A multi-domain direct boundary element formulation for particulate flow in microchannels

Abstract

A multi-domain direct boundary element formulation for particulate flow in microchannels By Alper Topuz August 2021We certify that we have read this thesis and that in our opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

DC‐electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

“…However, neither velocity nor traction values are known on the particle surface. We recently presented a boundary element formulation for tracking multiple particle trajectories in Stokes flow for microfluidic applications [39,40] through which a partitioning process was also described to speed up the calculations. As stated in our formulation, the constraints associated with rigid body motion can be imposed for the closure of the problem as: (16) where 𝐮 p is the velocity at a node on the boundary of the particle, 𝐮 B is the velocity of the selected center of the particle, 𝜔 B is the angular velocity, and 𝐫 𝑝 is the relative position vector of the boundary node to the center of the particle and 𝐮 S p is the slip-velocity on the particle surface given in Equation (3).…”

“…However, neither velocity nor traction values are known on the particle surface. We recently presented a boundary element formulation for tracking multiple particle trajectories in Stokes flow for microfluidic applications [39, 40] through which a partitioning process was also described to speed up the calculations. As stated in our formulation, the constraints associated with rigid body motion can be imposed for the closure of the problem as: $$\begin{equation} \mathbf {u}_{\text{p}} = \mathbf {u}^{\text{B}} + (\omega ^{\text{B}}\hat{k})\times \mathbf {r}_{\text{p}} + \mathbf {u}^{\text{S}}_{\text{p}} \end{equation}$$where $$\mathbf {u}_{\text{p}}$$ is the velocity at a node on the boundary of the particle, $$\mathbf {u}^{\text{B}}$$ is the velocity of the selected center of the particle, $$\omega ^{\text{B}}$$ is the angular velocity, and $$\mathbf {r}_p$$ is the relative position vector of the boundary node to the center of the particle and $$\mathbf {u}^{\text{S}}_{\text{p}}$$ is the slip‐velocity on the particle surface given in Equation ().…”

Isogeometric and NURBS-enhanced boundary element formulations for steady-state heat conduction with volumetric heat source and nonlinear boundary conditions

“…Variable condensation techniques have been implemented successfully for multi-domain boundary element formulations for the determination of the unknown variables on the interfaces of the multi-domains of the problem [10][11][12][13][14][15][16]. In addition, variable condensation technique has also been implemented for wave propagation problems (which is also named as impedance formulation in these studies) [17,18] and particulate flows for microfluidic applications [19][20][21][22]. More recently, Baranoğlu [23] proposed the use of variable condensation approach for the solution of heat conduction problems with non-linear boundary conditions.…”