The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion

The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface defor...

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Autores principales:	David J. Smith, Meurig T. Gallagher, Rudi Schuech, Thomas D. Montenegro-Johnson
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Stokes flow propulsion swimming regularised stokeslets double-layer squirmer Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/47196272e8e447c1895c04d68773a32c
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spelling	oai:doaj.org-article:47196272e8e447c1895c04d68773a32c2021-11-25T17:31:47ZThe Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion10.3390/fluids61104112311-5521https://doaj.org/article/47196272e8e447c1895c04d68773a32c2021-11-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/411https://doaj.org/toc/2311-5521The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface deformation. We describe a meshless approach enabling the inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial-slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretisation on a notebook computer with the inclusion of the double layer ranging from no-slip to free-slip limits; the neglect of the double-layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a small percent error when the double-layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and nonslender swimmers, whether or not the double layer is included, which may be due to the deformation’s ‘locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. The inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.David J. SmithMeurig T. GallagherRudi SchuechThomas D. Montenegro-JohnsonMDPI AGarticleStokes flowpropulsionswimmingregularised stokesletsdouble-layersquirmerThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 411, p 411 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Stokes flow propulsion swimming regularised stokeslets double-layer squirmer Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	Stokes flow propulsion swimming regularised stokeslets double-layer squirmer Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 David J. Smith Meurig T. Gallagher Rudi Schuech Thomas D. Montenegro-Johnson The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
description	The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface deformation. We describe a meshless approach enabling the inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial-slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretisation on a notebook computer with the inclusion of the double layer ranging from no-slip to free-slip limits; the neglect of the double-layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a small percent error when the double-layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and nonslender swimmers, whether or not the double layer is included, which may be due to the deformation’s ‘locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. The inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.
format	article
author	David J. Smith Meurig T. Gallagher Rudi Schuech Thomas D. Montenegro-Johnson
author_facet	David J. Smith Meurig T. Gallagher Rudi Schuech Thomas D. Montenegro-Johnson
author_sort	David J. Smith
title	The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
title_short	The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
title_full	The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
title_fullStr	The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
title_full_unstemmed	The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion
title_sort	role of the double-layer potential in regularised stokeslet models of self-propulsion
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/47196272e8e447c1895c04d68773a32c
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The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion

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