A Model for Stokes Flow in Domains with Permeable Boundaries

We derive a new computational model for the simulation of viscous incompressible flows bounded by a thin, flexible, porous membrane. Our approach is grid-free and models the boundary forces with regularized Stokeslets. The flow across the porous membranes is modeled with regularized source doublets...

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Autores principales:	Ricardo Cortez, Marian Hernandez-Viera, Owen Richfield
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	regularized stokeslets regularized source-dipoles permeable membranes permeable channel flow Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/bc0dd959a6064707b4aff46cdbe3a34c
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spelling	oai:doaj.org-article:bc0dd959a6064707b4aff46cdbe3a34c2021-11-25T17:31:27ZA Model for Stokes Flow in Domains with Permeable Boundaries10.3390/fluids61103812311-5521https://doaj.org/article/bc0dd959a6064707b4aff46cdbe3a34c2021-10-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/381https://doaj.org/toc/2311-5521We derive a new computational model for the simulation of viscous incompressible flows bounded by a thin, flexible, porous membrane. Our approach is grid-free and models the boundary forces with regularized Stokeslets. The flow across the porous membranes is modeled with regularized source doublets based on the notion that the flux velocity across the boundary can be viewed as the flow induced by a fluid source/sink pair with the sink on the high-pressure side of the boundary and magnitude proportional to the pressure difference across the membrane. Several validation examples are presented that illustrate how to calibrate the parameters in the model. We present an example consisting of flow in a closed domain that loses volume due to the fluid flux across the permeable boundary. We also present applications of the method to flow inside a channel of fixed geometry where sections of the boundary are permeable. The final example is a biological application of flow in a capillary with porous walls and a protein concentration advected and diffused in the fluid. In this case, the protein concentration modifies the pressure in the flow, producing dynamic changes to the flux across the walls. For this example, the proposed method is combined with finite differences for the concentration field.Ricardo CortezMarian Hernandez-VieraOwen RichfieldMDPI AGarticleregularized stokesletsregularized source-dipolespermeable membranespermeable channel flowThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 381, p 381 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	regularized stokeslets regularized source-dipoles permeable membranes permeable channel flow Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	regularized stokeslets regularized source-dipoles permeable membranes permeable channel flow Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 Ricardo Cortez Marian Hernandez-Viera Owen Richfield A Model for Stokes Flow in Domains with Permeable Boundaries
description	We derive a new computational model for the simulation of viscous incompressible flows bounded by a thin, flexible, porous membrane. Our approach is grid-free and models the boundary forces with regularized Stokeslets. The flow across the porous membranes is modeled with regularized source doublets based on the notion that the flux velocity across the boundary can be viewed as the flow induced by a fluid source/sink pair with the sink on the high-pressure side of the boundary and magnitude proportional to the pressure difference across the membrane. Several validation examples are presented that illustrate how to calibrate the parameters in the model. We present an example consisting of flow in a closed domain that loses volume due to the fluid flux across the permeable boundary. We also present applications of the method to flow inside a channel of fixed geometry where sections of the boundary are permeable. The final example is a biological application of flow in a capillary with porous walls and a protein concentration advected and diffused in the fluid. In this case, the protein concentration modifies the pressure in the flow, producing dynamic changes to the flux across the walls. For this example, the proposed method is combined with finite differences for the concentration field.
format	article
author	Ricardo Cortez Marian Hernandez-Viera Owen Richfield
author_facet	Ricardo Cortez Marian Hernandez-Viera Owen Richfield
author_sort	Ricardo Cortez
title	A Model for Stokes Flow in Domains with Permeable Boundaries
title_short	A Model for Stokes Flow in Domains with Permeable Boundaries
title_full	A Model for Stokes Flow in Domains with Permeable Boundaries
title_fullStr	A Model for Stokes Flow in Domains with Permeable Boundaries
title_full_unstemmed	A Model for Stokes Flow in Domains with Permeable Boundaries
title_sort	model for stokes flow in domains with permeable boundaries
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bc0dd959a6064707b4aff46cdbe3a34c
work_keys_str_mv	AT ricardocortez amodelforstokesflowindomainswithpermeableboundaries AT marianhernandezviera amodelforstokesflowindomainswithpermeableboundaries AT owenrichfield amodelforstokesflowindomainswithpermeableboundaries AT ricardocortez modelforstokesflowindomainswithpermeableboundaries AT marianhernandezviera modelforstokesflowindomainswithpermeableboundaries AT owenrichfield modelforstokesflowindomainswithpermeableboundaries
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A Model for Stokes Flow in Domains with Permeable Boundaries

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