Fluid flow shear-stress

There are two variables used in the description of fluid flow shear stress and shear strain. Stress is measured in units of Pascals and the strain is dimensionless. 

Kapur, S., D. J. Baylink, and K. H. Lau 2003. Fluid flow shear stress stimulates human osteoblast proliferation and differentiation through multiple interacting and competing signal transduction pathways. Bone 32(3) 241-51. 

Upper chamber" — Fluid flow Shear / stress... 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

The downstream pressure P2 acts on the element against the flow, as does the drag of the pipe wall on the fluid. The shear stress at the wall is called the wall shear stress and is denoted by tw. This shear stress acts over the area of the element in contact with the wall. The force acting against the flow is therefore given by... 

The concept of viscosity was first introduced by Newton in the seventeenth century as the proportionality factor between the velocity gradient dr/dx in the direction perpendicular to the flow direction (shear rate) and the force per unit area F/S required to maintain the flow (shear stress). We now call a fluid that obeys such a linear relation a Newtonian fluid. 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

Viscoelastic fluids have elastic properties in addition to their viscous properties. When under shear, such fluids exhibit a normal stress in addition to a shear stress. For example, if a vertical rod is partly immersed and rotated in a non-viscoelastic liquid the rod s rotation will create a centrifugal force that drives liquid outwards toward the container walls, as shown in Figure 6.16(a). If, on the other hand, the liquid is viscoelastic then as the liquid is sheared about the rod s axis of rotation, a stress normal to the plane of rotation is created which tends to draw fluid in towards the centre. At some rotational speed, the normal force will exceed the centrifugal force and liquid is drawn towards and up along the rod see Figure 6.16(b). This is called the Weissenberg effect. Viscoelastic fluids flow when stress is applied, but some of their deformation is recovered when the stress is removed [381]. 

For elastic bodies, the shear stress is related to the shear strain by the shear modulus. For viscous fluids, the shear stress is related to the shear strain rate by the viscosity. We note that for laminar viscous flow in a Margules viscometer (Figure 10.7), radial fluid displacement is zero (gr = 0). Thus, differentiating with respect to time ... 

The mechanical force most relevant to platelet-mediated thrombosis is shear stress. The normal time-averaged levels of venous and arterial shear stresses range between 1-5 dyn/cm2 and 6 10 dyn/cm2, respectively. However, fluid shear stress may reach levels well over 200 dyn/cm2 in small arteries and arterioles partially obstructed by atherosclerosis or vascular spasm. The cone-and-plate viscometer and parallel-plate flow chamber are two of the most common devices used to simulate fluid mechanical shearing stress conditions in blood vessels. 

Flow of Power Law Fluids in Smooth Pipes. Oil-in-water emulsions having oil volume fractions greater than 0.5 are often non-Newtonian shear-thinning fluids (3,10-13). For such fluids, the shear stress (t) and the shear rate (7) can be related by the power law model ... 

For the flow of incompressible fluids, the shear stress at the wall, could be represented in terms of the friction factor / by... 

Most fluids with pronounced nonnewtonian behavior have such high viscosities that their flow is laminar in most industrially interesting situations. We saw in Sec. 6.3 that for any fluid the shear stress at any point in a horizontal circular pipe is given by... 

Answer Based on the final result in part (e) for rfFsoUd on fluid, the shear stresses that must be considered are Xre and Newton s law of viscosity for this one-dimensional flow problem reveals that only Xrcf, is important, because... 

Based on viscosity of the samples, the flow of samples is broadly classified into three categories, namely, Newtonian, time independent non-Newtonian and time dependent non-Newtonian. Newtonian fluids show shear stress independent constant viscosity profile where as non-Newtonian fluids show a viscosity profile, which is dependent on the shear force and time. In time independent non-Newtonian fluids, the shear stress does not vary proportionally to the shear rate. The time independent non-Newtonian fluids show mainly three types of flow. A decreasing viscosity with an increase of shear rate is called shear thinning or pseudoplastic flow (Figure 46.12a). An increasing viscosity with an increase of shear rate is called shear thickening or dilatant flow. Some fluids need application of certain amount of force before any flow is induced that are known as Bingham plastics. 

The molten polymer is a power-law fluid, where shear stress r and shear rate y are related by T = ife-y" and k and n are constants (see note below). Show that the relations between volume flow-rate Q and pressure drop AP for the die and extruder screw may be written... 

Almost all the vegetable oils behave like Newtonian fluids (the shear stress is proportional to the shear strain) and the viscosity is proportional to the molecular weight. The viscosity of oil is defined as the resistance to flow under specified conditions and, as it is a liquid under ambient conditions, its viscosity is lower than that of polymers but higher than most of the... 

Pressure drop and loss due to friction. When the fluid is in steady-state laminar flow in a pipe, then for a Newtonian fluid the shear stress is given by Eq. (2.4-2), which is rewritten for change in radius dr rather than distance dy, as follows. 

For streamline flow, equation (3.3) applies right up to the wall and the velocity gradient at the wall can be readily calculated, and for a Newtonian fluid the shear stress obtained. It is, as those who attempt exercise 3.1 will find ... 

For a pseudoplastic slurry or power law fluid, the shear stress is expressed by Equation 3-43. By analogy with the method developed for a Bingham flow in a tube, the following equation is expressed ... 

Much of the early development of classical fluid mechanics was concerned with the mathematics of ideal (inviscid) fluids, i.e. fluids which have zero viscosity (Batchelor, 1967). In an ideal fluid, the shear stress is always zero even when the fluid is flowing. In this case, the momentum flux across the surface of a control volume would be by convection only. Figure 3.2 shows... 

As shown in Eqn. (6), the drag coefficient of a cylindrical fiber imder cross flow condition is a function of the Reynolds Number, which is generally expressed as Re = pUp,hd/p (i.e. the ratio of inertial force to viscous force). This definition holds true for Newtonian fluids, where shear stress < shear rate. However, the fluids that are often utilized in fiber sweep applications are non-Newtonian. Hence, the Reynolds Number must be redefined using the apparent viscosity function as Re = pUp>d/papp. The viscosity for Newtonian fluids is independent of the shear rate. However, for non-Newtonian fluids, the apparent viscosity varies with shear rate. Applying the Yield Power Law (YPL) rheology model, the apparent viscosity is expressed as ... 

---