Shear stress in fluid

Hanratty TJ and Campbell JA 1996 Chapter 9, Measurement of wall shear stress. In Fluid Mechanics Measurements, 2nd Edition, Editor Goldstein RJ, Taylor and Francis, Washington, DC, pp. 575-648. 

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

The shear stress in the fluid is much higher near the impeller than it is near the tank wall. The difference is greater in large tanks than in small ones. 

Fig. 5.10 shows an annular element of fluid of radius r and thickness dr subjected to a shear stress in the capillary. When the element of fluid emerges from the die it will recover to the form shown by ABCD. 

Viscosity, dynamic Sometimes called absolute viscosity, the shear stress in a fluid divided by the velocity gradient. 

R is the shear stress in the fluid and divelocity gradient or the rate of shear. It may be noted that R corresponds to r used by many authors to denote shear stress similarly, shear rate may be denoted by either dw,/dy or y. The proportionality sign may be replaced by the introduction of the proportionality factor n, which is the coefficient of viscosity, to give ... 

The ratio u/d represents the velocity gradient in the fluid, and thus the group (pu/d) is proportional to the shear stress in the fluid, so that (pu2)/(pu/d) = (dup/p) = Re is proportional to the ratio of the inertia forces to the viscous forces. This is an important physical interpretation of the Reynolds number. 

Close to the wall of a pipe, the effect of the curvature of the wall has been neglected and the shear stress in the fluid has been taken to be independent of the distance from the wall. However, this assumption is not justified near the centre of the pipe. 

Now R0 (the shear stress in the fluid at the surface) is equal and opposite to R, the shear stress acting on the surface, —q jQs is by definition the heat transfer coefficient at the surface (h), and (—NA)y=o/ CAjl - CAw) is the mass transfer coefficient ho). Then dividing both sides of equation 12.100 by pu, and of equation 12.101 by u, to make them dimensionless ... 

Iv) Shear stress and viscosity. As explained In Section 1 three Independent estimates of the shear stress can be made for this particular type of flow. For both systems they all agree within the limits of statistical uncertainty as shown In Table II. The shear stress In the micro pore fluid Is significantly lower than the bulk fluid, which shows that strong density inhomogeneities can induce large changes of the shear stress. 

Predictions on the effectiveness of a fluid loss additive formulation can be made on a laboratory scale by characterizing the properties of the filter-cake formed by appropriate experiments. Most of the fluids containing fluid loss additives are thixotropic. Therefore the apparent viscosity will change when a shear stress in a vertical direction is applied, as is very normal in a circulating drilling fluid. For this reason, the results from static filtering experiments are expected to be different in comparison with dynamic experiments. 

In 1971 Mizushina (M9) reviewed the limiting-current method with particular emphasis upon shear-stress and fluid-velocity measurements. Mass-transfer measurements, that is, limiting-current measurements in the original more restricted sense, are documented fairly extensively. The electrochemical analysis of limiting-current measurements is touched upon, but not elaborated. 

Chachisvilis, M., Zhang, Y. L. and Frangos, J. A. (2006). G protein-coupled receptors sense fluid shear stress in endothelial cells. Proc. Natl. Acad. Sci. USA 103, 15463-8. 

If the fluid flows in two pipes having internal diameters dti and dt2 with the same value of the wall shear stress in both pipes, then from equation 3.17 the values of the flow characteristic are equal in both pipes ... 

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 ... 

From the preceding equations we conclude that the pressure is a function of coordinate z only. Consequently, in the last equation the left-hand side is a function of z only, whereas the right-hand side is a function of y only. This is only possible if both equal a constant. Thus we conclude that the pressure gradient is constant, that is, pressure rises (or drops) linearly with z, and that the shear stress, in the presence of a pressure gradient, is a linear function of y, and in the absence of a pressure gradient it is constant across the gap. These observations follow from the momentum balance, and, they are therefore, true for all fluids, Newtonian and non-Newtonian alike. 

First ask yourself if there is any role for fluid shear stresses in determining and obtaining the desired process result. About half of the time the answer will likely be no. That is the percentage of mixing processes where fluid shear stresses either have no effect or seem to have no effect on the process result. In these cases, mixer design can be based on pumping capacity, blend time, velocities and other matters of that nature. Impeller type location and other geometric variables are major factors in these types of processes. 

The shear stress in the fluid at the surface R = —jiu jy From the equation given R = 0.03pu2(p/uspx)°-2... 

In the case of solids it is evident that deformation is either linear elastic - like a Hookean solid (most solids including steel and rubber) - or non-linear elastic or viscoelastic. In the case of liquids, fluids differ between those without yield stress and those with yield stress (so-called plastic materials). Fluids without yield stress will flow if subjected to even slight shear stresses, while fluids with yield stress start to flow only above a material-specific shear stress which is indicated by o0. 

In the case of elastic fluids and for simple shear flow, the first normal stress difference is N[ =on — o22- When shearing a fluid between two plates (x, direction), the first normal stress difference N( forces the plates apart (x2 direction). The first normal stress difference N i is shown together with the measured shear stress x as a function of the shear rate in Fig. 3.9. In the range of shear rates investigated, the shear stress in the case of silicone oil is substantially greater than the normal stress difference and we see substantially greater normal stress differences for viscoelastic PEO solution than for viscous silicone oil. 

Some simple methods of determining heat transfer rates to turbulent flows in a duct have been considered in this chapter. Fully developed flow in a pipe was first considered. Analogy solutions for this situation were discussed. In such solutions, the heat transfer rate is predicted from a knowledge of the wall shear stress. In fully developed pipe flow, the wall shear stress is conventionally expressed in terms of the friction factor and methods of finding the friction factor were discussed. The Reynolds analogy was first discussed. This solution really only applies to fluids with a Prandtl number of 1. A three-layer analogy solution which applies for all Prandtl numbers was then discussed. 

In the case of the Bingham plastic type of fluids, if the yield stress is higher than the characteristic shear stress in the contactor, the gas bubbles may not have any relative motion with respect to the rest of the fluid. For viscoelastic... 

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