Wall Shear Stress Measurements

As yet there appear to be no reports of wall shear stress measurements in liquid films with cocurrent gas streams. 

The wall shear stress measures the tangential component (per unit area) of the force exerted on a wall by a fluid flowing over it. It is a function of the velocity gradient of the fluid near the surface. Since direct methods are difficult to apply in micro- and nanofluidics, wall shear stress measiu ements mainly rely on the determination of the velocity gradient close to the wall. In this entry, different recording and evaluation methods are analyzed, and their uncertainty in estimating the wall shear stress is evaluated and compared to assess the performance of the methods. 

Wall Shear Stress Measurements, Fig. 1 Velocity profile in a microchannel and zoomed region close to the wall left and middle left). Velocity gradients in biological flows middle right) and structured walls with slip right)... 

Wall Shear Stress Measurements, Fig. 2 Schematic of a typical /tPIV system (/ ) and principle schematic of the imaging with reversed colors (right) (After [3])... 

Wall Shear Stress Measurements, Fig. 3 Schematic of in-plane velocity measurement. The inhomogeneous particle distribution and defocused particle images with different velocities due to out-of-plane gradients bias the results... 

Wall Shear Stress Measurements, Fig. 4 In-plane velocity profiles at the center of a microchannel evaluated with single-pixel ensemble correlation and particle tracking velocimetry... 

Wall Shear Stress Measurements, Fig. 5 Schematic of out-of-plane velocity gradient measurement. The velocity profiles are obtained from a scan of /tPIV... 

It is known that the structure of turbulence is altered by additives, particularly near the wall for example, the low speed streak spacing increases and the bursting frequency decreases. Moreover, velocity fluctuations in the mean flow direction become more violent, whereas the intensity of the fluctuations normal to the wall and the correlation between the two velocity fluctuations both decrease. With the help of additives the experimenter thus has a knob in hand with which he can control the structure of turbulence. In spite of this tool, it has still not been possible to better understanding of the mechanism of turbulence to the present date. On the contrary, drag reduction by additives poses additional problems. The measurement, for example, of turbulent velocity fluctuations is made much more difficult. Since the drag reduction phenomenon can only be observed when the wall shear stress measures at least about 7 N/m2 (46) measurements at small turbulent Reynolds numbers become almost impossible, and thus the region near the wall is practically inaccessible to anemometric measurements (either laser or hot film). It should therefore also prove very difficult to directly verify the existence of streamwise vortices in flows with polymer additives and thus answer the question posed by Willmarth and Bogar (42) as to whether the small-scale vortical structure near the wall is inhibited by polymer additives. 

A slit die is designed on the assumption that the material is Newtonian, using apparent viscous properties derived from capillary rheometer measurements, at a particular wall shear stress, to calculate the volumetric flow rate through the slit for the same wall shear stress. Using the correction factors already derived, obtain an expression for the error involved in this procedure due to the melt being non-Newtonian. Also obtain an expression for the error in pressure drop calculated on the same basis. What is the magnitude of the error in each case for a typical power law index n = 0.377... 

Like the von Karman equation, this equation is implicit in/. Equation (6-46) can be applied to any non-Newtonian fluid if the parameter n is interpreted to be the point slope of the shear stress versus shear rate plot from (laminar) viscosity measurements, at the wall shear stress (or shear rate) corresponding to the conditions of interest in turbulent flow. However, it is not a simple matter to acquire the needed data over the appropriate range or to solve the equation for / for a given flow rate and pipe diameter, in turbulent flow. 

By solving Eqs. (4) and (7) simultaneously, the mass flux can be calculated provided the wall shear stress is known as a function of particle superficial volume flow rate. Botterill and Bessant (1973) have proposed several relationships for shear stress, however, these are not general. LaNauze (1976) also proposed a method to measure this shear stress experimentally. 

This simple force balance has provided an extremely important result the wall shear stress for flow in a pipe can be determined from the frictional component of the pressure drop. In practice it is desirable to use the conditions in Example 1.7 so that the frictional component is the only component of the total pressure drop, which can be measured directly. 

The flow rate-pressure drop measurements shown in Table 3.1 were made in a horizontal tube having an internal diameter d, = 6 mm, the pressure drop being measured between two tappings 2.00 m apart. The density of the fluid, p, was 870 kg/m3. Determine the wall shear stress-flow characteristic curve and the shear stress-true shear rate curve for this material. 

In order to determine whether slip occurs with a particular material, it is essential to make measurements with tubes of various diameters. In equation 3.66, the value of the integral term is a function of the wall shear stress only. Thus, in the absence of wall slip, the flow characteristic 8 u/dt is a unique function of tw. However, if slip occurs, the term 8vjd will be different for different values of d, at the same value of tu., as shown in Figure 3.11. It is clear from equation 3.66 that for a given value of the slip velocity vs, the effect of slip is greater in tubes of smaller diameter. If the effect of slip is dominant, that is the bulk of the material experiences negligible shearing, then it can be seen from equation 3.66 that on a plot of... 

If the material whose viscometric properties were determined in question 3-4 were pumped through a 25 mm diameter pipe so that the wall shear stress had the value corresponding to the last measurement in that question, what would be the volumetric average velocity and what value of pressure gradient would be required ... 

The melt Index test measures the flow property at a fixed wall shear stress In the capillary. The shear stress depends on the load specified for the condition and it is provided in Table 3.8. The apparent shear rate at the capillary wall that the resin experiences depends on the Ml value measured, and it can be calculated using a modification of Eq. 3.33 as follows ... 

Consider the fully developed steady flow of an incompressible around a circular channel that has an inner radius of n and an outer radius of rD (Fig. 4.28). The objective is to derive a general relationship for the friction factor as a function of flow parameters (i.e., Reynolds number) and channel geometry (i.e., hydraulic diameter Dh and the ratio = r, /r0). A friction factor /, which is a nondimensional measure of the wall shear stress, may be defined as... 

Experimental measurements of the wall shear stress exerted by a falling liquid film have been reported for the cases of film flow outside a vertical tube (B14) and in a channel of variable slope (F7). In both cases the experimental results in the zone of smooth laminar flow were in agreement... 

Adomi et al. (Ala), 1963 An instrument is described for measuring the wall shear stress in a two-phase flow in the presence of a pressure gradient and a changing velocity profile. 

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