Control of superheated fluid stability in a toroidal convective loop using a swarm of microbots

Abstract


In recent years, the attention of researchers has been attracted by an active fluid that includes elements (cells, macromolecules, bacteria) capable of self-motion. The behavior of such a fluid is determined by the ability of the elements to transform the energy of the medium into mechanical work and create new medium states. The use of programmable microbots opens up opportunities to achieve such states that are not observed in natural 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. Since the density of the bots themselves can be set during their production, the swarm can locally create a density that differs from the density of the pure medium. Thus, the collective actions of bots to redistribute the swarm concentration in the liquid can potentially compensate for changes in the density of a critically overheated liquid in real time.In this paper, we theoretically study the possibility of a swarm to actively control a physical system considering a toroidal thermosyphon, which is a narrow closed channel with a circular cross-section, under the action of gravity and a given heat flow through the boundaries. We develop a mathematical model of the phenomenon, which includes equations of fluid motion, heat transfer, and microbots concentration. Then we apply the Galerkin method to obtain a finite-dimensional dynamic model of the 7th order, in which the first equation describes the fluid velocity in the channel, two equations describe the dynamics of thermal modes, and remaining equations determine the dynamics of the swarm of bots. Nonlinear analysis of the resulting model ODEs shows that under certain conditions, a swarm of microbots is able to switch stationary thermal convection to periodic and chaotic regimes. We demonstrate that the control critically depends on the speed of the swarm's reaction to external changes and the density of microbots.

Full Text

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About the authors

A. V Stupnikova

Perm National Research Polytechnic University

D. A Bratsun

Perm National Research Polytechnic University

References

  1. Ладиков, Ю.П. Стабилизация процессов в сплошных средах / Ю.П. Ладиков. – М.: Наука, 1978. – 432 с.
  2. Singer, J. Active control of convection / J. Singer, H. Bau // Phys. Fluids A. – 1991. – Vol. 3. – P. 2859–2865. doi: 10.1063/1.857831
  3. Wang, Y. Controlling chaos in a thermal convection loop / Y. Wang, J. Singer, H. Bau // J. Fluid Mech. – 1992. – Vol. 237. – P. 479–498. doi: 10.1017/S0022112092003501
  4. Об активном управлении равновесием жидкости в термосифоне / Д.А. Брацун, А.В. Зюзгин, К.В. Половинкин, Г.Ф. Путин // ПЖТФ. – 2008. – Т. 34, Вып. 15. – С. 36–42. doi: 10.1134/S1063785008080075
  5. Bratsun, D.A. Delay-induced oscillations in a thermal convection loop under negative feedback control with noise / D.A. Bratsun, I.V. Krasnyakov, A.V. Zyuzgin // Commun. Nonlinear Sci. Numer. Simul. – 2017. – Vol. 47. – P. 109–126. doi: 10.1016/j.cnsns.2016.11.015
  6. Bratsun, D. Active Control of Thermal Convection in a Rectangular Loop by Changing its Spatial Orientation / D. Bratsun, I. Krasnyakov, A. Zyuzgin // Microgravity Sci. Technol. – 2018. – Vol. 30, No. 1–2. – P. 43–52. doi: 10.1007/s12217-017-9573-6
  7. Saintillan, D. Rheology of Active Fluids // Annu. Rev. Fluid Mech. – 2018. – Vol. 50. – P. 563–592. doi: 10.1146/annurev-fluid-010816-060049
  8. Pismen, L. Morphogenesis Deconstructed: An Integrated View of the Generation of Forms / L. Pismen. – Springer Cham, Switzerland, 2020. – 146 p.
  9. Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision / N. Bellomo, N. Outada, J. Soler, Y. Tao, M. Winkler // Mathematical Models and Methods in Applied Sciences. – 2022. – Vol. 32, no. 4. – P. 713–792. doi: 10.1142/S0218202522500166
  10. Gou, W. Application of Lotka-Volterra Algorithm Model in Ecosystem Assessment / W. Gou, H. Xue, J. Chang // Smart Infrastructures in the IoT Era. – Springer Cham, Switzerland. – 2025. – P. 437–451. doi: 10.1007/978-3-031-72509-8_37
  11. Huang, Q. An Ecological Network Analysis Based on The Lotka-Volterra Model / Q. Huang, J. Huang // Highlights in Science, Engineering and Technology. – 2024. – Vol. 101. – P. 340–347. doi: 10.54097/z125v270
  12. Su, Y. Symbiosis Evolution of Regional Knowledge Innovation Ecosystem: The Relevance of Lotka–Volterra Model / Y. Su, Y. Yan, C. Liu // Science, Technology and Society. – 2024. – Vol. 29, № 3. doi: 10.1177/09717218241232857
  13. Hill, N.A. Bioconvection / N.A. Hill, T.J. Pedley // Fluid Dynamics Research. – 2005. – Vol. 37, no. 1-2. – P. 1. doi: 10.1016/j.fluiddyn.2005.03.002
  14. Bellomo, N. From amultiscale derivation of nonlinear cross-diffusion models to Keller–Segel models in a Navier–Stokes fluid / N. Bellomo, A. Bellouquid, N. Chouhad // Mathematical Models and Methods in Applied Sciences. – 2016. – Vol. 26, № 11. – P. 2041–2069. doi: 10.1142/S0218202516400078
  15. Liu, Y. Boundedness in a high-dimensional forager–exploiter model with nonlinear resource consumption by two species / Y. Liu, Y. Zhuang // Zeitschrift für angewandte Mathematik und Physik. – 2020. – Vol. 71, № 5. – P. 151. doi: 10.1007/s00033-020-01376-8
  16. Winkler, M. Does fluid interaction affect regularity in the three-dimensional Keller–Segel system with saturated sensitivity? / M. Winkler // Journal of Mathematical Fluid Mechanics. – 2018. – Vol. 20. – P. 1889–1909. doi: 10.1007/s00021-018-0395-0
  17. Winkler, M. A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: global weak solutions and asymptotic stabilization / M. Winkler // Journal of Functional Analysis. – 2019. – Vol. 276, № 5. – P. 1339–1401. doi: 10.1016/j.jfa.2018.12.009
  18. Morphogenesis in robot swarms / I. Slavkov, D. Carrillo-Zapata, N. Carranza, X. Diego, F. Jansson, J. Kaandorp, S. Hauert, J. Sharpe // Science Robotics. – 2018. – Vol. 3, № 25. – P. 1–16. doi: 10.1126/scirobotics.aau9178
  19. Bratsun, D.A. Phase Transition in a Dense Swarm of Self-Propelled Bots / D.A. Bratsun, K.V. Kostarev // Fluid Dynamics & Materials Processing. – 2024. – Vol. 20, iss. 8. – P. 1785–1798. doi: 10.32604/fdmp.2024.048206
  20. Leaman, E.J. Hybrid centralized/decentralized control of bacteria-based bio-hybrid microrobots / E.J. Leaman, B.Q. Geuther, B. Behkam // 2018 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS): proceedings, Nagoya, Japan, 4–8 July 2018. – IEEE, 2018. – P. 1–6. doi: 10.1109/MARSS.2018.8481144
  21. Leaman, E.J. Hybrid centralized/decentralized control of a network of bacteria-based bio-hybrid microrobots / E.J. Leaman, B.Q. Geuther, B. Behkam // Journal of Micro-Bio Robotics. – 2019. – Vol. 5, iss. 1. – P. 1–12. doi: 10.1007/s12213-019-00116-0
  22. Welander, P. On the oscillatory instability of a differentially heated fluid loop // Journal of Fluid Mechanics. – 1967. – Vol. 29, no. 1. – С. 17–30. doi: 10.1017/S0022112067000606
  23. Nonlinear analysis of tilted toroidal thermosyphon models / A. Pacheco-Vega, W. Franco, H.C. Chang, M. Sen // Int. J. Heat Mass Transf. – 2002. – Vol. 3, no. 7. – P. 1379–1391. doi: 10.1016/S0017-9310(01)00265-4
  24. Powers, J.M. Mathematical Methods in Engineering / J.M. Powers, M. Sen. – Cambridge University Press, 2015. – 633 p. doi: 10.1017/CBO9781139583442
  25. Канторович, Л.В. Приближенные методы высшего анализа / Л.В. Канторович, В.И. Крылов. – М.: Физматгиз, 1962. – 708 с.
  26. Берже, П. Порядок в хаосе. О детерминистском подходе к турбулентности / П. Берже, И. Помо, К. Видаль. – М.: Мир, 1991. – 368 с.

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