Effect of Varying Viscosity on Two-Layer Model of Pulsatile Flow through Blood Vessels with Porous Region near Walls

Transport in Porous Media - The present work concerns the effect of hematocrit-dependent viscosity on pulsatile flow of blood through narrow tube with porous walls. Two-fluid model of blood is...     

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.     

A Model of Arterial Adaptation to Alterations in Blood Flow

Mechanisms of arterial adaptation to changes in blood flow rates were tested by comparing the predictions of a proposed theoretical model with available experimental data. The artery was modeled as an elastic membrane made of a nonlinear, incompressible, elastic material. Stimulation of the vascular smooth muscle was modeled through the generation of an active component of circumferential stress. The muscular tone was modulated by flow-induced shear stress sensed by the arterial endothelium, and is responsible for the vasomotor adjustment of the deformed arterial diameter in response to changes in blood flow. This study addresses the hypothesis that the synthetic and proliferative activity of smooth muscle cells, leading to a change in arterial dimensions, is shear stress dependent and is associated with changes in the contractile state of the smooth muscle cells and changes in the circumferential wall stress. Remodeling to a step change in flow was formulated as an initial-value problem for a system of first order autonomous differential equations for the evolution of muscular tone and evolution of arterial geometry. The governing equations were solved numerically for model parameters identified from experimental data available in the literature. The model predictions for the time variation of the geometrical dimensions and their asymptotic values were found to be in qualitative agreement with available experimental data. Experiments for validating the introduced hypotheses and further generalizations of the model were discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computational Modelling of Non-Newtonian Effects on Flow in Channels with Moving Wall Indentations

Non-Newtonian effects in a channel with moving wall indentations are assessed numerically by a finite volume method for solving the unsteady incompressible Navier-Stokes equations and using a power-law model exhibiting shear thinning viscosity and Casson's model as the constitutive equations for the non-Newtonian fluid. The computations show that for a non-Newtonian fluid, there are differences in the velocity profiles and in the structure and size of the reversed flow regions as compared with the corresponding Newtonian fluid. The comparison of non-Newtonian and Newtonian wall shear stress reveals a slight decrease in the magnitude on the average for the non-Newtonian case, eventually resulting in the strength of the “wave train” being slightly weaker than those corresponding to a Newtonian fluid.     

局部狭窄血管中血液振荡流的速度和切应力

本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型，给出了血液的轴向流速，径向流速和切应力的包含压力梯度项的解析表达式，并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算，详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明，与均匀管情况相比，在狭窄段内，血液振荡流轴向流速无论平均值还是脉动幅值均明显增大，且径向流速不再为零。但径向流速仍远小于轴向流速。同时，切应力也不再仅由轴向流速梯度提供，径向流速梯度也将产生切应力，但是在计算管壁切向上的切应力时，径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力（平均值和脉动值）将随着狭窄高度的增大而增大，在狭窄最大高度处达到最大，因而沿流动方向产生了较大的切应力梯度。     

Accurate Modelling of Pore-Scale Films and Layers for Three-Phase Flow Processes in Clastic and Carbonate Rocks with Arbitrary Wettability

Three-phase flow is a key process occurring in subsurface reservoirs, for example, during $\text{ CO }_2$ sequestration and enhanced oil recovery techniques such as water alternating gas (WAG) injection. Predicting three-phase flow processes, for example, the increase in oil recovery during WAG, requires a sound understanding of the fundamental flow physics in water- to oil-wet rocks to derive physically robust flow functions, i.e. relative permeability and capillary pressure. In this study, we use pore-network modelling, a reliable and physically based simulation tool, to predict the flow functions. We have developed a new pore-scale network model for rocks with variable wettability, from water- to oil-wet. It comprises a constrained set of parameters that mimic the wetting state of a reservoir. Unlike other models, it combines three main features: (1) A novel thermodynamic criterion for formation and collapse of oil layers. The new model hence captures wetting film and layer flow of oil adequately, which affects the oil relative permeability at low oil saturation and leads to accurate prediction of residual oil. (2) Multiple displacement chains, where injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows for the accurate modelling of the mobilisation of many disconnected phase clusters that arise, in particular, during higher order WAG floods. (3) The model takes realistic 3D pore-networks extracted from pore-space reconstruction methods and CT images as input, preserving both topology and pore shape of the sample. For water-wet systems, we have validated our model with available experimental data from core floods. For oil-wet systems, we validated our network model by comparing 2D network simulations with published data from WAG floods in oil-wet micromodels. This demonstrates the importance of film and layer flow for the continuity of the various phases during subsequent WAG cycles and for the residual oil saturations. A sensitivity analysis has been carried out with the full 3D model to predict three-phase relative permeabilities and residual oil saturations for WAG cycles under various wetting conditions with different flood end-points.     

A Structural Model of the Left Venricle Including Muscle Fibres and Coronary Vessels: Mechanical Behaviour in Normal Conditions

A structural model of the left ventricle is presented. It is a cylindricalthick-walled model composed of muscle fibre models and coronaryvessel models. The ventricular wall is divided in ten layers to accountfor the transmural variation of myofibre and coronary vessel orientation.These structures give the global performance of the ventricular modeldepending on their own behaviour and on the way they are interfaced.The results refer both to the global ventricular performance and thebehaviour of the different components. In particular they suggest anappreciable contribute of the coronary capillary during the early fillingphase in enlarging the ventricle; during this phase the capillary vesselsexert an extensive force in the radial direction, due to inner coronarypressure, equal to 20--30 percent -- depending on the layer -- of the forceexerted by the fibres. This occurrence explains, in our opinion, theobserved cardiac function improvement when the arterial coronarypressure is increased, known as gardenhose effect.     

Unidirectional Heat-Gravitational Motion of Viscous Fluid in A Flat Channel with A Given Flow Rate

This paper touches upon an initial-boundary-value problem that describes the unidirectional heat-gravitational motion of fluid in a plane channel in the case of solid immobile upper and lower walls with temperature distribution thereon and in the case of a heat-insulated upper wall. The motion is caused by a joint effect of the longitudinal temperature gradient and given nonstationary flow rate. The initial-boundary-value problem is inverse relative to the pressure gradient along the channel. An exact stationary solution is obtained. A solution of the nonstationary problems in Laplace images is determined, and the results of numerical calculations are presented.     

缓凝砂浆在单螺杆挤出机中的流动分析

在预应力钢筋上连续包裹一层缓凝砂浆是新型缓粘结预应力混凝土体系得以工程应用的关键。为了弄清包覆过程,了解物料性能、加工条件和螺杆参数等输入变量对包覆输出结果的影响,基于缓凝预应力筋包覆试验,运用Polyflow软件,对宾汉姆体的缓凝砂浆在螺旋槽内流动和变形情况进行CFD(computational fluid dynamics)模拟。得到了可视化的速度场和剪切速率场,模拟了分析螺杆转速、螺杆几何参数对物料流变特性的影响。模拟结果可视,且直观地验证了包覆试验现象,揭示了包覆机理,为包覆装置可靠作业和结构优化提供了理论依据。     

Flow in porous media I: A theoretical derivation of Darcy's law

Stokes flow through a rigid porous medium is analyzed in terms of the method of volume averaging. The traditional averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The equation of motion contains integrals involving spatial deviations of the pressure and velocity, the Brinkman correction, and other lower-order terms. The analysis clearly indicates why the Brinkman correction should not be used to accommodate ano slip condition at an interface between a porous medium and a bounding solid surface.The presence of spatial deviations of the pressure and velocity in the volume-averaged equations of motion gives rise to aclosure problem, and representations for the spatial deviations are derived that lead to Darcy's law. The theoretical development is not restricted to either homogeneous or spatially periodic porous media; however, the problem ofabrupt changes in the structure of a porous medium is not considered.Roman Letters A interfacial area of the - interface contained within the macroscopic system, m² - A _e area of entrances and exits for the -phase contained within the macroscopic system, m² - A interfacial area of the - interface contained within the averaging volume, m² - A ^* interfacial area of the - interface contained within a unit cell, m² - Ae area of entrances and exits for the -phase contained within a unit cell, m² - B second order tensor used to represent the velocity deviation (see Equation (3.30)) - b vector used to represent the pressure deviation (see Equation (3.31)), m^–1 - d distance between two points at which the pressure is measured, m - g gravity vector, m/s² - K Darcy's law permeability tensor, m² - L characteristic length scale for volume averaged quantities, m - characteristic length scale for the -phase (see Figure 2), m - characteristic length scale for the -phase (see Figure 2), m - n unit normal vector pointing from the -phase toward the -phase (n =–n ) - n _e unit normal vector for the entrances and exits of the -phase contained within a unit cell - p pressure in the -phase, N/m² - p intrinsic phase average pressure for the -phase, N/m² - p –p , spatial deviation of the pressure in the -phase, N/m² - r ₀ radius of the averaging volume and radius of a capillary tube, m - v velocity vector for the -phase, m/s - v phase average velocity vector for the -phase, m/s - v intrinsic phase average velocity vector for the -phase, m/s - v –v , spatial deviation of the velocity vector for the -phase, m/s - V averaging volume, m³ - V volume of the -phase contained within the averaging volume, m³ Greek Letters V/V, volume fraction of the -phase - mass density of the -phase, kg/m³ - viscosity of the -phase, Nt/m² - arbitrary function used in the representation of the velocity deviation (see Equations (3.11) and (B1)), m/s - arbitrary function used in the representation of the pressure deviation (see Equations (3.12) and (B2)), s^–1     

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

Transport in Porous Media - The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes but also in materials science and...     

A Derivation of the Volume-Averaged Boussinesq Equations for Flow in Porous Media with Viscous Dissipation

The volume-averaged equations are derived for convective flow in porous media. In the thermal energy equation viscous dissipation is taken into account, and a suitable form is obtained which is valid when Brinkman effects are significant.     

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient to the filtration or Darcy velocity in a coupled nonlinear form explicitly given by

Fast X-ray Micro-Tomography of Multiphase Flow in Berea Sandstone: A Sensitivity Study on Image Processing

Synchrotron-based fast micro-tomography is the method of choice to observe in situ multiphase flow and displacement dynamics on the pore scale. However, the image processing workflow is sensitive to a suite of manually selected parameters which can lead to ambiguous results. In this work, the relationship between porosity and permeability in response to systematically varied gray-scale threshold values was studied for different segmentation approaches on a dataset of Berea sandstone at a voxel length of 3  \(\upmu \) m. For validation of the image processing workflow, porosity, permeability, and capillary pressure were compared to laboratory measurements on a larger-sized core plug of the same material. It was found that for global thresholding, minor variations in the visually permissive range lead to large variations in porosity and even larger variations in permeability. The latter is caused by changes in the pore-scale flow paths. Pore throats were found to be open for flow at large thresholds but closed for smaller thresholds. Watershed-based segmentation was found to be significantly more robust to manually chosen input parameters. Permeability and capillary pressure closely match experimental values; for capillary pressure measurements, the plateau of calculated capillary pressure curves was similar to experimental curves. Modeling on structures segmented with hysteresis thresholding was found to overpredict experimental capillary pressure values, while calculated permeability showed reasonable agreement to experimental data. This demonstrates that a good representation of permeability or capillary pressure alone is not a sufficient quality criterion for appropriate segmentation, but the data should be validated with both parameters. However, porosity is the least reliable quality criterion. In the segmented images, always a lower porosity was found compared to experimental values due to micro-porosity below the imaging resolution. As a result, it is recommended to base the validation of image processing workflows on permeability and capillary pressure and not on porosity. Decane-brine distributions from a multiphase flow experiment were modeled in a thus validated \(\upmu \) -CT pore space using a morphological approach which captures only capillary forces. A good overall correspondence was found when comparing (capillary-controlled) equilibrium fluid distributions before and after pore-scale displacement events.     

A Lattice Gas Automaton Simulation of the Nonlinear Diffusion Equation: A Model for Moisture Flow in Unsaturated Porous Media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local density of fluid particles which statistically determines the collision rate and thus, the mean free path of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moisture flow in unsaturated porous media. The capability of the LGA to account for unsaturated flow is tested through a set of numerical experiments simulating one-dimensional infiltration in a simplified semi-infinite homogenous isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid–solid interfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagation of the infiltration front is visualized at different time steps through concentration profiles parallel to the applied concentration gradient and the infiltration rate is measured continuously until steady-state flow is reached. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t ^1/2 dependence. The evolution of the effective diffusion coefficient with the particle concentration is estimated from the measured density profiles for the various porous materials. Depending on the applied fluid–solid interactions, the macroscopic effective diffusivity may vary by more than two orders of magnitude with density.     

与医用CT配套的便携式材料试验机的研制及其在混凝土损伤研究中的应用

混凝土内部细观裂纹的演化规律研究可以解释其动态特性和损伤破坏机理.X射线CT技术是无损探测混凝土内部细观裂纹萌生、扩展、贯通的有效手段.与医用CT配套的便携式材料试验机是进行混凝土CT试验的关键加载设备.本文概要介绍研制便携式材料试验机的研制过程.论述实现动态加载的几个关键技术问题,包括加载设备的便携式要求、加载波形显示、加载控制、试件安装和粘结技术等.经过试验,表明所研制的加载设备达到了使用要求.混凝土动力压缩条件下突发性裂纹的出现是其动态强度提高的原因之一.     

A Direct Numerical Study of Transport and Anisotropy in a Stably Stratified Turbulent Flow with Uniform Horizontal Shear

Direct numerical simulations of homogeneous turbulence in stably stratified shear flow have been performed to aid the understanding of turbulence and turbulent mixing in geophysical flow. Two cases are compared. In the first case, which has been studied in the past, the mean velocity has vertical shear and the mean density is vertically stably stratified. In the second case, which has not been studied systematically before, the mean velocity has horizontal shear and the mean density is again vertically stably stratified. The critical value of the gradient Richardson number, for which a constant turbulence level is obtained, is found to be an order of magnitude larger in the horizontal shear case. The turbulent transport coefficients of momentum and vertical mass transfer are also an order of magnitude larger in the horizontal shear case. The anisotropy of the turbulence intensities are found to be in the range expected of flows with mean shear with no major qualitative change in the range of Richardson numbers studied here. However, the anisotropy of the turbulent dissipation rate is strongly affected by stratification with the vertical component dominating the others. This revised version was published online in July 2006 with corrections to the Cover Date.