جستجوی مقالات مرتبط با کلیدواژه « womersley number » در نشریات گروه « مکانیک »

Murray’s law, as the best-known optimal relationship between bifurcation calibers, is obtained based on the assumption of steady-state Poiseuille blood flow and is mostly accurate in small vessels. In middle sized and large vessels such as the aorta and coronary arteries, the pulsatile nature of the flow is dominant and deviations from Murray law have been observed. In the present study, a general scaling law is proposed, which describes the optimum relationship between the characteristics of bifurcations and pulsatile flow. This scaling law takes into account the deviations from Murray law in large vessels, and proposes optimal flow (i.e. less flow resistance) for the full range of the vascular system, from the small vessels to large ones such aorta. As a general scaling law, it covers both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is that bifurcation characteristics solely depend on the Womersley number of parent vessels. The diameter ratios suggested by this scaling law are in acceptable agreement with available clinical morphometric data such as those reported for coronary arteries and aortoiliac bifurcations. A numerical simulation of pulsatile flow for several Womersley numbers in bifurcation models according to the proposed scaling law and Murray law has been performed, which suggests that the general scaling law provides less flow resistance and more efficiency than Murray law in pulsatile flow.

In a bifurcation including a mother artery and two daughter arteries, the energy drop is minimum, if, the cube of the radius of the mother artery equals the sum of the cube of the radii of daughter arteries. This is the expression of Murray’s law (or cubic law) assuming the flow is steady. In this paper, an extension of Murray’s law is investigated using the minimum energy hypothesis, totally analytical for pulsating flow. In addition to the two terms that Murray considered in his calculations, there is additional energy to move fluid toward and back in the pulsating flow. This additional energy is calculated and added to two other parts of energy in Murray’s analysis, and then optimized. The relationships for diameters and the angle between daughter arteries are extended. The effect of frequency and Womersley number have appeared as coefficients in the relations. According to the results, the most difference between Murray’s law for both diameters and the angle between daughter arteries, and the relationship derived in the present paper, occurs in Womersley number between 2 and 5. For a special case which in the daughter arteries have the same diameter, the power of diameters varies up from 3 to 3.2. Also, for this special case, there is maximum 6 degrees difference with Murray’s law for the angle between daughter arteries. In short, the obtained relations, assuming pulsating flow, do not yield very different results from Murray's law assuming steady flow.

In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin’s inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-slip and slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-slip and slip boundary conditions using nondimensional numbers. Special attention is paid to the effect of slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series