Parisa Mirbod

On the generation of lift forces in random soft porous media

In this paper, we examine the generation of pressure and lift forces in a random soft fibrous media layer that is confined between two planar surfaces, an infinite horizontal lower boundary and a horizontal inclined upper boundary, in the lubrication limit where the characteristic thickness of the fibre layer HL the length of the inclined surface. The model for the fibre layer is a Brinkman equation and the Darcy permeability Kp is described by the widely used Carman-Kozeny equation for random porous media. Two cases are considered: (a) an inclined upper boundary which slides freely on top of a stationary fibre layer which is firmly attached to the lower boundary and (b) an inclined stationary upper boundary with an attached fibre layer in which the horizontal lower boundary slides freely in its own plane beneath it. Superficially, the problems appear equivalent to the classical problem for a slider bearing where the solutions for the pressure distribution and lift force are independent of which boundary is moving. In this problem there is an optimum compression ratio k = h1/h2 =2 .2, where h1 and h2 are the heights at the leading and trailing edges, for maximum lift force. However, this symmetry is lost if the intervening space is filled with a soft porous fibrous material since the Brinkman equation is not invariant under a transformation of coordinates in which the inherently unsteady problem in case (a) is transformed to a steady reference frame in which the inclined upper boundary is stationary and the horizontal boundary with the adhered fibre layer moves below it. Although in the steady reference frame case (a) now appears to resemble case (b), the solutions are strikingly different and depend critically on the value of the dimensionless fibre interaction layer thickness α = H/ � Kp .F orα � 1 the solutions for both cases approach the classical solution for a slider bearing. For α � 1 we show, using asymptotic analysis that the solutions diverge dramatically. In case (a) the pressure and lift force increase as α 2 and asymptotically approach a limiting behaviour for large values of α, first predicted in Feng and Weinbaum (J. Fluid Mech., vol. 422, 2000, p. 288), while in case (b) the pressure and lift force decay as α −2 since the inclined upper boundary is screened by the fibre layer and the amount of fluid dragged through the fluid gap decreases as α increases and vanishes for α � 1. The solution in case (a), where the inclined upper boundary moves, is of particular interest since it reveals the potential to generate enormous lift forces using commercially available inexpensive soft porous materials provided the lateral leakage at the edge of the planform can be eliminated through the use of a channel with impermeable sidewalls as first proposed in the work by Wu, Andreopolous and Weinbaum (Phys. Rev. Lett., vol. 93, 2004, p. 194501). The behaviour is illustrated for

Free surface flow between two horizontal concentric cylinders

Results are reported on a combined experimental and numerical investigation of a free surface flow at small Reynolds numbers. The flow is driven by the rotation of the inner of two horizontal concentric cylinders, with an inner to outer radius ratio of 0.43. The outer cylinder is stationary. The annular gap is partially filled, from 0.5 to 0.95 full, with a viscous liquid leaving a free surface. When the fraction of the annular volume filled by liquid is 0.5, a thin liquid film covers the rotating inner cylinder and reenters the liquid pool. For relatively low rotation speeds, the evolution of the film thickness is consistent with the theory for a plate being withdrawn from an infinite liquid pool. The overall liquid flow pattern at this condition consists of two counter-rotating cells: one is around the inner cylinder and the other with weaker circulation rate is in the bottom part of the annulus and nearly symmetric about the vertical axis. With increasing rotation rate, the free surface becomes more deformed, and the dynamics of the stagnation line and the cusp line dividing the cells are tracked as quantitative measures of the interface shape. In addition, the recirculating flow cells lose symmetry and the cusp deforms the free surface severely. A comparison of numerically computed flow which describes the interface by a phase-field method confirms the dynamics of the two cells and the interface deformation. For filling fraction 0.75, the liquid level is slightly above the inner cylinder and a significant decrease in size of the bottom cell with increasing rotation rate is found. For filling fractions approaching unity, the liquid flow consists of one single cell and the surface deformation remains small.

Three-dimensional flow patterns in the feto-placental vasculature system of the mouse placenta.

In this study, three-dimensional (3D) blood flow of the feto-placental vasculature system of the mouse placenta was investigated using computational fluid dynamics (CFD) methods and finite element analysis. Micro-computerized tomography (micro-CT) images were used to acquire the 3D geometry of the feto-placental vasculature system, and image-processing software has been used to calculate the 3D morphology of the placenta. The flow was analyzed numerically and compared to the experimental data received from the same model. The numerical and experimental results agree well. Experimentally measured time dependent blood velocity data, available in the literature, was used as the inlet boundary condition to represent the fetal blood pulsatile flow. Velocity profiles and pressure distributions are investigated during different phases of the unsteady flow. The results clearly illustrate the important role of the vasculature structure (e.g., diameter and curvature) in the fetal hemodynamics, which to our knowledge has not been examined previously. The data also show that, at each bifurcation, the blood flow velocity decreases significantly in the transition from the parent vessel (i.e., umbilical artery) to the daughter vessels because of the higher total cross-sectional area of the daughter vessels compared to the parent vessel. It can also be observed that pressure drop at the umbilical artery and pressure drop across the arterial trees obtained in this study agree well with the physiological data reported in the literature. Moreover, the velocity profiles after each bifurcation are symmetric. Finally, from the results no secondary flow has been observed in the vasculature system. This study provides a foundation in understanding and modeling the complex structure of the feto-placental vasculature system and serves as a first step towards developing new concepts for computational analysis of the feto-placental vasculature systems of both human and mouse to better understand how the placenta functions and how gas and nutrient exchange between the mother and fetus.

Analysis of bolus formation in micropipette ejection systems

The ejection of drugs from micropipettes is practiced frequently in biomedical research and clinical studies however, little is known about the dynamics of this process. The fundamentals of disperse fluid injection via a capillary into an ambient immiscible fluid have been investigated extensively. Here, we experimentally investigate the bolus formation in micropipette ejection systems, where the injection and ambient fluid are the same. We experimentally measure the temporal evolution of the bolus formation in the same fluid. There are three different bolus formation mechanisms that arise from different Ret regimes: a) a nearly spherical bolus, b) a pear-like bolus, and c) a large distortion or axial jet. We examine the scaled dimensions of the bolus, Rb/Dt, Lb/Dt, H/Dt, and α, as a function of the dimensionless parameters such as tip Reynolds number, Ret, dimensionless value of g/(Dt. Vt), the dimensionless time, tVt/Dt, and the distance between the edge of the micropipette and the free surface, D/Dt. The bolus radius for 0.2 < Ret < 30 grows according to t1/2 in the entire time range, which allows us to estimate the time for complete bolus formation.Graphical abstract

Laminar flow drag reduction on soft porous media

While researches have focused on drag reduction of various coated surfaces such as superhydrophobic structures and polymer brushes, the insights tso understand the fundamental physics of the laminar skin friction coefficient and the related drag reduction due to the formation of finite velocity at porous surfaces is still relatively unknown. Herein, we quantitatively investigated the flow over a porous medium by developing a framework to model flow of a Newtonian fluid in a channel where the lower surface was replaced by various porous media. We showed that the flow drag reduction induced by the presence of the porous media depends on the values of the permeability parameter α = L/(MK)1/2 and the height ratio δ = H/L, where L is the half thickness of the free flow region, H is the thickness and K is the permeability of the fiber layer, and M is the ratio of the fluid effective dynamic viscosity μe in porous media to its dynamic viscosity μ. We also examined the velocity and shear stress profiles for flow over the permeable layer for the limiting cases of α → 0 and α → ∞. The model predictions were compared with the experimental data for specific porous media and good agreement was found.

Analytical model of the feto-placental vascular system: consideration of placental oxygen transport

The placenta is a transient vascular organ that enables nutrients and blood gases to be exchanged between fetal and maternal circulations. Herein, the structure and oxygen diffusion across the trophoblast membrane between the fetal and maternal red blood cells in the feto-placental vasculature system in both human and mouse placentas are presented together as a functional unit. Previous models have claimed that the most efficient fetal blood flow relies upon structures containing a number of ‘conductive’ symmetrical branches, offering a path of minimal resistance that maximizes blood flow to the terminal villi, where oxygen diffusion occurs. However, most of these models have disregarded the actual descriptions of the exchange at the level of the intermediate and terminal villi. We are proposing a ‘mixed model’ whereby both ‘conductive’ and ‘terminal’ villi are presumed to be present at the end of single (in human) or multiple (in mouse) pregnancies. We predict an optimal number of 18 and 22 bifurcation levels in the human and the mouse placentas, respectively. Wherever possible, we have compared our models predictions with experimental results reported in the literature and found close agreement between them.

Experimental analysis of the flow near the boundary of random porous media

The aim of this work is to experimentally examine flow over and near random porous media. Different porous materials were chosen to achieve porosity ranging from 0.95 to 0.99. In this study, we report the detailed velocity measurements of the flow over and near random porous material inside a rectangular duct using a planar particle image velocimetry (PIV) technique. By controlling the flow rate, two different Reynolds numbers were achieved. We determined the slip velocity at the interface between the porous media and free flow. Values of the slip velocity normalized either by the maximum flow velocity or by the shear rate at the interface and the screening distance K1/2 were found to depend on porosity. It was also shown that the depth of penetration inside the porous material was larger than the screening length using Brinkman’s prediction. Moreover, we examined a model for the laminar coupled flow over and inside porous media and analyzed the permeability of a random porous medium. This study provided ...

Experimental Study of Non-Colloidal Mono and Polydisperse Suspension in Taylor-Couette Flow

Monodisperse and polydisperse suspension flows form an extensive section of natural and technological flows. These flow structures can be categorized to sedimenting or neutrally buoyant suspensions considering the density ratio between particle phase to dispersion phase. Biological systems, food processing, ceramic injection, dynamic filtration and air conditioning are examples of areas that such flows arise. Various complicated interparticle interactions and their inevitable influence on and from the continuous phase result in some interesting phenomena which are challenging to justify. This research studies axial instabilities of suspension flow in a partially filled Taylor-Couette setup. Previous observations show that when a monodisperse suspension undergoes a rotational shear motion in a partially filled horizontal Couette cell, particles leave their initial uniform distribution and migrate to regions with lower shear rate. This migration helps formation of ring-shape axial concentrated bands. This study examines the noncolloidal neutrally buoyant suspensions of hard spherical particles with average diameters of 150, 360, 850 micron. Using UCON oil (poly ethylene glycol-ran-glycol) as suspending fluid, monodisperse and polydisperse suspensions in partially filled Stokesian Couette-Taylor flow were studied. The results show strong dependence of band number and profile on suspension concentration and filling level. Moreover interesting phenomena in polydisperse suspensions such as different band shape and weak dependence of band formation time on size of constituents were observed.Copyright