Microscopic heat engines with hydrodynamic flow

Hydrodynamic flows are often generated in colloidal suspensions. Since colloidal particles are frequently used to construct stochastic heat engines, we study how the hydrodynamic flows influence the output parameters of the engine. We study a single colloidal particle confined in a harmonic trap with time-periodic stiffness that provides the engine protocol, in the presence of an externally applied steady linear shear flow. The nature of the flow (circular, elliptic, or hyperbolic) is externally tunable. In the quasistatic limit, the work done by the flow field is shown to dominate over the thermodynamic (Jarzynski) work done by the trap, if there is an appreciable deviation from the circular flow. The work by the time-dependent trap is the sole contributor only for a perfectly circular flow. The work done by the elliptic flow is positive whereas in the case of hyperbolic flows, in the limit of low trapping strength, it can be negative, so as to allow for harnessing the work from the flow field. We also study an extended model, where a microscopic spinning particle (spinor) is tethered close to the colloidal particle, the latter being the working substance of the engine, such that the flow generated by the spinor influences the dynamics of the colloidal particle. We simulate the system and explore the influence of such a flow on the thermodynamics of the engine. We further find that for larger spinning frequencies, the work done by the flow dominates and the system cannot produce thermodynamic work.