Boundary element methods for particles and microswimmers in a linear viscoelastic fluid
The consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalise...
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| Format: | Journal article |
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Cambridge University Press
2017
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| _version_ | 1797077926842204160 |
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| author | Ishimoto, K Gaffney, E |
| author_facet | Ishimoto, K Gaffney, E |
| author_sort | Ishimoto, K |
| collection | OXFORD |
| description | The consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalised reciprocal relation and viscoelastic force singularities, a boundary element method is developed for linear viscoelastic flows. We proceed to explore finite-deformation microswimming in a linear Maxwell fluid. We firstly deduce a finite-amplitude generalisation of a previously reported result that the flow field is unchanged between a Newtonian and linear Maxwell fluid for prescribed small-amplitude deformations. Hence Purcell’s theorem holds for a linear Maxwell fluid. We proceed to consider deformation swimming in a linear Maxwell fluid given an external forcing. Boundary scattering trajectories for an exemplar squirmer approaching a surface are observed to exhibit a weak dependence on the Deborah number, while the trajectories of a sperm and monotrichous bacterium near a surface are predicted to be essentially unaffected at moderate Deborah number. In turn, the latter supports the common simplification of using Newtonian Stokes flows for studying flagellate swimming in linear Maxwell media. In addition, the motion of a magnetic helix under the influence of an external magnetic field is considered, and highlights that linear viscoelasticity can significantly impact the propagation of the helix, in turn demonstrating that even linear rheology is important to consider for forced swimmers. Finally, the presented framework requires minimalistic adjustments to Newtonian boundary element codes, enabling rapid implementation, and is more generally applicable, for instance to studies of particle interactions in active linear rheology on the microscale. |
| first_indexed | 2024-03-07T00:25:03Z |
| format | Journal article |
| id | oxford-uuid:7ddbae8a-a741-4477-8b2e-c9aa541e019b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:25:03Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:7ddbae8a-a741-4477-8b2e-c9aa541e019b2022-03-26T21:06:21ZBoundary element methods for particles and microswimmers in a linear viscoelastic fluidJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7ddbae8a-a741-4477-8b2e-c9aa541e019bSymplectic Elements at OxfordCambridge University Press2017Ishimoto, KGaffney, EThe consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalised reciprocal relation and viscoelastic force singularities, a boundary element method is developed for linear viscoelastic flows. We proceed to explore finite-deformation microswimming in a linear Maxwell fluid. We firstly deduce a finite-amplitude generalisation of a previously reported result that the flow field is unchanged between a Newtonian and linear Maxwell fluid for prescribed small-amplitude deformations. Hence Purcell’s theorem holds for a linear Maxwell fluid. We proceed to consider deformation swimming in a linear Maxwell fluid given an external forcing. Boundary scattering trajectories for an exemplar squirmer approaching a surface are observed to exhibit a weak dependence on the Deborah number, while the trajectories of a sperm and monotrichous bacterium near a surface are predicted to be essentially unaffected at moderate Deborah number. In turn, the latter supports the common simplification of using Newtonian Stokes flows for studying flagellate swimming in linear Maxwell media. In addition, the motion of a magnetic helix under the influence of an external magnetic field is considered, and highlights that linear viscoelasticity can significantly impact the propagation of the helix, in turn demonstrating that even linear rheology is important to consider for forced swimmers. Finally, the presented framework requires minimalistic adjustments to Newtonian boundary element codes, enabling rapid implementation, and is more generally applicable, for instance to studies of particle interactions in active linear rheology on the microscale. |
| spellingShingle | Ishimoto, K Gaffney, E Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title | Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title_full | Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title_fullStr | Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title_full_unstemmed | Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title_short | Boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| title_sort | boundary element methods for particles and microswimmers in a linear viscoelastic fluid |
| work_keys_str_mv | AT ishimotok boundaryelementmethodsforparticlesandmicroswimmersinalinearviscoelasticfluid AT gaffneye boundaryelementmethodsforparticlesandmicroswimmersinalinearviscoelasticfluid |