Einstein’s Active Suspension

The study of active matters such as bacterial suspensions, microtubule networks, artificial swimmers, and active liquid crystals has attracted a lot of attention. The particle transport in active suspensions has been covered in a lot of the existing literature.

Recent studies on bacterial suspensions show that they can exist in a variety of exotic phases such as swarming, laning, jamming, and also in turbulence.  Out of these, the turbulent phase sparked a lot of interest in researchers and led to many significant development in the field of active fluids.  An interesting question that naturally arises is whether such fluids that are far from equilibrium contain some invariant measures that could lead to the existence of a fluctuation-dissipation relations (FDR).

In order to answer the question, in this paper, the authors which include Mr.Sanjay C. P. and Prof. Ashwin Joy from the Department of Physics, Indian Institute of Technology Madras, Chennai, India, conducted various analytical and numerical studies on the motion of a distribution of interacting particles in a dense suspension of bacteria.

The results of this study, using a steady state Fokker-Planck equation associated with the particles, showed that interacting particles immersed in an active fluid can be described by an effective temperature.  This effective temperature is then shown to be linear in the particle diffusivity that verifies the existence of the Einstein’s relationthe simplest FDR, for particles advected by a dense bacterial flow. The results also showed that the mobility was found to be higher when the background fluid was in a globally ordered polar phase, and lower when the fluid was in isotropic equilibrium.  Excellent agreement between the analytical and numerical observations confirms the robustness of the results reported in this paper. This results of this paper find application in the field of micrometer sized heat engines where bacterial suspensions are used as temperature reservoirs.

Prof. Samriddhi Sankar Ray from the International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, India, acknowledged the importance of this study by giving the following comments: “The issue of fluctuation-dissipation like ideas working in systems far from equilibrium without detailed balance is an extremely delicate one. Sanjay and Ashwin have handled this long-standing problem in a system of “living fluids” in a masterful way. This work is an important one for at least two reasons. One, it uses ideas from equilibrium systems in an unfamiliar setting which opens avenues to think of such problems. And secondly, the system they consider — dense bacterial suspensions — is one which is one of the more interesting examples of driven-dissipative dynamics at the interface of biology and physics. While in my opinion the results are important from the point of view of fundamental physics; it is possible that they will have some impact in future explorations of miniature heat engines fed by a bacterial bath.”

Article by Akshay Anantharaman
Here is the original link to the paper:
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.065114

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