Simulations of magnetorheological suspensions in Poiseuille flow

Particle-level simulations are conducted to study magnetorheological fluids in plane Poiseuille flow. The importance of the boundary conditions for the particles at the channel walls is examined by considering two extreme cases: no friction and infinite coefficient of friction. The inclusion of friction produces Bingham fluid behavior, as commonly observed experimentally for MR suspensions. Lamellar structures, similar to those reported for electrorheological fluids in shear flow, are observed in the post-yield region for both particle boundary conditions. The formation of these lamellae is accompanied by an increase in the bulk fluid velocity. The slip boundary condition produces higher fluid velocities and thicker lamellar structures.     

Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall

An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid?Cliquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid?Cliquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress.     

Influence of wall slip on the hydrodynamic behavior of a two-dimensional slider bearing

In the present paper, a multi-linearity method is used to address the nonlinear slip control equation for the hydrodynamic analysis of a two-dimensional (2-D) slip gap flow. Numerical analysis of a finite length slider bearing with wall slip shows that the surface limiting shear stress exerts complicated influences on the hydrodynamic behavior of the gap flow. If the slip occurs at either the stationary surface or the moving surface (especially at the stationary surface), there is a transition point in the initial limiting shear stress for the proportional coefficient to affect the hydrodynamic load support in two opposite ways: it increases the hydrodynamic load support at higher initial limiting shear stresses, but decreases the hydrodynamic load support at lower initial limiting shear stresses. If the slip occurs at the moving surface only, no fluid pressure is generated in the case of null initial limiting shear stress. If the slip occurs at both the surfaces with the same slip property, the hydrodynamic load support goes off after a critical sliding speed is reached. A small initial limiting shear stress and a small proportionality coefficient always give rise to a low friction drag. The project supported by the National Natural Science Foundation of China (10421002, 10332010), the National Basic Research Program of China (2006CB601205), and the Science Research Foundation of Liaoning Province (20052178). The English text was polished by Yunming Chen.     

Newtonian flow in a triangular duct with slip at the wall

We consider the Newtonian Poiseuille flow in a tube whose cross-section is an equilateral triangle. It is assumed that boundary slip occurs only above a critical value of the wall shear stress, namely the slip yield stress. It turns out that there are three flow regimes defined by two critical values of the pressure gradient. Below the first critical value, the fluid sticks everywhere and the classical no-slip solution is recovered. In an intermediate regime the fluid slips only around the middle of each boundary side and the flow problem is not amenable to analytical solution. Above the second critical pressure gradient non-uniform slip occurs everywhere at the wall. An analytical solution is derived for this case and the results are discussed.     

A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

In this paper, Poiseuille flow of a polar fluid (model of a red blood cell suspension) under various boundary conditions at the wall, viz., slip or no-slip in the axial velocity and couple stresses zero or non-zero at the boundary, is considered from the point of view of its applications to blood flow. Analytic expressions for axial and rotational velocities, flow rate, effective viscosity and stresses are obtained. The magnitudes of the length ratioL and the coupling number N are determined in accordance with concentration and tube radius (in the existing literature, values ofL andN are chosen arbitrarily). Velocity profiles (both axial and rotational) and the variation of the effective viscosity with concentration, tube radius and for various values of the boundary condition parameters are shown graphically. The analytic results obtained are compared with experimental results (for blood flow). It is found that they are in a reasonably good agreement. The effective viscosity exhibits the Inverse Fahraeus-Lindquist Effect in all the cases (including the slip or no-slip in the velocity fields). A method is given for determining the non-zero couple stress boundary condition for a given concentration. Applications of this theory to blood flow are briefly discussed.     

滑滚表面间的流体膜壁面滑移和流体动力学

经典雷诺润滑理论建立在无壁面滑移的假设基础之上。近年来许多试验报告了发生在流体膜流动的壁面滑移证据。本文研究了两固体表面间的流体膜流动特性和流体动力学,发现壁面滑移显著影响膜的流体动力学问题,流体动压力不仅受黏度和几何间隙的影响,而且还由壁面滑移和表面运动强力控制,通过控制表面的吸附性质,甚至可以得到零摩擦表面。另一方面,如果两个表面具有相同的滑移特性,存在一个临界滑动速度使得流体动压效应完全消失;但是在纯滚动条件下,即使界面极限剪应力很小,仍然有相当可观的流体动压效应。     

EFFECT OF WALL SLIP ON SQUEEZE FLOW OF RIGID-PLASTIC MEDIA BETWEEN PARALLEL DISK

The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium with the following four different slip boundary conditions are obtained. (1) The Coulombic friction condition is applied, and the stress distribution on the wall is derived, which is linear or exponential distribution in the no-slip area or slip area. (2) It is assumed that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, with the stress distribution and the squeeze force gained. (3) The assumption that the slip velocity at the disks is related to the shear stress component is used, with the stress distribution and the squeeze force obtained, which is equivalent to the result given in (2). (4) Rational velocity components are introduced, and the stress distribution is satisfied.     

Stick-slip transition in capillary flow of linear polyethylene: 3. Surface conditions

Effects of surface topology and energy on the stick-slip transition were studied in capillary flow of highly entangled polyethylene (PE) melts. Surface roughness was shown to increase the critical stress of the stick-slip transition because of the increased resistance to interfacial disentanglement. Lowering the surface energy of a smooth die wall by treatment with a fluorocarbon completely eliminates the stick-slip transition and produces massive interfacial slip at PE/wall boundary down to a stress level of 0.05 MPa. On the other hand, considerable roughness on the same low energy surface can produce a stick hydrodynamic boundary condition and restore the stick-slip transition despite the weak PE/wall interfacial interactions. Additionally, a slip-slip transition was found in the die with a nearly non-adsorbing wall that appears to involve a secondary chain-debonding process.     

压力相关的壁面滑移在滑动间隙流体动压力产生中的作用

近年来,壁面滑移在纳米流变学、微流体力学、薄模润滑和微机电系统(MEMS)等领域越来越引起关注。以前大部分研究集中于表面初始极限剪应力对薄模润滑的壁面滑移和流体动力学的影响。本文通过一个极限剪切应力比例系数主要研究了与压力相关的壁面滑移滑动间隙流体动压力产生中的作用,发现极限剪切应力比例系数以相反的两种方式影响着流体膜的流体动力学:在高初始剪应力区使流体动力增加,但在低初始剪应力区使流体动力减小,这意味着就极限剪切应力比例系数影响流体动压力而言,存在一个初始极限剪切应力的转换点。但是在界面滑移存在时,较小的极限剪切应力比例系数总是产生较小的摩擦阻力。     

Injection and suction of an upper-convected maxwell fluid through a porous-walled tube

The steady-state, similarity solutions of the flow of an upper-convected Maxwell fluid through a tube with a porous wall are constructed by asymptotic and numerical analyses as functions of the direction of flow through the tube, the amount of elasticity in the fluid, as measured by the Deborah number De, and the degree of fluid slip along the tube wall. Fluid slip is assumed to be proportional to the local shear stress and is measured by a slip parameter β that ranges between no-slip (β = 1) and perfect slip (β = 0). The most interesting results are for fluid injection into the tube. For β = 1, the family of flows emanating from the Newtonian limit (De = 0) has a limit point where it turns back to lower values of De. These solutions become asymptotic to De = 0) and develop an O(De) boundary layer near the tube wall with singularly high stresses matched to homogeneous elongational flow in the core. This solution structure persists for all nonzero values of the slip parameter. For β ≠ 1, a family of exact solutions is found with extensional kinematics, but nonzero shear stress convected into the tube through the wall. These flows differ for low De from the Newtonian asymptote only by the absence of the boundary layer at the tube wall. Finite difference calculations evolve smoothly between the Newtonian-like and extensional solutions because of approximation error due to under-resolution of the boundary layer. The radial gradient of the axial normal stress of the extensional flow is infinite at the centerline of the tube for De > 1; this singularity causes failure of the finite difference approximations for these Deborah numbers unless the variables are rescaled to take the asymptotic behavior into account.     

The “Twin capillary” a simple device to separate shear- and slip-flow of fluids

When the flow behaviour of fluids is investigated with capillary-or rotational rheometers, adhesion of the fluid to the wall is normally one of the boundary conditions. For many fluids, especially for suspensions, this assumption is not valid. These fluids tend to slip at the wall. Therefore the normal evaluation of rheometer measurements leads to apparent but not compatible flow functions. The flow behaviour of these fluids can be characterized with two material functions which describe separately slipping in the boundary layer and shearing within the fluid. Only if both functions are known, correct predictions of flow processes are possible. A simple equipment to separate the shear function and the slip function is described.List of symbols Y^* apparent shear rate - Y _w ^* apparent wall shear rate - Y_w wall shear rate corrected with Rabinowitsch and Weissenberg correction - Y_s reduced shear rate (slip corrected) - Y_ws reduced wall shear rate (slip corrected) - * (r) velocity distribution in a capillary - _G slip velocity (at the wall) - * (r) velocity distribution in a capillary (without slip) - shear stress - _w wall shear stress - V_S total volume rate - V_G shear volume rate - V_G slip volume rate - p ₁ pressure in the reservoir channel of the capillary rheometer - p ₀ athmospheric pressure - L capillary length - R capillary radius     

Wall shear stress and void fraction in Poiseuille bubbly flows: Part II: experiments and validity of analytical predictions

In a companion paper, a simple analytical formulation has been established which provides the wall shear stress in laminar bubbly flows for idealised transverse void fraction distributions. In the present paper, this approach is applied to Poiseuille bubbly flows in circular ducts. New measurements of the void fraction profiles and wall friction angular distribution in a pipe are presented for a wide range of flow parameters. Approximating the void profiles by step-functions allows us to evaluate the wall friction with the above mentioned model. Results are shown to agree satisfactorily with measurements. Notably, negative wall shear stress and wall shear stress much higher than their single-phase flow counterpart at the same liquid flow rate are recovered. Therefore, the principal mechanisms responsible for friction modification are captured with this simple model.     

Quadratic programming algorithm for wall slip and free boundary pressure condition

Wall slip is often observed in a highly sheared fluid film in a solid gap. This makes a difficulty in mathematical analysis for the hydrodynamic effect because fluid velocity at the liquid–solid interfaces is not known a priori. If the gap has a convergent–divergent wedge, a free boundary pressure condition, i.e. Reynolds pressure boundary condition, is usually used in the outlet zone in numerical solution. This paper, based on finite element method and parametric quadratic programming technique, gives a numerical solution technique for a coupled boundary non‐linearity of wall slip and free boundary pressure condition. It is found that the numerical error decreases with the number of elements in a negative power law having an index larger than 2. Our method does not need an iterative process and can simultaneously gives rise to fluid film pressure distribution, wall slip velocity and surface shear stress. Wall slip always decreases the hydrodynamic pressure. Large wall slip even causes a null hydrodynamic pressure in a pure sliding solid gap. Copyright © 2005 John Wiley & Sons, Ltd.     

Molecular dynamics simulation of liquid argon flow at platinum surfaces

The micro Poiseuille flow for liquid argon flowing in a nanoscale channel formed by two solid walls was studied in the present paper. The solid wall material was selected as platinum, which has well established interaction potential. We consider the intermolecular force not only among the liquid argon molecules, but also between the liquid argon atoms and the solid wall particles, therefore three regions, i.e. the liquid argon computation domain, the top and bottom solid wall regions are included for the force interaction. The present MD (Molecular Dynamics) simulation was performed without any assumptions at the wall surface. The objective of the study is to find how the flow and the slip boundaries at the wall surface are affected by the applied gravity force, or the shear rate. The MD simulations are performed in a nondimensional unit system, with the periodic boundary conditions applied except in the channel height direction. Once the steady state is reached, the macroscopic parameters are evaluated using the statistical mechanics approach. For all the cases tested numerically in the present paper, slip boundaries occur, and such slip velocity at the stationary wall surface increases with increasing the applied gravity force, or the shear rate. The slip length, which is defined as the distance that the liquid particles shall travel beyond the wall surfaces to reach the same velocity as the wall surface, sharply decreases at small shear rate, then slightly decreases with increasing the applied shear rate. We observe that the liquid viscosity remains nearly constant at small shear rates, and the Newtonian flow occurs. However, with increasing the shear rate, the viscosity increases and the non-Newtonian flow appears.     

Slip yield stress effects in start-up Newtonian Poiseuille flows

Analytical solutions are derived for various start-up Newtonian Poiseuille flows assuming that slip at the wall occurs when the wall shear stress exceeds a critical value, known as the slip yield stress. Two distinct regimes characterise the steady axisymmetric and planar flows, which are defined by a critical value of the pressure gradient. If the imposed pressure gradient is below this critical value, the classical no-slip, start-up solution holds. Otherwise, no-slip flow occurs only initially, for a finite time interval determined by a critical time, after which slip does occur. For the annular case, there is an additional intermediate (steady) flow regime where slip occurs only at the inner wall, and hence, there exist two critical values of the pressure gradient. If the applied pressure gradient exceeds both critical values, the velocity evolves initially with no-slip at both walls up to the first critical time, then with slip only along the inner wall up to the second critical time and finally with slip at both walls.     

An adaptive finite element method for viscoplastic flows in a square pipe with stick–slip at the wall

This paper presents the numerical solution of non-linear yield stress phenomena by using a new mixed anisotropic auto-adaptive finite element method. The Poiseuille flow of a Bingham fluid with slip yield boundary condition at the wall is considered. Despite its practical interest, for instance for pipeline flows of yield-stress fluids such as concrete and cements, this problem has not been addressed yet to our knowledge. The case of a pipe with a square section has been investigated in detail. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are completely identified.     

Direct simulation of multiphase flows with modeling of dynamic interface contact angle

We describe a modeling technique for dynamic contact angle between a phase interface and a solid wall using a generalized Navier boundary condition in the context of a front-tracking-based multiphase method. The contact line motion is determined by the generalized Navier slip boundary condition in order to eliminate the infinite shear stress at the contact line. Applying this slip boundary condition only to the interface movement with various slip ratios shows good agreement with experimental results compared to allowing full fluid slip along the solid surface. The interface slip model performs well on grid convergence tests using both the slip ratio and slip length models. A detailed energy analysis was performed to identify changes in kinetic, surface, and potential energies as well as viscous and contact line dissipation with time. A friction coefficient for contact line dissipation was obtained based on the other computed energy terms. Each energy term and the friction coefficient were compared for different grid resolutions. The effect of varying the slip ratio as well as the contact angle distribution versus contact line speed was analyzed. The behavior of drop impact on a solid wall with different advancing and receding angles was investigated. Finally, the proposed dynamic contact model was extended to three dimensions for large-scale parallel calculations. The impact of a droplet on a solid cylinder was simulated to demonstrate the capabilities of the proposing formulation on general solid structures. Widely different contact angles were tested and showed distinctive characteristic behavior clearly.     

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.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.