Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

Effects of couple stresses on the blood flow through an artery with mild stenosis

An analysis of the effects of couple stresses on the blood flow through thin artery in the presence of very mild stenosis has been carried out with the help of two nondimensional parameters, alpha (the length ratio parameter) and eta (the parameter characterizing the antisymmetric property of the couple stress tensor). It is shown that an increase in the couple stress (small value of alpha and eta), increases the resistance to the flow and the wall shear stress. These characteristics are further enhanced by the presence of the stenosis.     

Numerical schemes for unsteady fluid flow through collapsible tubes

The study of fluid flow through compliant tubes is a fluid-structure type problem, in which a dynamic equilibrium is maintained between the fluid and the tube wall. The analogy between this flow and gas dynamics initiated the use of a number of numerical methods which were originally developed to solve compressible flow in rigid ducts. In this study we investigate the solutions obtained by applying the Lax-Wendroff and MacCormack schemes to one-dimensional incompressible flow through a straight collapsible tube. The time-evolving numerical results were compared with exact steady-state solutions. For boundary conditions which were held fixed after a prescribed rise time, the unsteady numerical solution converges to the exact steady-state solution with very good accuracy. The stability and accuracy of all the methods depend on the amount of viscous pressure loss dictated by wall friction. Flows with undamped oscillations cannot, however, be solved with these techniques.     

A note on "effects of couple stresses on the blood flow through an artery with mild stenosis"

Some errors have been observed in the analytical expression for the resistance to flow (lambda R), and in the computation of shear stress distribution (tau R) in the analysis of Prawal Sinha and Chandan Singh (1). These errors have been rectified in the present analysis. Also, better values have been suggested for the couple stress parameter alpha for getting better results for lambda R and tau R.     

Effect of non-well-mixed compartment and bulk flow on diffusion through a pore

The assumptions of well-mixed and zero bulk flow in compartmental analysis are reexamined. Using Poiseuille flow inside and radial flow outside a pore, the mass-transfer equations are solved by perturbations on simple diffusion. Formulas are obtained for solute distribution, total mass transfer, and apparent permeability. The effects of non-well mixing and bulk flow are discussed.     

Prediction of fluid forces acting on a hand model in unsteady flow conditions

The aim of this study was to develop a method to predict fluid forces acting on the human hand in unsteady flow swimming conditions. A mechanical system consisting of a pulley and chain mechanism and load cell was constructed to rotate a hand model in fluid flows. To measure the angular displacement of the hand model a potentiometer was attached to the axis of the rotation. The hand model was then fixed at various angles about the longitudinal axis of the hand model and rotated at different flow velocities in a swimming flume for 258 different trials to approximate a swimmer's stroke in unsteady flow conditions. Pressures were taken from 12 transducers embedded in the hand model at a sampling frequency of 200Hz. The resultant fluid force acting on the hand model was then determined on the basis of the kinetic and kinematic data taken from the mechanical system at the frequency of 200Hz. A stepwise regression analysis was applied to acquire higher order polynomial equations that predict the fluid force acting on the accelerating hand model from the 12 pressure values. The root mean square (RMS) difference between the resultant fluid force measured and that predicted from the single best-fit polynomial equation across all trials was 5N. The method developed in the present study accurately predicted the fluid forces acting on the hand model.     

Steady flow of couple stress fluid through tubes of slowly varying cross-sections--application to blood flows

Steady laminar flow of a non-Newtonian fluid based on couple stress fluid theory, through narrow tubes of varying cross-sections has been studied theoretically. Asymptotic solutions are obtained for the basic equations and the expressions for the velocity field and the wall shear stress are derived for a general cross-section. Computation and discussions are carried out for the geometries which occur in the context of physiological flows or in particular blood flows. The tapered tubes and constricted tubes are of special importance. It is observed that increase in certain parameters results in erratic flow behaviour proximal to the constricted areas which is further enhanced by the increase in the geometric parameters. This elucidates the implications of the flow in the development of vascular lesions.     

Flow of couple stress fluid through stenotic blood vessels

The effects of an axially symmetric mild stenosis on the flow of blood, when blood is represented by a couple stress fluid model, have been studied. It is found that, for a fixed stenosis size, the resistance to flow and wall shear stress increase as the couple stress parameter eta decreases from unity. A comparison of the results with those of the Newtonian case shows that the magnitude of resistance to flow and wall shear under a given set of conditions, is greater in the case of the couple stress fluid model. It is seen that even in the case of a mild stenosis (19% area reduction), resistance to flow and wall shear values are increased over those for no stenosis by 60% and 62%, respectively, when compared with the case of a Newtonian fluid.     

Effect of convective flow on the oxygen tension profile in the cornea

The effect of convective flow on the distribution of a diffusing substance that is being consumed is analyzed. For the mammalian cornea, one of the few tissues where convection, diffusion and consumption simultaneously exist, the effect of convection on the distribution of oxygen is shown to be small.     

Cilia-assisted flow of viscoelastic fluid in a divergent channel under porosity effects

Biomechanics and Modeling in Mechanobiology - Cilia-driven laminar flow of an incompressible viscoelastic fluid in a divergent channel has been conducted numerically using the BVP4C technique. The...     

Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis

The laminar steady flow of non-Newtonian fluid (biviscosity fluid) through an axisymmetric stenosis is calculated using the finite element methods. The flow pattern, the separation and reattachment points, and the distributions of pressure and shear stress at the wall are obtained. Then, the axial force acting on the stenosis is evaluated. It is suggested by the authors that this force can become one of the causes of post-stenotic dilatation. Calculated results show that the non-Newtonian property of blood weakens the distortion of flow pattern, pressure and shear stress at the wall associated with the stenosis and that the non-Newtonian property of blood decreases the axial force acting on the stenosis.     

An analysis of turbulent shear stresses in leakage flow through a bileaflet mechanical prostheses

In this work, estimates of turbulence were made from pulsatile flow laser Doppler velocimetry measurements using traditional phase averaging and averaging after the removal of cyclic variation. These estimates were compared with estimates obtained from steady leakage flow LDV measurements and an analytical method. The results of these studies indicate that leakage jets which are free and planar in shape may be more unstable than other leakage jets, and that cyclic variation does not cause a gross overestimation of the Reynolds stresses at large distances from the leakage jet orifice.     

Numerical characterization of diffusion-based extraction in cell-laden flow through a microfluidic channel

Cells are routinely cryopreserved in dimethyl sulfoxide (DMSO), a cryoprotective agent, for medical applications. Infusion of a DMSO-laden cell suspension results in adverse patient reactions, but current DMSO extraction processes result in significant cell losses. A diffusion-based numerical model was employed to characterize DMSO extraction in fully developed channel flow containing a wash stream flowing parallel to a DMSO-laden cell suspension. DMSO was allowed to diffuse across cell membranes as well as across the channel depth. A variety of cases were considered with the ultimate goal of characterizing the optimal geometry and flow conditions to process clinical volumes of cell suspension in a reasonable time (2-3 ml/min). The results were dependent on four dimensionless parameters: depth fraction of the DMSO-laden stream, Peclet number, cell volume fraction in the DMSO-laden stream, and cell membrane permeability parameter. Smaller depth fractions led to faster DMSO extraction but channel widths that were not practical. Higher Peclet numbers led to longer channels but smaller widths. For the Peclet values and channel depths considered (>or=500 microm) and appropriate permeability values, diffusion across cell membranes was significantly faster than diffusion across the channel depth. Cell volume fraction influenced the cross-stream diffusion of DMSO by limiting the fluid volume fraction available in the contaminant stream but did not play a significant role in channel geometry or operating requirements. The model was validated against preliminary experiments in which DMSO was extracted from suspensions of B-lymphoblast cells. The model results suggest that a channel device with practical dimensions can remove a sufficient level of contaminant within a mesoscale volume of cells in the required time.     

Fluid particle diffusion through high-hematocrit blood flow within a capillary tube

Fluid particle diffusion through blood flow within a capillary tube is an important phenomenon to understand, especially for studies in mass transport in the microcirculation as well as in solving technical issues involved in mixing in biomedical microdevices. In this paper, the spreading of tracer particles through up to 20% hematocrit blood, flowing in a capillary tube, was studied using a confocal micro-PTV system. We tracked hundreds of particles in high-hematocrit blood and measured the radial dispersion coefficient. Results yielded significant enhancement of the particle diffusion, due to a micron-scale flow-field generated by red blood cell motions. By increasing the flow rate, the particle dispersion increased almost linearly under constant hematocrit levels. The particle dispersion also showed near linear dependency on hematocrit up to 20%. A scaling analysis of the results, on the assumption that the tracer trajectories were unbiased random walks, was shown to capture the main features of the results. The dispersion of tracer particles was about 0.7 times that of RBCs. These findings provide good insight into transport phenomena in the microcirculation and in biomedical microdevices.     

Ion permeation in a K+ channel inChara australis: Direct evidence for diffusion limitation of ion flow in a maxi-K channel

Summary We report a study of a potassium-selective channel in the membrane delineating cytoplasmic drops fromChara australis. The relatively large conductance (170 pS in 150 mol/m³ (mm) KCl), high ion selectivity (P _Cl/P _K=0.015±0.01) and voltagedependent kinetics of this channel indicate that it is a type of maxi-K channel commonly found in animal cells but not previously detected in any plant cell.The current-voltage (I/V) characteristic of these channels was examined in drop-attached and in excised outside-out patches using the patch-clamp technique, over the unusually large voltage range of –250 to 200 mV. TheI/V characteristic is nonlinear and shows saturation at extreme voltages; the current also saturates at high [K⁺]. In solutions with symmetrical KCl concentrations the saturation behavior of the current is asymmetrical. The permeability of the channel depends on whether it is observed in excised or in drop-attached membrane patches.Here we investigate the main factors affecting the permeation of K⁺ ions through this maxi-K channel. We present the first direct evidence for the importance of diffusion external to the pore in limiting ion flow through maxi-K channels. The data are consistent with an ion translocation mechanism whose current is limited (i) at high voltages by ion diffusion external to the pore and (ii) at high [K⁺] by the maximum transport rate of the channel. We fit the data to a diffusion-limited pore model in which the pore exhibits saturation described by Michaelis-Menten kinetics with aK _m=50±25 mol/m³ andG _max=300±20 pS.     

Numerical solution of unsteady blood flow through an indented tube with atherosclerosis

The unsteady blood flow through an indented tube with atherosclerosis in the presence of mild stenosis has been studied numerically by finite difference method. The effects of hematocrit, frequency parameter, height of stenosis, parameter determining the shape of the constriction on velocity field, volumetric flow rate, pressure gradient of the fluid in stenotic region and wall shear stress at the surface of stenosis are obtained and shown graphically.     

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.