-field and far-field dipolar velocity fields and associated stream functions. For two quenched (fixed orientation) dipoles, we obtain exact analytic solutions in both the near- and far-field regimes. Although generic dipoles reorient under local membrane vorticity, we show that the far-field dipolar flow is vorticity-free; force-free motors therefore retain fixed orientations and obey a position-based Hamiltonian dynamics in which the positions of $N$ dipoles evolve via an effective Hamiltonian built from the dipolar stream function. In the near field, where the flow possesses finite vorticity, a Hamiltonian formulation is recovered in the quenched-orientation limit. For identical dipoles, the far-field Hamiltonian produces rapid clustering from random initial conditions, whereas the near-field Hamiltonian suppresses collapse leading to non-aggregating configurations. The phase portraits reveal that the many-body collapse observed in the time evolution of the far field Hamiltonian arises from angular transport across phase space enabled by the screened hydrodynamic interaction. Our work thus provides a concrete realization of a position-based Hamiltonian formulation for active particles in incompressible fluid membranes and shows that hydrodynamic screening can reorganize both the dynamical phase space and the collective organization of active dipoles.

cond-mat.soft↗