Dr Lyndon Koens L.M.Koens@hull.ac.uk
Lecturer
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and computationally. Alternatively, one can solve the Stokes equations by using an appropriate distribution of flow singularities of the right strength within the boundary, a method that is particularly useful to describe the dynamics of long slender objects for which the numerical implementation of the BI representation becomes cumbersome. While the BI approach is a mathematical consequence of the Stokes equations, the singularity method involves making judicious guesses that can only be justified a posteriori. In this paper, we use matched asymptotic expansions to derive an algebraically accurate slender-body theory directly from the BI representation able to handle arbitrary surface velocities and surface tractions. This expansion procedure leads to sets of uncoupled linear equations and to a single one-dimensional integral equation identical to that derived by Keller & Rubinow (J. Fluid Mech., vol. 75, 1976, p. 705) and Johnson (J. Fluid Mech., vol. 99, 1979, p. 411) using the singularity method. Hence, we show that it is a mathematical consequence of the BI approach that the leading-order flow around a slender body can be represented using a distribution of singularities along its centreline. Furthermore, when derived from either the single-layer or the double-layer modified BI representation, general slender solutions are only possible in certain types of flow, in accordance with the limitations of these representations.
Koens, L., & Lauga, E. (2018). The boundary integral formulation of Stokes flows includes slender-body theory. Journal of Fluid Mechanics, 850, Article R1. https://doi.org/10.1017/jfm.2018.483
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 9, 2018 |
Online Publication Date | Jul 2, 2018 |
Publication Date | Sep 10, 2018 |
Deposit Date | Jan 25, 2022 |
Journal | Journal of Fluid Mechanics |
Print ISSN | 0022-1120 |
Electronic ISSN | 1469-7645 |
Publisher | Cambridge University Press |
Peer Reviewed | Peer Reviewed |
Volume | 850 |
Article Number | R1 |
DOI | https://doi.org/10.1017/jfm.2018.483 |
Public URL | https://hull-repository.worktribe.com/output/3916599 |
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