Biomedical subjects

K N Mehta

Publications and source records attributed to K N Mehta.

9 recordsLinked to original sources

PubMed2000

Shear augmented dispersion of a solute in a casson fluid flowing in a conduit.

The unsteady dispersion of a solute in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model of Gill and Sankarasubramanian. With this approach, the entire dispersion process is described appropriately in terms of a simple diffusion process with the effective diffusion coefficient as a function of time, in addition to its dependence on the yield stress of the fluid. The results are accurate up to a first approximation for small times, but verified with Sharp to be exact for large times. The model brings out mainly the effect of yield stress, or equivalently, the plug flow region on the overall dispersion process. It is found that the rate of dispersion is reduced (i.e., the effective diffusivity decreases) due to the yield stress of the fluid, or equivalently, the plug flow region in the conduit. Also, the effective diffusivity increases with time, but eventually attains its steady state value below a critical time [0.48(a2/Dm) for dispersion in a pipe and 0.55(a2/Dm) for dispersion in a channel-the critical transient time for a Newtonian fluid-where "a" is the radius of the pipe and Dm is the molecular diffusivity]. At steady state, for dispersion in a pipe with the plug flow radius one tenth of the radius of the pipe, the effective diffusivity is reduced to about 0.78 times of the corresponding value for a Newtonian fluid at equivalent flow rates; for dispersion in a channel, the reduction factor is about 0.73 confirming the earlier result of Sharp. Further, the location of the center of mass of a passive species over a cross section is found to remain unperturbed during the course of dispersion and for different values of the plug flow parameter (i.e., the yield stress of the fluid). The study can be used as a starting first approximate solution for studying the dispersion in the cardiovascular system or blood oxygenators.

Biomechanical Phenomena↗

PubMed1999

Flow in a catheterized curved artery with stenosis.

The fluid mechanics of blood flow in a catheterized curved artery with stenosis is studied through a mathematical analysis. Blood is modelled as an incompressible Newtonian fluid and the flow is assumed to be steady and laminar. An approximate analytic solution to the problem is obtained through a double series perturbation analysis for the case of small curvature and mild stenosis. The effect of catheterization on various physiologically important flow characteristics (i.e. the pressure drop, impedance and the wall shear stress) is studied for different values of the catheter size and Reynolds number of the flow. It is found that all these flow characteristics vary markedly across a stenotic lesion. Also, increase in the catheter size leads to a considerable increase in their magnitudes. These results are used to obtain the estimates of increased pressure drop across an arterial stenosis when a catheter is inserted into it. Our calculations, based on the geometry and flow conditions existing in coronary arteries, suggest that, in the presence of curvature and stenosis, and depending on the value of k (ratio of catheter size to vessel size) ranging from 0.1 to 0.4, the pressure drop increases by a factor ranging from 1.60 to 5.16. But, in the absence of curvature and stenosis, with the same range of catheter size, this increased factor is about 1.74-4.89. These estimates for the increased pressure drop can be used to correct the error involved in the measured pressure gradients using catheters. The combined effects of stenosis and curvature on flow characteristics are also studied in detail. It is found that the effect of stenosis is more dominant than that of the curvature. Due to the combined effect of stenosis, curvature and catheterization, the secondary streamlines are modified in a cross-sectional plane. The insertion of a catheter into the artery leads to the formation of increased number of secondary vortices.

Arteries↗

PubMed1996

Estimation of increased flow resistance in a narrow catheterized artery--a theoretical model.

The changed flow pattern in a narrow catheterized artery is studied and an estimate of the increased flow resistance is made. The anomalous behaviour of blood in small blood vessels has been taken into account by modelling blood as a Casson fluid possessing some finite yield stress. Both the cases of steady and pulsatile flow situations are studied. The pulsatile flow is analysed by considering the pressure gradient as a periodic function of time with small inertial effects. The resulting quasi-steady non-linear coupled implicit system of differential equations governing the flow are solved using a perturbation analysis, where it is assumed that the Womersley frequently parameter is small (alpha < 1) which is reasonable for physiological situations in small blood vessels as well as in coronary arteries. The effect of pulsatility, catheter radius and yield stress of the fluid on the yield plane locations, velocity distribution, flow rate, shear stress and frictional resistance are investigated. Because of the yield stress theta, two yield surfaces are found to be located in the flow field. Depending on the ration kappa (catheter size/vessel size) ranging from 0.3 to 0.7 (which is widely used in coronary angioplasty procedures), the frictional resistance to flow in large blood vessels, where the effect of yield stress can be neglected (i.e. theta = 0), increases by a factory ranging from 3 to 33. In small blood vessels with the same range of catheter size and an unit pressure gradient, frictional resistance increase was by a factor of 7-21 when theta = 0.05 and 11-294 when theta = 0.1. For small values of kappa and theta, the frictional resistance increased to several hundred times thus implying that the combined effect of increased catheter radius and yield stress is to obstruct the fluid movement considerably.

Animals↗

PubMed1969