The non-equilibrium thermodynamics of active suspensions

Active suspensions composed of self-propelled colloidal particles are considered. The propulsion of these micrometric particles is generated by chemical reactions occurring by heterogeneous catalytic at their surface and by diffusiophoresis coupling the concentration gradients of the reacting molecular species to the fluid velocity. By this mechanism, chemical free energy is transduced into mechanical motion. The non-equilibrium thermodynamics of such active suspensions is developed by explicitly taking into account the internal degrees of freedom of the active particles, which are the Eulerian angles specifying their orientation. Accordingly, the distribution function of the colloidal particles is defined in the six-dimensional configuration space of their position and their orientation, which fully characterises the polar, nematic, and higher orientational orders in the active system. The local Gibbs and Euler thermodynamic relations are expressed in terms of the colloidal distribution function, the dynamics of which is ruled by a six-dimensional local conservation equation. All the processes contributing to the entropy production rate are derived from the local conservation and kinetic equations for the colloids, the molecular species, mass, linear momentum, and energy, identifying their thermodynamic forces – also called affinities – and their dissipative current densities. The non-equilibrium constitutive relations between them are obtained using the Curie symmetry principle and the Onsager-Casimir reciprocal relations based on microreversibility. In this way, all the coefficients of mechanochemical coupling are completely determined for isothermal, incompressible, dilute suspensions composed of spherical Janus particles on the basis of the interfacial properties between the fluid solution and the solid particles and chemohydrodynamics. The complete expression of the entropy production rate is thus established for such active systems.