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The general system of images for regularized Stokeslets (GSIRS) developed by Cortez and Varela [] is used extensively to model Stokes flow phenomena such as microorganisms swimming near a boundary. Our collaborative team uses dynamically similar scaled macroscopic experiments to test theories for forces and torques on spheres moving near a boundary and uses these data and the method of regularized Stokeslets (MRS) created by Cortez [] to calibrate the GSIRS. We find excellent agreement between theory and experiments, which provides experimental validation of exact series solutions for spheres moving near an infinite plane boundary. We test two surface discretization methods commonly used in the literature: the 6-patch method and the spherical centroidal Voronoi tessellation (SCVT) method. Our data show that a discretization method, such as SCVT, that uniformly distributes points provides the most accurate results when the motional symmetry is broken by the presence of a boundary. We use theory and the MRS to find optimal values for the regularization parameter in free space for a given surface discretization and show that the optimal regularization parameter values can be fit with simple formulas when using the SCVT method. We also present a regularization function with higher-order accuracy when compared with the regularization function previously introduced by Cortez []. The simulated force and torque values compare very well with experiments and theory for a wide range of boundary distances. However, we find that for a fixed discretization of the sphere, the simulations lose accuracy when the gap between the edge of the sphere and the wall is smaller than the average distance between discretization points in the SCVT method. We also show an alternative method to calibrate the GSIRS to simulate sphere motion arbitrarily close to the boundary. Our computational parameters and methods along with our matlab and python implementations of the series solution of Lee and Leal [], MRS, and GSIRS provide researchers with important resources to optimize the GSIRS and other numerical methods, so that they can efficiently and accurately simulate spheres moving near a boundary.
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A regularised force-doublet framework for self-propelled microswimmers
A single particle representation of a self-propelled microorganism in a viscous incompressible fluid is derived based on regularised Stokeslets in three dimensions. The formulation is developed from a limiting process in which two regularised Stokeslets of equal and opposite strength but with different size regularisation parameters approach each other. A parameter that captures the size difference in regularisation provides the asymmetry needed for propulsion. We show that the resulting limit is the superposition of a regularised stresslet and a potential dipole. The model framework is then explored relative to the model parameters to provide insight into their selection. The particular case of two identical particles swimming next to each other is presented and their stability is investigated. Additional flow characteristics are incorporated into the modelling framework with in the addition of a rotlet double to characterise rotational flows present during swimming. Lastly, we show the versatility of deriving the model in the method of regularised Stokeslets framework to model wall effects of an infinite plane wall using the method of images.
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- PAR ID:
- 10634484
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1009
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1017/jfm.2025.138
