Modeling hydrodynamic interactions in active fluids
update: 2021-11-17 08:30:04     

Active suspensions of microswimmers demonstrate novel emergent behaviors (self-organization, active turbulence, etc.) on macroscopic length scales [1]. For such systems with, minimally, thousands of microswimmers, brute force approaches (e.g., boundary element method, or the method of Stokeslets) of the hydrodynamic interactions are just infeasible in the foreseeable future. In the meantime, existing reduced models are not satisfactory in describing the hydrodynamic interactions between microswimmers in close proximity with even qualitatively erroneous predictions, indicating a pressing need for an adequate model.

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Fig.1. The E. coli bacterium can be entrapped by the passive sphere with an orbital motion in real space (figure on the left), which can be related to a stable fixed point in the two-dimensional phase plane defined by the surface distance d, and incoming angle θ (figure on the right).

 

Theorists at Beijing Computational Science Research Center, led by Prof. Yang Ding from Mechanics Division, and Prof. Xinliang Xu from Complex Systems Division, recently proposed an effective model that solved this long-standing problem by capturing the essence of the hydrodynamic interactions through the resistance tensor. In a critical test case that studies the scattering angle of the pair dynamics between one E. coli bacterium and one passive sphere, it is proved that the near field hydrodynamic interaction can make a qualitative difference: Calculations based on the proposed model reveal a region in parameter space where the E. coli bacterium is trapped by the passive sphere, a phenomenon that is regularly observed in experiments but cannot be explained by any previous model (figure 1). Beyond its physical effectiveness, it is demonstrated that the model allows efficient simulation of active fluids with tens of thousands of microswimmers, sufficiently large for investigations of many emergent behaviors [2].

 

[1] D. Saintillan, Annu. Rev. Fluid Mech. 50, 563-592 (2018).

[2] B. K. Zhang, P. Leishangthem, Y. Ding*, and X. L. Xu*, Proc. Natl. Acad. Sci. USA 118, e2100145118 (2021).

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