The boundary integral formulation of Stokes flows includes slender-body theory

Abstract

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 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 and Rubinow (1976) and Johnson (1979) 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 double-layer modified BI representation, general slender solutions are only possible in certain types of flow, in accordance with the limitations of these representations.

References in corpus (3)

• Bistability in the synchronization of actuated microfilaments
• Slender-ribbon theory
• The passive diffusion of Leptospira interrogans

Cited by in corpus (15)

• An integral-based spectral method for inextensible slender fibers in Stokes flow
• Coarse-graining the dynamics of immersed and driven fiber assemblies
• Slender Phoretic Theory of chemically active filaments
• Local drag of a slender rod parallel to a plane wall in a viscous fluid
• Slender body theories for rotating filaments
• Efficient Convergent Boundary Integral Methods for Slender Bodies
• A hydrodynamic slender-body theory for local rotation at zero Reynolds number
• A single-layer based numerical method for the slender body boundary value problem
• Geometric phase methods with Stokes theorem for a general viscous swimmer
• Modeling of Sedimentation of Particles near Corrugated Surface by Boundary Singularity Method
• Rheology of moderated dilute suspensions of star colloids: the shape factor
• Effective and efficient modeling of the hydrodynamics for bacterial flagella
• Instability and self-propulsion of flexible autophoretic filaments
• Regularized Stokeslets lines suitable for slender bodies in viscous flow
• Method of regularised stokeslets: Flow analysis and improvement of convergence