Particle Image Velocimetry Evaluation of a Novel Oscillatory-Flow Flexible Chamber Mixer

Abstract

This paper describes a novel oscillatory-flow mixer consisting of a pair of flexible chambers connected by a perforated plate, or septum. During operation, the septum undergoes reciprocating motion such that the two chambers are alternately compressed and expanded. During compression, fluid is forced from one chamber to the other through the septum holes, creating an array of jets that drive the mixing process. Flow characterization within the mixer was conducted using particle image velocimetry. Tests were performed for Reynolds numbers ranging from 4 to 23,000, which encompass the creeping, laminar, and turbulent flow regimes. Results include mean and rms velocity maps, shear rate maps, vertical velocity profiles, and flow development data. The results suggest that the mixer is capable of gentle, continuous stirring (important for biological applications), as well as vigorous agitation. Finally, a comparison between this mixer and other existing mixing technologies is presented.

Galerkin Boundary Elements for a Computation of the Surface Tractions in Exterior Stokes Flows

“…Indirect formulations for creeping (or Stokes) flows, with Reynolds numbers Re < 1, are commonly related to hydrodynamic single-and double-layer potentials [14][15][16]. Examples of creeping flows in fluid engineering and biomedical engineering include multilevel BEM for steady Stokes flows in irregular domains [17]; low Reynolds number flows in spiral microchannels used in DNA identifying lab-on-a-chip devices [18]; creeping flow regime in oscillatory-flow mixers with flexible chambers [19], micro-electromechanical systems (MEMS) [20,21], and laminar flow in compact heat exchangers and microcoolers in electronics packaging [22]. Ingber and Mammoli [23] have analyzed the case of BIE for creeping flows, and showed comparisons among three different formulations:…”

Validation of a Galerkin technique on a boundary integral equation for creeping flow around a torus

“…The computation of steady Stokes flows around closed rigid bodies can be of interest in fluid and biomedical engineering. Possible applications are multilevel boundary element method (BEM) for steady Stokes flows in irregular two-dimensional domains (Dargush and Grigoriev 2005); low Reynolds number flow of an incompressible fluid in spiral microchannels that are used in DNA identifying lab-on-a-chip devices (Lepchev and Weihs 2010); creeping flow regime in oscillatory-flow mixers with flexible chambers (Shipman et al 2007); laminar flow in compact heat exchangers and microcoolers in electronics packaging (Galvis 2012); laminar fully developed flow in micro-/minichannels with non-circular cross sections (Tamayol and Bahrami 2010); as well as micro-electro-mechanical systems (MEMS) (Berli and Cardona 2009;Méndez et al 2008;Wang 2002).…”

“…Indirect formulations in this flow case are commonly related to hydrodynamic doubleand single-layer potentials (Ladyzhenskaya 1969;Pozrikidis 1996). An indirect Boundary Integral Equation (BIE) uses as a starting point the potentials produced by surface layers of (fictitious) singularities (Sauter and Schwab 2011). These surface singularity layers generate the physical fields of interest, which are distributed on the boundary and its intensities have to be determined such that the integrated response is equal to the prescribed boundary data.…”

“…From a mathematical point of view, the unknowns in the indirect BIE are the jumps of the traces across the boundary of the Cauchy data of both the interior and the exterior BVP (Hsiao and Wendland 2008;Sauter and Schwab 2011).…”