Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels

The problem of peristaltic transport of a couple stress fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a couple stress fluid (a fluid which its particles size are taken into account, a special case of a non-Newtonian fluid). It is found that the pressure rise decreases as the couple stress fluid parameter gamma increases (i.e., small size fluid particle). So the pressure rise for a couple stress fluid (as a blood model) is greater than that for a Newtonian fluid. Also the pressure rise increases as the amplitude ratio phi increases for different values of gamma. Further, the pressure rise in the case of non-uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the maximum pressure rise when the mean flow rate over one period of the wave, Q = 0, increases as phi increases and gamma decreases.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

A Mathematical Study on Three Layered Oscillatory Blood Flow Through Stenosed Arteries

A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube (stenosed arteries).The proposed model basically consists three layers of blood (viscous fluids with different viscosities) named as core layer (red blood cells),intermediate layer (platelets/white blood cells) and peripheral layer (plasma).The analysis was restricted to propagation of small-amplitude harmonic waves,generated due to blood flow whose wave length is larger compared to the radius of the arterial segment.The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces,average flow rate,mechanical efficiency,trapping and reflux are discussed with the help of numerical and computational results.This model is the generalized form of the preceding models.On the basis of present discussion,it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer,whereas,opposite effect is observed for viscosity of fluid in intermediate layer.Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers,however,the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.     

Effects of aggregation on the flow properties of red blood cell suspensions in narrow vertical tubes

The flow properties of aggregating red cell suspensions flowing at low rates through vertical tubes with diameters from 30 microns to 150 microns are analyzed using a theoretical model. Unidirectional flow is assumed, and the distributions of velocity and red cell concentration are assumed to be axisymmetric. A three-layer approximation is used for the distribution of red cells, with a cylindrical central core of aggregated red cells moving with uniform velocity, a cell-free marginal layer near the tube wall, and an annular region located between the core and the marginal layer containing suspended non-aggregating red cells. This suspension is assumed to behave approximately as a Newtonian fluid whose viscosity increases exponentially with red cell concentration. Physical arguments concerning the mechanics of red cell attachment to, and detachment from the aggregated core lead to a kinetic equation for core formation. From this kinetic equation and the equation for conservation of red cell volume flux, a relationship between core radius and pressure gradient is obtained. Then the relative viscosity is calculated as a function of pseudo-shear rate. At low flow rates, it is shown that the relative viscosity decreases with decreasing flow and that the dependence of relative viscosity on shear rates is more pronounced in larger tubes. It is also found that the relative viscosity decreases with increasing aggregation tendency of suspension. These theoretical predictions are in good qualitative and quantitative agreement with experimental results.     

Geometrical focusing of cells in a microfluidic device: an approach to separate blood plasma

It is well known that when a suspension of cells flows in small vessels (arterioles or venules), there exists a cell-free layer of a few microns adjacent to the vascular walls. Using an in vitro model, we show experimentally that for a fixed flow rate a geometrical constriction in the flow can artificially enhance the cell-free layer. Also, we show that rapid variation of the geometry coupled to the deformability of the cells can dramatically modify their spatial distribution in the channel. The effects of the constriction geometry, flow rate, suspending fluid viscosity, cell concentration, and cell deformability are studied and the results are interpreted in terms of a model of the hydrodynamic drift of an ellipsoidal cell in a shear flow. We propose a microfluidic application of this focusing effect for separation of the red blood cells from the suspending plasma.     

Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis

The effects of peripheral layer viscosity on physiological characteristics of blood flow through the artery with mild stenosis have been studied. It has been shown that the resistance to flow and the wall shear decrease as the peripheral layer viscosity decreases.     

Peristaltic transport of multilayered power-law fluids with distinct viscosities: a mathematical model for intestinal flows

This paper is concerned with the theoretical study of two-dimensional peristaltic flow of power-law fluids in three layers with different viscosities. The analysis is carried out under low Reynolds number and long wavelength approximations. The shapes of the interfaces are described by a system of non-linear algebraic equations which are solved numerically as streamlines. It is found that the non-uniformity in the intermediate and peripheral layers diminishes when the viscosity of the intermediate layer is increased and that of the outermost layer is kept unaltered for both the pseudo-plastic and dilatant fluids. Similar are the observations when the viscosity of the outermost layer is increased and that of the intermediate layer is kept fixed. The flow rate increases with the viscosities of the peripheral and the intermediate layers but the viscosity of the outermost layer is more effective. However, the knowledge of the effect of the viscosity of the intermediate layer facilitates us to achieve the required flow rate without disturbing the outermost layer. An increase in the flow behaviour index too favours larger flow rates. The trapping limits increase with the viscosity of the intermediate layer but decrease with the viscosity of the outermost layer and the flow behaviour index. Thus, a medicinal intervention that creates a more viscous intermediate layer and reduces pseudo plasticity may reduce constipation.     

A semi-empirical model for flow of blood and other particulate suspensions through narrow tubes

A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using pressure drop, flow rate and hematocrit reduction data. It has been found from the available data in the literature that for a given sample of blood the extent of plug flow increases with decreasing tube diameter. Also for a flow through a given tube it increases with hematocrit. The wall layer thickness is found to decrease with increase in blood hematocrit. A comparison between the results of rigid particulate suspensions and blood reveals that the thicker wall layer and smaller plug flow radius in the case of blood may be attributed to the deformability of the erythrocytes.     

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Using a CFD model to understand the fluid dynamics promoting E. coli breakage in a high-pressure homogenizer

A Computational Fluid Dynamic (CFD) model of flow in a high-pressure homogenizing valve (APV Gaulin model 30CD) was developed with the Fluent software. The 2D model consists of an unstructured hexagonal mesh, dense in the regions of high gradients. The flow (single-phase) was modeled as laminar upstream of and in the channel (gap) and turbulent downstream of the channel exit. Applying a realizable kappa-epsilon turbulence model, the CFD model accurately predicted the effect of gap space on fluid dynamic conditions upstream (inlet pressure and pressure gradient) and downstream (impact pressure) of the channel for a valve with a standard (CD-0) impact distance (0.25 mm) and a 1 cP fluid. This CFD model was then used to estimate the magnitude of the fluid dynamic parameters (except cavitation effects) presumed to be responsible for cell breakage, as a function of gap space, impact distance and fluid viscosity. The CFD models predicted that for a given volumetric flowrate the upstream fluid conditions (inlet pressure gradient, maximum channel strain rate) and the maximum energy dissipation rate in the post-gap jet depend only on the gap space and the fluid viscosity and not on the impact distance. The impact pressure however depends on the gap spacing, the fluid viscosity and especially the impact distance. Experimental results indicate that higher inlet pressures are required to break cells, if the impact distance is increased. By conducting experiments to isolate individual cell breakage mechanisms for a single pass, threshold values were identified for breaking Escherichia coli cells: pressure gradient, 1.2 x 10(12) Pa/m; energy dissipation rate, 1.0 x 10(10) m(3)/s(2); and impact pressure, 160 psig. By isolating the wall impact as the sole mechanism responsible for breaking the E. coli cells between 3000 and 6000 psig inlet pressure, a relationship between E. coli cell breakage rate and maximum wall impact pressure was established (eq 5).     

Modelling and simulation of the behaviour of a biofluid in a microchannel biochip separator

This paper reports an investigation into the flow behaviour of a biofluid in a microchannel systems through conceptual analysis and modelling. The application is the design of a microfluidic chip developed for the separation of plasma from blood. The effect of key design features of the microchannels on the flow behaviour of the biofluid is explored. These include geometric features such as the constriction, bending channel, bifurcation and the channel length ratio between the main and side channels. The performance of each design is discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. Particular phenomena such as the Fahraeus and Fahraeus-Lindqvist effects, the Zweifach-Fung bifurcation law and the cell-free layer are discussed. In this paper, the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviour to investigate the effect of the fluid viscosity on both flow and separation efficiency. For a flow rate-controlled Newtonian flow system, it is found that viscosity and outlet pressure have little effect on the velocity distribution through each of the microchannels. For a diluted fluid where the flow in the whole channel system is modelled with a uniform viscosity, less plasma is separated from blood than observed in the non-Newtonian case. This results in an increase in the flow rate ratio between the main and side channels. A comparison of Newtonian and non-Newtonian flows shows that both flows tend to behave identically with an increase in the shear strain rate.     

Peripheral-layer viscosity and microstructural effects on the capillary-tissue fluid exchange

A theoretical investigation of capillary-tissue fluid exchange has been studied including the characteristics and influence of the boundaries and media through which the fluid flows. Filtration from a cylindrical capillary into the concentrically surrounding tissue space and flow from a capillary into the tissue across a thin membrane are analyzed in detail. In has been observed that the filtration efficiency of the functional unit decreases as the viscosity of the peripheral layer increases. Contrary to the results of Apelblat [17], the slip velocity at the porous boundary plays a dominant role in filtration efficiency. It has also been noticed that the filtration efficiency decreases as the slip velocity at the porous boundary increases.     

Computer simulation of arterial flow with applications to arterial and aortic stenoses

A computer model for simulating pressure and flow propagation in the human arterial system is developed. The model is based on the one-dimensional flow equations and includes nonlinearities arising from geometry and material properties. Fifty-five arterial segments, representing the various major arteries, are combined to form the model of the arterial system. Particular attention is paid to the development of peripheral pressure and flow pulses under normal flow conditions and under conditions of arterial and aortic stenoses. Results show that the presence of severe arterial stenoses significantly affects the nature of the distal pressure and flow pulses. Aortic stenoses also have a profound effect on central and peripheral pressure pulse formation. Comparison with the published experimental data suggests that the model is capable of simulating arterial flow under normal flow conditions as well as conditions of stenotic obstructions in a satisfactory manner.     

Modelling and simulation of the behaviour of a biofluid in a microchannel biochip separator

This paper reports an investigation into the flow behaviour of a biofluid in a microchannel systems through conceptual analysis and modelling. The application is the design of a microfluidic chip developed for the separation of plasma from blood. The effect of key design features of the microchannels on the flow behaviour of the biofluid is explored. These include geometric features such as the constriction, bending channel, bifurcation and the channel length ratio between the main and side channels. The performance of each design is discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. Particular phenomena such as the Fahraeus and Fahraeus–Lindqvist effects, the Zweifach–Fung bifurcation law and the cell-free layer are discussed. In this paper, the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviour to investigate the effect of the fluid viscosity on both flow and separation efficiency. For a flow rate-controlled Newtonian flow system, it is found that viscosity and outlet pressure have little effect on the velocity distribution through each of the microchannels. For a diluted fluid where the flow in the whole channel system is modelled with a uniform viscosity, less plasma is separated from blood than observed in the non-Newtonian case. This results in an increase in the flow rate ratio between the main and side channels. A comparison of Newtonian and non-Newtonian flows shows that both flows tend to behave identically with an increase in the shear strain rate.     

Simulation of the effects of mechanical nonhomogeneities on expiratory flow from human lungs

A computational model for expiration from lungs with mechanical nonhomogeneities was used to investigate the effect of such nonhomogeneities on the distribution of expiratory flow and the development of alveolar pressure differences between regions. The nonhomogeneities used were a modest constriction of the peripheral airways and a 50% difference in compliance between regions. The model contains only two mechanically different regions but allows these to be as grossly distributed as left lung-right lung or to be distributed as a set of identical pairs of parallel nonhomogeneous regions with flows from each merging in a specified bronchial generation. The site of flow merging had no effect on the flow-volume curve but had a significant effect on the development of alveolar pressure differences (delta PA). With the peripheral constriction, greater values of delta PA developed when flows were merged peripherally rather than centrally. The opposite was true in the case of a compliance nonhomogeneity. The delta PA values were smaller at submaximal flows. Plots of delta PA vs. lung volume were similar to those obtained experimentally. These results were interpreted in terms of the expression used for the fluid mechanics of the merging flows. delta PA was greater when the viscosity of the expired gas was increased or when its density was reduced. Partial forced expirations were shown to indicate the presence of mechanical nonhomogeneity.     

Distribution of hepatic venous blood in the total cavo pulmonary connection: an in vitro study into the effects of connection geometry.

The total cavo pulmonary connection, or TCPC, is a surgical correction to congenital heart defects. The geometry of this connection has been shown to determine the fluid power loss as well as the distribution of hepatic fluid that enters through the inferior vena cava. In vitro studies were performed to measure the power loss and hepatic fluid distribution in models of the TCPC with four different geometries. It was found that a zero offset straight geometry provided good hepatic fluid distribution but large power loss. A zero offset flared geometry provided low power loss but poor hepatic fluid distribution. The optimal geometry from those tested was found to be the zero offset cowl geometry whereby an enlargement was made on one side of the inferior and superior vena cava. So long as the cowl was directed toward the pulmonary artery of lowest flow rate, low power loss and relatively good distribution of hepatic flow could be obtained.     

Forces and stresses acting on fusion pore membrane during secretion

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.     

Studies on the effects of structure on the behavior of enzyme systems

The effects of structural features on various properties of enzyme systems are studied. Some of the effects are: in a homogeneous reaction, enzyme compartmentalization decreases the rate; in a heterogeneous reaction, compartmentalization increases the rate. The steady-state concentration of intermediates is larger in a non-uniform than in uniform systems. Periodicities do not generally occur in the common kinetic systems; they do occur in autocatalytic systems, but compartmentalization reduces their probability of occurrence. The conditions for overshoot are different for uniform and non-uniform systems. Multiple stable steady states are not a common occurrence among biologically typical reactions; they do occur in combined autocatalytic and surface systems (a mechanism for the gener position effect is suggested by this property). The local pH is affected by the enzyme aggregation as well as by the geometry of the enzyme structure. A 2-step system can give rise to the characteristic rate vs. pH curve, where the optimum is not necessarily at isoelectric point. The expression for the osmotic pressure inside a spherical particle is deduced. The pressure is shown to be dependent on the radius. The rate inside a cell particle is shown to be determined by the shape of the particle.     

The fluid mechanics of bolus ejection from the oral cavity

The squeezing action of the tongue against the palate provides driving forces to propel swallowed material out of the mouth and through the pharynx. Transport in respose to these driving forces, however, is dependent on the material properties of the swallowed bolus. Given the complex geometry of the oral cavity and the unsteady nature of this process, the mechanics governing the oral phase of swallowing are not well understood. In the current work, the squeezing flow between two approaching parallel plates is used as a simplified mathematical model to study the fluid mechanics of bolus ejection from the oral cavity. Driving forces generated by the contraction of intrinsic and extrinsic lingual muscles are modeled as a spatially uniform pressure applied to the tongue. Approximating the tongue as a rigid body, the motion of tongue and fluid are then computed simultaneously as a function of time. Bolus ejection is parameterized by the time taken to clear half the bolus from the oral cavity, t_1/2. We find that t_1/2 increases with increased viscosity and density and decreases with increased applied pressure. In addition, for low viscosity boluses (μapproximately 1000 cP), viscosity dominates. A transition region between these two regimes is found in which both properties affect the solution characteristics. The relationship of these results to the assessment and treatment of swallowing disorders is discussed.