An experimental study is reported of the motion, deformation, and breakup of a synthetic capsule that is freely suspended in Couette flow. The capsule is a liquid drop surrounded by a thin polymeric membrane. The shape and orientation of the capsule are measured in steady flow and following the start-up of Couette flow. Results are compared with predictions of the small-deformation theory of Barthes-Biesel and co-workers. The data suggest that the capsule membrane is viscoelastic, and comparisons with theory yield values of the membrane elastic modulus and the membrane viscosity. The values of the elastic modulus of the capsule membrane deduced from the flow data are compared with independent measurements for the same capsule.When the flow-induced deformation becomes sufficiently large, the capsules break. Breakup begins at points on the membrane surface near the principal strain axis of the undisturbed flow. By examining the local deformation within the membrane, it is shown that breakup is correlated with local thinning of the membrane and is initiated at points where the thickness is a minimum.

This numerical study investigates flow and turbulence structure through and around a circular array of solid circular cylinders of diameter d. The region containing the array of rigid cylinders resembles a porous circular cylinder of diameter D. The porous cylinder Reynolds number defined with the steady incoming flow velocity is Re D = 10 000. Fully three-dimensional (3D) large eddy simulations (LES) are conducted to study the effects of the volume fraction of solids of the porous cylinder (0.023 < SVF < 0.2) and d/D on the temporal variation and mean values of the drag/lift forces acting on the solid cylinders and on the porous cylinder. The effects of the bleeding flow through the circular porous cylinder on the wake structure and the influence of the SVF and d/D on the onset of flow three-dimensionality within or downstream of the porous cylinder and transition to turbulence are discussed. Results are compared with experimental data, predictions of theoretical models available in the literature and also with the canonical case of a solid cylinder (SVF = 1, d/D = 1). Three-dimensional LES predict that large-scale wake billows are shed in the wake of the porous cylinder for SVF > 0.05, similar to the von Karman vortex street observed for solid cylinders. As the SVF decreases, the length of the separated shear layers (SSLs) of the porous cylinder and the distance from the back of the porous cylinder at which wake billows form increase. For sufficiently low volume fractions of solids (e.g. SVF = 0.05, 0.023), no wake billows are shed and the interactions among the wakes of the solid cylinders are weak. Even for SVF = 0.023, SSLs containing large-scale turbulent eddies form on the two sides of the porous cylinder, but their ends cannot interact to generate wake billows. In both regimes, the force acting on some of the solid cylinders within the array is highly unsteady. As opposed to results obtained based on 2D simulations, no intermediate regime in which the force acting on the solid cylinders is close to steady is present. Interestingly, an energetic low frequency corresponding to a Strouhal number defined with the diameter of the porous cylinder of approximately 0.2 is present within the porous cylinder and near-wake regions not only for cases where wake billows are generated but also for cases where no wake billows form. In the latter cases, this frequency is due to an instability acting on the SSLs which induces in-phase large-scale undulatory deformations of the two SSLs. A combined drag parameter for the porous cylinder Γ D = C d aD/(1 − SVF) is introduced, where aD is the non-dimensional frontal area per unit volume of the porous cylinder. This parameter characterizes by how much the † Email address for correspondence: sconstan@engineering.uiowa.edu 162 K. Chang and G. Constantinescu velocity of the bleeding flow at the back of the porous cylinder is reduced compared with the incoming flow velocity for a given total drag force acting on the porous cylinder. Results from simulations conducted with differen...

The three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel is investigated using large-eddy simulation (LES). The aspect ratio (length/depth) of the cavity is $L/D\,{=}\,2$ and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3360. The sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases: a developing laminar boundary layer upstream of the cavity and when the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. For the laminar inflow case it is found that the flow becomes unstable but remains laminar as it is convected over the cavity. Due to the three-dimensional flow instabilities and the interaction of the jet-like flow inside the recirculation region with the separated shear layer, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing-edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case in which the momentum thickness of the incoming boundary layer is much larger compared to the laminar inflow case, the jittering of the shear layer on top of the cavity by the incoming near-wall coherent structures strongly influences the formation and convection of the eddies inside the separated shear layer. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster when the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream of the cavity with the separated shear layer and also to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream of the cavity can play an important role in accelerating the extraction of high-concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single-valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole ejection process.

Experiments are described to study the motion and deformation of a synthetic, liquid-filled capsule that is freely suspended in hyperbolic extensional flow. The capsule is a composite particle consisting of a viscous liquid drop surrounded by a thin polymeric membrane. The method used to fabricate capsules suitable for macroscopic flow experiments is described. The deformation of the capsule is measured as a function of strain rate for an extensional flow generated in a four-roll mill. The data agree well with results from small-deformation theory developed by Barthes-Biesel and co-workers, provided the deformation of the capsule is not too large. Using the theory to correlate the experimental data produces an estimate for the elastic modulus of the membrane that agrees reasonably well with the elastic modulus obtained by an independent technique. However, for sufficiently large strain rates, the membrane exhibits strain hardening and a permanent change in its structure, both of which are reflected in the shape of the capsule.