On the fluid stabilization in a toroidal thermosyphon with thermotaxis of microbots

Abstract

A liquid with programmable microbots represents a new kind of medium with special properties. Such a medium can reach states that are not observed under normal conditions. In this paper, we assume that freely floating microbots have the property of thermotaxis, i.e., they exhibit a motor response to a temperature gradient, moving in the direction of an increasing value. Since the density of the bots is a parameter that is specified during their production, the swarm density can differ significantly from the liquid density. Therefore, swarm movements in the liquid can result in local changes in the total density of the medium. Thus, collective actions of bots aimed at redistributing the swarm concentration can potentially compensate for changes in the density of the heated liquid in real time. In this paper, we theoretically study the capability of microbots to actively influence the convective stability of a physical system using the example of a toroidal thermosyphon, which is represented by a narrow closed channel with a circular cross section, under the action of gravity and a given heat flux at the boundaries. We propose a simple mathematical model of the phenomenon, which includes equations of fluid motion, heat transfer, and microbots concentration. Since the cross section of the thermosyphon is much smaller than its diameter, the governing equations can be averaged across the channel. For a specific type of boundary conditions for temperature, an analytical solution of nonlinear partial differential equations was obtained, describing stationary convection in the thermosyphon. We show that for certain values ​​of the swarm control parameters, which include the density of microbots and their velocities in the medium, the fluid motion in the channel can completely fade out.