Shear, force

Betzig E, Finn P L and Weiner J S 1992 Combined shear force and near-field scanning optical microscopy/4pp/. Phys. Lett. 60 2484... 

Figure Bl.20.15. Shear force as a fimction of time for (a) bare mica in toluene and (b) polystyrene-covered mica in toluene. Reproduced with pennission from [9],...

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

Figure C2.9.2 Shear force versus time during (a) sliding and (b) stick-slip motion. The motion of the surface beneath the sliding block of figure C2.9.1 is at constant velocity.

Three common types of nozzle are shown diagrammatically. Types A and K are similar, with sharp cutoffs on the ends of the outer and inner capillaries to maximize shear forces on the liquid issuing from the end of the inner tube. In types K and C, the inner capillary does not extend to the end of the outer tube, and there is a greater production of aerosol per unit time. These concentric-tube nebulizers operate at argon gas flows of about 1 1/min. 

There are three major aspects of polymer viscosity discussed in this chapter. First, we shall consider the fact that most bulk polymers display shear-dependent viscosity that is, this property does not have a single value but varies with the shearing forces responsible for the flow. Second, the molecular weight dependence of polymer viscosity is examined. We may correctly expect a... 

The radius R also applies to the entire fluid sample. Since torque equals the product of force and R, canceling out one power of R leaves the shearing force acting on the fluid on the left-hand side of Eq. (2.7). 

Figure 2.5 Shearing force per unit area versus shear rate. The experimental points are measured for polyethylene, and the labeled lines are drawn according to the relationship indicated. (Data from J. M. McKelvey, Polymer Processing, Wiley, New York, 1962.)...

Figure 2.7 Potential energy as a function of location along the reaction coordinate. The solid line describes an undisturbed liquid the broken line applies to liquids subjected to shearing force.

Suppose we divide the flow segments into classes according to relaxation times and index the various states by the subscript i. Thus the relaxation time and the component of shear stress borne by the segments in class i are and Fj, respectively. The applied shear force is related to the Fj s through... 

Until now we have restricted ourselves to consideration of simple tensile deformation of the elastomer sample. This deformation is easy to visualize and leads to a manageable mathematical description. This is by no means the only deformation of interest, however. We shall consider only one additional mode of deformation, namely, shear deformation. Figure 3.6 represents an elastomer sample subject to shearing forces. Deformation in the shear mode is the basis... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

In Sec. 2.2 we saw that the coefficient of viscosity is defined as the factor of proportionality between the shearing force per unit area = F /A and the velocity gradient dv/dy within a liquid [Eq. (2.2)] ... 

The shearing force that is part of the definition of viscosity can also be analyzed in terms of Newton s second law and written as... 

From Eq. (9.1) we see that the viscous force associated with this motion equals [i7(dv/dr)] (area), where the pertinent area is proportional to the surface of the sphere and varies as. This qualitative argument suggests that the viscous force opposing the relative motion of the liquid and the sphere is propor tional to [t7(v /R)] (R ). The complete solution to this problem reveals that both pressure and shear forces arising from the motion are proportional tc 77Rvj., and the total force of viscous resistance is given by... 

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... 

Now we return to consider the energy that must be dissipated in a unit volume of suspension to produce a unit gradient, as we did above with the pure solvent. The same fraction applied to the shearing force will produce the unit gradient, and the same fraction also describes the volume rate of energy dissipation compared to the situation described above for pure solvent. Since the latter was Po, we write for the suspension, in the case of dv/dy = 1,... 

Fig. 1. Normal and shear forces on a differential volume dx-dy-dz, where + di and + (- ) di.

To illustrate the use of the momentum balance, consider the situation shown in Figure 21c in which the control volume is bounded by the pipe wall and the cross sections 1 and 2. The forces acting on the fluid in the x-direction are the pressure forces acting on cross sections 1 and 2, the shear forces acting along the walls, and the body force arising from gravity. The overall momentum balance is... 

The work term IF is restricted to the mechanical work deflvered to the outside via normal and shear forces acting on the boundary. Electrochemical work, ie, by electrolysis of the fluid, is excluded. Evaluation of the integral requires knowledge of the equation of state and the thermodynamic history of the fluid... 

Surface Tension. Interfacial surface tension between fluid and filter media is considered to play a role in the adhesion of blood cells to synthetic fibers. Interfacial tension is a result of the interaction between the surface tension of the fluid and the filter media. Direct experimental evidence has shown that varying this interfacial tension influences the adhesion of blood cells to biomaterials. The viscosity of the blood product is important in the shear forces of the fluid to the attached cells viscosity of a red cell concentrate is at least 500 times that of a platelet concentrate. This has a considerable effect on the shear and flow rates through the filter. The surface stickiness plays a role in the critical shear force for detachment of adhered blood cells. 

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