Theory for flow of Casson and Herschel-Bulkley fluids in cone-plate viscometers

Mathematical models for blood flow in cone-plate viscometer have been considered, by assuming blood as a Casson/Herschel-Bulkley fluid. Three different cases have been analyzed (i) when there is no shearing, (ii) partial shearing and (iii) full shearing. The relationships between the angular velocity and torque have been obtained for the above three cases. By assuming total shearing, the analytical expression for apparent viscosity has been obtained. Variation of apparent viscosity with yield stress, angular velocity, Casson co-efficient of viscosity, consistency index and flow behaviour index has been computed. It is observed that as the angular velocity increases, the apparent viscosity decreases for both fluids. Further, it is found that as the cone angle increases, the apparent viscosity increases. This behaviour of apparent viscosity in cone-plate viscometer is interesting and unexpected and is being reported first time.     

Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

Entry flow in a circular tube of aortic arch dimensions

Steady flow within a uniform circular curved tube formed by two 90-deg elbows was studied as a function of psi, the angle between the planes of curvature of the two elbows. Boundary layer separation was found at two locations. The sites of these separation zones were observed to be essentially independent of psi while the Reynolds number at which separation was first detected was found to decrease as psi increased. The relation between separation and the pathogenesis of atherosclerosis is discussed. Secondary flow pattern was found to depend on psi and in some instances on Reynolds number as well.     

One-dimensional steady inviscid flow through a stenotic collapsible tube

A one-dimensional inviscid solution for flow through a compliant tube with a stenosis is presented. The model is used to represent an artery with an atherosclerotic plaque and to investigate a range of conditions for which arterial collapse may occur. The coupled equations for flow through collapsible tubes are solved using a Runge-Kutta finite difference scheme. Quantitative results are given for specific physiological parameters including inlet and outlet pressure, flow rate, stenosis size, length and stiffness. The results suggest that high-grade stenotic arteries may exhibit collapse with typical physiological pressures. Critical stenoses may cause choking of flow at the throat followed by a transition to supercritical flow with tube collapse downstream. Greater amounts of stenosis produced a linear reduction of flow rate and a shortening of the collapsed region. Changes in stenosis length created proportional changes in the length of collapse. Increasing the stiffness of the stenosis to a value greater than the nominal tube stiffness caused a greater amount of flow limitation and more negative pressures, compared to a stenosis with constant stiffness. These findings assist in understanding the clinical consequences of flow through atherosclerotic arteries.     

A model for blood flow through a stenotic tube

This article deals with the introduction of the modified Casson's fluid model as the true representation for the blood for the steady laminar flow through a small diameter artery with axi-symmetric identical double stenoses in series. The governing equations are solved by using the finite element method. The results for the velocity profiles, the pressure and the wall shear stress distributions in addition to the location and length of the flow reversal zones have been brought out and discussed in reference to the severity of the disease. It has been observed that the non-Newtonian nature of the blood helps in reducing the magnitude of the peak wall shear stress at the throat and the length of the reversed flow regions in the post stenotic dilatation.     

Properties and principles of mycelial flow: a tube rheometer system for fermentation fluids

A tube rheometer system has been constructed for aseptic study of the rheology and fundamental flow properties of mycelial fermentation fluids. The rheometer consists of a U-formed tube circuit starting and ending inside the fermentor. The mash is pumped through the tubes with a lobe rotor pump. The flow is measured by an electromagnetic flow meter. Pressure drops have been measured with a system of differential membrane transducers for different flow rates. The rheometer system was tested with Newtonian and non-Newtonian fluids.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

The effects of polar nature of blood and pulsatility on flow through a stenosed tube have been analysed by assuming blood as a micropolar fluid. Linearized solutions of basic equations are obtained through consecutive applications of finite Hankel and Laplace transforms. The analytical expressions for axial and particle angular velocities, wall shear stress, resistance to flow and apparent viscosity have been obtained. The axial velocity profiles for Newtonian and micropolar fluids have been compared. The interesting observation of this analysis is velocity, in certain parts of cycle, for micropolar fluid is higher than Newtonain fluid. Variation of apparent viscosity eta a with tube radius shows both inverse Fahraeus-Lindqvist and Fahraeus-Lindqvist effects. Finally, the resistance to flow and wall shear stress for normal and diseased blood have been computed and compared.     

The role of the Womersley number in pulsatile blood flow a theoretical study of the Casson model.

The purpose of this Note is to clarify the meaning of the Womersley number alpha in pulsatile blood flow in small vessels. In particular. we explain why the use of alpha as aperturbation parameter to obtain approximate solutions of the Casson model (frequently used in the literature) is not appropriate. Using the techniques of dimensional analysis and scaling, we show that alpha is the product of the Reynolds and Strouhal numbers. Since the latter is very small for physiological flows, the result is that alpha < 1 even at relatively high values of the Reynolds number (i.e., for non-negligible inertia) and we validate our perturbation theory results by comparison with a numerical integration of the full model. Although this analysis is based on the Casson model, our method has general validity and may be applied to other models which describe more accurately the rheological properties of blood.     

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.     

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.