Laboratoire Matière et Systèmes Complexes

Transport Processes in Active Fluids

Katherine Klymko

Transport phenomena has been traditionally addressed in the framework of non-equilibrium  thermodynamics pioneered by Onsager, Prigogine, deGroot, and Mazur. The connection to statistical mechanics was established through the development of Onsager’s reciprocal relations and Green-Kubo relations using the invocation of a regression hypothesis for the fluctuations, and the principle of microscopic reversibility or time reversal symmetry (TRS). Active systems, which break TRS at the microscopic level, provide the opportunity to revisit the development of non-equilibrium thermodynamics from a fresh perspective. In this talk we will explore the extent to which the framework of non-equilibrium thermodynamics can be extended to active systems, with a focus on understanding how transport properties are affected by active driving forces.

A particular transport property in active matter, related to breaking TRS, that has received much attention is the emergence of odd viscosity. In this talk we will discuss our recent efforts to understand viscous properties in active systems by extending the formalism of traditional irreversible thermodynamics to systems that break time reversal symmetry at the microscale. We will first discuss the derivations for the continuum conservation laws, and discuss how different microscopic active forces manifest at the collective level [1,2]. We will then consider viscous transport of active matter and discuss the consequences of breaking TRS breakdown on the breakdown of Onsager’s reciprocal relations [3], and the emergence of odd viscosity. We will focus on numerical results testing the newly obtained Green-Kubo relations in a system of actively torqued dumbbells [4], derived through invocation of Onsager’s regression hypothesis in active steady states. We will show that the viscosity values (for both shear and odd viscosities) obtained through these Green-Kubo relations are in good agreement with independently obtained non-equilibrium molecular dynamics flow simulations [4].

References:

[1] K. Klymko, D. Mandal, K. K. Mandadapu, Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics (2017), arxiv:1706.02694 (also in J. Chem. Phys.). [2] J. M. Epstein, K. Klymko, K. K. Mandadapu, Statistical mechanics of transport processes in active fluids II: Equations of hydrodynamics for active Brownian particles (2018), arXiv: 1809.01114 (also in J. Chem. Phys.). [3] J. M. Epstein, K. Mandadapu, Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids (2019), arXiv:1907.10041. [4] C. Hargus, K. Klymko, J. M. Epstein, K. K. Mandadapu,  Time reversal symmetry breaking and odd viscosity in active fluids: Green-Kubo and NEMD results (2020), arXiv:2002.10437.