Dynamic numerical simulations of magnetically interacting suspensions in creeping flow

Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

“…However, not every solution to (1)-( 2) can be represented by a double layer potential alone; for instance, as noted in References [67, 8, p. 119], the force and torque exerted on any particle by the flow from a double layer potential will always be zero, whereas a Stokes flow in general can exert a nonzero force and torque on the particles (which is a central point of the resistance and mobility problems mentioned in Section 1). This is related to the presence of a nontrivial nullspace of the operator q  → [Γ, q] for external flows, which can be immediately seen from the stresslet identity (5).…”

“…In order to estimate the error during the parameter selection process, we apply a constant densityq such that |q| = 1 to the surface and evaluate the stresslet identity (5). ** This may seem like an overly simple test case since both the density and the solution are constant.…”

“…3 Suspensions of rigid particles in Stokes flow are important both in various applications and in fundamental fluid mechanics. [4][5][6][7] In this article, we describe a boundary integral method that can be used to study the motion of rigid particles of different shapes in Stokes flow. The particle suspension may also be confined in a container geometry, such as a pipe or a pair of flat walls.…”

Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

“…Applications are found in biology, for example in the swimming of microorganisms [20] and in blood ow [34], as well as in the eld of micro uidics, which concerns the design and construction of miniaturized uid devices [51]. Suspensions of rigid particles in Stokes ow are important both in various applications and in fundamental uid mechanics [46,16,36,19]. In this paper, we describe a boundary integral method that can be used to study the motion of rigid particles of di erent shapes in Stokes ow.…”

Rheology of a very dilute magnetic suspension with micro-structures of nanoparticles

“…More recently, Gontijo and Cunha (2015) have carried out dynamic simulations of a magnetic suspensions with particles interacting magnetically in a periodic box in the presence of an applied magnetic field. These simulations demonstrate the gradual formation of particle structures like aggregates and its transition to anisotropic chains of aligned particles induced by magnetic effects.…”