Retarded forces

Before we move on to consider the interaction between macroscopic bodies, let us look briefly at the phenomenon of retardation . The electric field emitted by an instantaneously polarized neutral molecule takes a finite time to travel to another, neighbouring molecule. If the molecules are not too far apart the field produced by the induced dipole will reach the first molecule before it has time to disappear, or perhaps form a dipole in the opposite direction. The latter effect does, however, occur at larger separations ( 5 nm) and effectively strengthens the rate of decay with distance, producing a dependence of 1/R instead of 1/R . 

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From the value given above for maximum retarding force... 

If the drag force of the atmosphere is negligible, the retarding force for laminar flow is attributable to the viscous drag in the liquid at the distance v from the surface given by ... 

A shear force resulting from the shear stress Ro acting at the surface. This is a retarding force and therefore Rq is negative. 

Thus, the net force acting F is just the retarding force attributable to the shear stress at the surface only and... 

Equating die net momentum flux out of the element to the net retarding force (equations 11.6 and 11.7) and simplifying gives ... 

It is assumed here that the fluid in contact with the surface is at rest and therefore h(j must be zero. Furthermore, all the fluid close to the surface is moving at very low velocity and therefore any changes in its momentum as it flows parallel to the surface must be extremely small. Consequently, the net shear force acting on any element of fluid near the surface is negligible, the retarding force at its lower boundary being balanced by the accelerating force at its upper boundary. Thus the shear stress Ro in the fluid near the surface must approach a constant value. 

The mean velocity of migration Vj depends on the external driving force = ZjFE and on the resistance to motion set up by the medium s viscosity. This retarding force as a rule is proportional to the velocity. Under the influence of the external force, the velocity will increase until it attains the value Vj where the retarding force VjQ (9 is the drag coefficient) becomes equal to the external driving force. Hence,... 

The retarding force F2 on the particle from the fluid is given by the equation... 

The movement of the analyte is an essential feature of separation techniques and it is possible to define in general terms the forces that cause such movement (Figure 3.1). If a force is applied to a molecule, its movement will be impeded by a retarding force of some sort. This may be as simple as the frictional effect of moving past the solvent molecules or it may be the effect of adsorption to a solid phase. In many methods the strength of the force used is not important but the variations in the resulting net force for different molecules provide the basis for the separation. In some cases, however, the intensity of the force applied is important and in ultracentrifugal techniques not only can separation be achieved but various physical constants for the molecule can also be determined, e.g. relative molecular mass or diffusion coefficient. 

The stress at the interface was measured as a function of temperature and sliding velocity for the resin using the equipment shown in Fig. 4.11, and the data are shown in Fig. 12.33. The stress curve had two maximums the first peak was at the Tg of the resin at 150 °C, and the second peak occurred at a temperature of about 240 °C. In order to maximize solids conveying while maintaining a viable process, the optimal forwarding forces would occur at a barrel surface temperature near 240 °C, and the retarding forces at the screw surfaces would be minimized at temperatures less than about 120 °C. In order to maintain the high rate of this line and the inside barrel wall at a temperature near 240 °C, the first zone of the extruder needed to be maintained at a temperature of 310 °C. 

Fs= retarding force and centered on surface. p4= retarding force and centered on surface. 

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