On the Role of the Interface Mechanical Interaction in a Gravity-Driven Shear Flow of an Ice-Till Mixture

The ice-till mixtures at the base of glaciers and ice sheets play a very important role in the movement of the glaciers and ice sheets. This mixture is modelled as an isothermal flow which is overlain by a layer of pure ice. In this model, ice is treated as usual as a very viscous fluid with a constant true density, while till, which is assumed to consist of sediment and bound (that is, moving with the sediment) interstitial water and/or ice, is also assumed in a first approximation to behave such as a fluid. For an isothermal flow below the melting point the water component can be neglected. Therefore, only the mass and momentum balances for till and ice are needed. To complete the model, no-slip and stress-free boundary conditions are assumed at the base and free-surface, respectively. The transition from the till-ice mixture layer to the overlying pure ice layer is idealized in the model as a moving interface representing in the simplest case the till material boundary, at which jump balance relations for till and ice apply. The mechanical interactions are considered in the mixture basel layer, as well as at the interface via the surface production. The interface mechanical interaction is supposed to be only a function of the volume fraction jump across the interface. In the context of the thin-layer approximation, numerical solutions of the lowest-order form of the model show a till distribution which is reminiscent to the ice-till layer in geophysical environment.     

基于微流体装置的微血管网内红细胞流动和分布特性的研究

实体肿瘤血管具有扩张、扭曲、不规则分支以及分支间连接絮乱等特征. 为了考察这些特征对血液流动的影响,将肿瘤血管简化为垂直相互贯通的微血管网,借助微流体实验装置,以一定浓度的红细胞悬液作为流动介质,研究红细胞在微血管网中的流动和分布特性. 具体实验方案如下:首先,采用软刻蚀技术,在聚二甲基硅氧烷（polydimethylsiloxane, PDMS）上加工出微血管网;然后,采用微注射泵控制微血管网入口处的红细胞悬液流量,使用倒置显微镜和高速摄影系统观察并记录实验过程;最后,通过Matlab 软件包Piv-lab 及高速摄影配套软件对获得的视频图像进行处理,提取红细胞在微血管网中的流动和分布数据. 数据处理结果显示,红细胞在微血管网中的流动和分布特性受悬液内的红细胞压积（hematocit, Hct）的影响. 红细胞随悬液Hct 的不同呈现2 种运动轨迹:一种为仅沿着轴向微管道流动;另一种是从轴向微管道流入并穿过径向微管道,再进入另一侧的轴向微管道. 另外,入口流量相同时,红细胞在微血管网中的流动速度随Hct 变化呈现不同,Hct 为3% 和5% 的红细胞速度要明显高于Hct 为1% 的红细胞速度.      

基于微流体装置的微血管网内红细胞流动和分布特性的研究简

实体肿瘤血管具有扩张、扭曲、不规则分支以及分支间连接絮乱等特征. 为了考察这些特征对血液流动的影响,将肿瘤血管简化为垂直相互贯通的微血管网,借助微流体实验装置,以一定浓度的红细胞悬液作为流动介质,研究红细胞在微血管网中的流动和分布特性. 具体实验方案如下：首先,采用软刻蚀技术,在聚二甲基硅氧烷（polydimethylsiloxane, PDMS）上加工出微血管网;然后,采用微注射泵控制微血管网入口处的红细胞悬液流量,使用倒置显微镜和高速摄影系统观察并记录实验过程;最后,通过Matlab 软件包Piv-lab 及高速摄影配套软件对获得的视频图像进行处理,提取红细胞在微血管网中的流动和分布数据. 数据处理结果显示,红细胞在微血管网中的流动和分布特性受悬液内的红细胞压积（hematocit, Hct）的影响. 红细胞随悬液Hct 的不同呈现2 种运动轨迹：一种为仅沿着轴向微管道流动;另一种是从轴向微管道流入并穿过径向微管道,再进入另一侧的轴向微管道. 另外,入口流量相同时,红细胞在微血管网中的流动速度随Hct 变化呈现不同,Hct 为3% 和5% 的红细胞速度要明显高于Hct 为1% 的红细胞速度.     

Flow of non-newtonian particulate suspension with a compressible particle phase

Continuum equations for a two-phase fluid-particle flow are developed and applied to the problem of steady, laminar flow over an infinite porous flat plate. Both phases are assumed to behave as non-Newtonian power-law fluids. The effects of particle-particle interaction and diffusion of particles are taken into account in the mathematical model. In addition, the particle phase is assumed to have a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate boundary conditions using an iterative, implicit finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to elucidate interesting features of the solutions.     

The rheologic properties of erythrocytes: a study using an automated rheoscope

Red blood cells (RBCs) suspended in a high-viscosity medium were filmed while flowing through a microchannel using an automated rheoscope. Under these conditions, erythrocytes take different orientations and undergo varying deformation according to their location in the velocity profile. Measurements of the mean deformation at several distances from the center of the microchannel at a constant flow rate were acquired for normal and thalassemia erythrocytes. The measurements demonstrate how diagnosis can be made based on a single flow rate in contrast to conventional methods where shear is mechanically controlled. The spatial distribution and velocity of RBCs and rigid microspheres (1 μm) were measured. The maximum slip velocity was found to be linearly correlated to the flow rate for both cells and microspheres. RBCs showed enhanced inward lateral migration compared to the rigid spheres, which is attributed to RBC deformation. The results demonstrate the coupling between RBC mechanical properties and their motion in microvessels. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27-29, 2006.     

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.     

Cellular-level near-wall unsteadiness of high-hematocrit erythrocyte flow using confocal μPIV

In hemodynamics, the inherent intermittency of two-phase cellular-level flow has received little attention. Unsteadiness is reported and quantified for the first time in the literature using a combination of fluorescent dye labeling, time-resolved scanning confocal microscopy, and micro-particle image velocimetry (μPIV). The near-wall red blood cell (RBC) motion of physiologic high-hematocrit blood in a rectangular microchannel was investigated under pressure-driven flow. Intermittent flow was associated with (1) the stretching of RBCs as they passed through RBC clusters with twisting motions; (2) external flow through local obstacles; and (3) transitionary rouleaux formations. Velocity profiles are presented for these cases. Unsteady flow clustered in local regions. Extra-cellular fluid flow generated by individual RBCs was examined using submicron fluorescent microspheres. The capabilities of confocal μPIV post-processing were verified using synthetic raw PIV data for validation. Cellular interactions and oscillating velocity profiles are presented, and 3D data are made available for computational model validation.     

Unsteady flow of a dusty Bingham fluid through a porous medium in a circular pipe

A time-varying flow through a porous medium of a dusty viscous incompressible Bingham fluid in a circular pipe is studied. A constant pressure gradient is applied in the axial direction, whereas the particle phase is assumed to behave as a viscous fluid. The effect of the medium porosity, the non-Newtonian fluid characteristics, and the particle phase viscosity on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is investigated. A numerical solution is obtained for the governing nonlinear momentum equations by using the method of finite differences.     

Transient rheology in a new type of couette apparatus. Application to blood

By using our new air-bearing viscometer different types of transient flow can be studied; in the present work this viscometer was specifically applied to non-Newtonian blood suspensions. To observe the influence of both the aggregation and the deformation of red blood cells (RBCs), different concentrations of fibrinogen and dextran were used: the suspended RBCs were simply washed or rigidified with diamide. From the data three rheological parameters were determined, two of which are relative to the behavior at low and at high shear gradients, respectively. Their values were related to the theory of Taylor, and the internal viscosity of RBCs was estimated to be around 3 cp.     

Transient non-Newtonian flow of a suspension with a compressible particle phase

Equations governing transient two-phase fluid-particle laminar flow over an infinite porous flat plate are developed. Both phases are assumed to behave as non-Newtonian power-law fluids. The mathematical model accounts for particle-phase viscous and diffusive effects. The particles are assumed spherical in shape and having a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate initial and boundary conditions using an iterative, implicit, tri-diagonal finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to illustrate special trends of the solutions.     

Electrical classification of single red blood cell deformability in high-shear microchannel flows

A sensor that can efficiently and sequentially measure the deformability of individual red blood cell (RBC) flowing along a microchannel is described. Counter-electrode-type microsensors are attached to the channel bottom wall, and as RBCs pass between the electrodes, the time series of the electric resistance is measured. An RBC is deformed by the high shear flow to a degree dependent upon its elastic modulus. Hence, the profile of the resistance, which is unique to the shape of the RBC, can be analyzed to obtain the deformability of each cell. First, theoretical and experimental analyses were conducted to identify the specific AC frequency at which the effect of the electric double layer formed on the electrode surface is minimized. Measurements were then conducted upon samples of normal human RBCs and glutaraldehyde-treated (rigidified) RBCs to evaluate the feasibility of the present method. In addition, simultaneous visualization of RBC deformation was performed using a high-speed camera. Normal RBCs were observed to have a degree of deformation index (DI) of around 0.57, whereas the rigidified RBCs was DI = 0 in the microchannel. The experimental measurements showed a strong correlation between the half-width of the maximum of the resistance distribution and the DI of the RBC.     

A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for unsteady, one-dimensional self-similar flow behind a strong shock wave, driven by a moving piston, in a dusty gas. The dusty gas is assumed to consist of a mixture of small solid particles and a non-ideal gas, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. Solutions are obtained under both the isothermal and adiabatic conditions of the flow-field. The spherical case is worked out in detail to investigate to what extent the flow-field behind the shock is influenced by the non-idealness of the gas in the mixture as well as by the mass concentration of the solid particles, by the ratio of density of the solid particles to the initial density of the mixture and by the energy input due to moving piston. A comparison is also made between isothermal and adiabatic cases.     

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.     

A lattice Boltzmann fictitious domain method for modeling red blood cell deformation and multiple‐cell hydrodynamic interactions in flow

To model red blood cell (RBC) deformation and multiple‐cell interactions in flow, the recently developed technique derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain method is extended to employ the mesoscopic network model for simulations of RBCs in flow. The flow is simulated by the lattice Boltzmann method with an external force, while the network model is used for modeling RBC deformation. The fluid–RBC interactions are enforced by the Lagrange multiplier. To validate parameters of the RBC network model, stretching tests on both coarse and fine meshes are performed and compared with the corresponding experimental data. Furthermore, RBC deformation in pipe and shear flows is simulated, revealing the capacity of the current method for modeling RBC deformation in various flows. Moreover, hydrodynamic interactions between two RBCs are studied in pipe flow. Numerical results illustrate that the leading cell always has a larger flow velocity and deformation, while the following cells move slower and deform less.Copyright © 2013 John Wiley & Sons, Ltd.     

ENERGY AND MASS TRANSPORT PROCESSES IN THE GRANULAR BED OF AN INDIRECTLY HEATED ROTARY KILN

The transport mechanisms of momentum,mass,species,and energy are invertigated in detail for the ro-tary kiln process.The residence time prediction of the granular bed is well improved by considerng differet flow patterns in the drum.Introducing a mixed flow pattern of the basic slipping and slumping behaviour has the most important effect on the improvement of the residence time prediction.The granular bed is assumed to hehave as a Bingham fluid in the active layer of the bed.The transport mechanisms of momentum,species,and energy are modelled on the basis of this assumption and using the kinetic gas theory.Additionally,a mathematical transformation is presented to save comput a-tional time.The model results of the temperature field are in very good agreement with experimental data.     

A two-fluid model of non-Newtonian blood flow induced by peristaltic waves

The problem of blood flow induced by peristaltic waves in a uniform small diameter tube has been investigated. Blood has been represented by a two-fluid model consisting of a core region of suspension of all the erythrocytes, assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. The expressions for dimensionless pressure drop and friction force have been obtained. The results obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories both analytically and numerically.     

Study on the packed volume and the void ratio of idealized human red blood cells using a ?nite-discrete element method

Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Self-similar solution of cylindrical shock wave propagation in a rotational axisymmetric mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has a variable azimuthal fluid velocity together with a variable axial fluid velocity. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. The shock Mach number is not infinite, but has a finite value. The azimuthal and axial component of the fluid velocity in the ambient medium are assumed to be vary and obey power laws, and the density of the ambient medium is taken to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of the variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of the density of solid particles to the initial density of the gas are investigated.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.