Hydrodynamics Of Viscous Fluids Research Articles

Hydrodynamics of viscous fluid through porous slit with linear absorption

The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.

Investigation of power-type variational principles in liquid-filled system

Starting from the basic equations of hydrodynamics, the maximum powertype variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic-liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liquid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.

Acoustic propagation in viscous fluid with uniform flow and a novel design methodology for ultrasonic flow meter

Ultrasonic flow meter with non-invasive no-moving-parts construction has good prospective application for space on-orbit fluid gauging. In traditional pulse transit time flow meter, inconsistency of ultrasonic transducers leads to measurement error and plane wave theory, bases of transit time flow meter, is valuable only for low-frequency wave propagation in inviscid fluid and will lose feasibility when fluid viscosity is considered. In this paper, based on the hydrodynamics of viscous fluid, wave propagation with uniform flow profile is mathematically formulated and a novel solution for viscous fluid using potential theory is firstly presented. Then a novel design methodology of continuous ultrasonic flow meter is proposed, where high measurement rangeability and accuracy are guaranteed individually by solving the integral ambiguity using multi-tone wide laning strategy and the fractional phase shift using phase lock loop tracking method. A comparison with transit time ultrasonic flow meter shows the advantage of proposed methodology. In the end, parametric analysis of viscosity on wave propagation and ultrasonic flow meter is compressively investigated.

The instability of the front of magnetization reversal in anisotropic superconductors

The mechanism of instability of the front of magnetization reversal, i.e., of the boundary separating the regions of existence of vortices with mutually opposite orientations of the magnetic flux (vortex and anti-vortex regions) in type II superconductors, is suggested. The instability is associated with the anisotropy of flow of a vortex fluid, caused by planar defects in the ab plane of high-temperature superconducting single crystals of the 1-2-3 system. The anisotropy of the dynamic properties of vortex matter brings about a jump of the tangential component of the vortex velocity at the front of magnetization reversal; as is known from the classical hydrodynamics of viscous fluids, this leads to the turbulization of flow. It is demonstrated that the hydrodynamic approach to the description of vortex flow helps explain the emergence of a positive increment of the rise of vortex density fluctuations under conditions of a fairly strong anisotropy. The results of magnetooptical investigations of macroturbulence in the vortex system of Y-123 single crystal with a high density of the twinning boundaries lend qualitative support to the theoretical inferences.

Anwendungen von Tensorfunktionen in der Kontinuumsmechanik anisotroper Materialien

During the last three decades much effort has been devoted to the elaboration of phenomenological theories describing the relation between force and deformation in bodies of materials which do not obey either the linear laws of the classical theories of elasticity or the hydrodynamics of viscous fluids. Such problems will play a central role for mathematicians, physicists, and engineers also in the future [1]. - Material laws and constitutive theories are the fundamental bases for describing the mechanical behaviour of materials under multi-axial states of stress involving actual boundary conditions. In solving such complex problems, the tensor function theory has become a powerful tool. This paper will provide a short survey of some recent advances in the mathematical modelling of materials behaviour including anisotropy and damage. The mechanical behaviour of anisotropic solids (materials with orientated internal structures, produced by forming processes and manufacturing procedures, or induced by permanent deformation) requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour, This paper presents certain principles, methods, and recent successful applications of tensor functions in solid mechanics. The rules of specifying irreducible sets of tensor invariants, and tensor generators of material tensors of rank two and four are also discussed. Furthermore, it is very important to determine the scalar coefficients in constitutive and evolutional equations as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determinded by using tensorial interpolation methods. Some examples for practical use are discussed. Finally, we have carried out our own experiments in order to examine the validity of the mathematical modelling. - Like applications in solid mechanics, tensor functions also play a significant role in mathematical modelling in fluid mechanics. This paper, however, is restricted to the mechanical behaviour of solids.

On the inverse problem in calculus of variations

The inverse problem in calculus of variations is studied. By introducing a new concept called Variational Integral, a new method to systematically study the inverse problem in calculus of variations is given. Using this new method to the elastodynamics and hydrodynamics of viscous fluids, some kinds of variational principles and generalized variational principles are obtained respectively.

A note on the hydrodynamics of viscous fluids

The cross-product of the velocity and the vorticity in a viscous incompressible fluid is formulated and its properties investigated. When the cross-product is identically null, either the flow is vortex-free, or the velocity and the vorticity are parallel to each other. The second case yields the following important result for three-dimensional flows: if the velocity and the vorticity are related by a position-independent scalar function, that function must be time-independent as well. (English translation of the seventy-five-years old Czech text — Trkal V.: Casopis pro pěstovani mathematiky a fysiky48 (1919) 302–311.)

Variational principles and generalized variational principles in hydrodynamics of viscous fluids

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.

Some flow properties of concentrated high-polymer solutions

A review is given of a theoretical investigation of the flow properties of fluids in which .the assumptions underlying the classical hydrodynamics of viscous fluids no longer holds. For an incompressible visco-inelastic fluid—or visco-elastic fluid in steady-state laminar flow— the stress-strain-velocity relations involve two physical parameters which may or may not depend on the state of flow. One of these is the viscosity and the other the normal stress coefficient. On a simple model of a concentrated high-polymer solution, it is shown that the normal stress coefficient may have an appreciable value. Finally, the manner in which the basic assumptions of the theory may be inapplicable to real concentrated high-poyimer solutions is discussed.