Internal friction weakness

A pressure dependence of the internal angle of friction is known to represent the quantification of the pore space dependence of internal friction [3], Such a dependence has also been observed in wall friction experiments for the bed friction angle [5, 13] of soil. So, we must assume 6 = 6(p) and pressure dependence of friction angle with pressure [3,5,13], the simplest parameterisation is linear and we choose... 

We shall see that the sum p(V u) + T E on the right-hand side of (2 52) represents the conversion of kinetic energy to heat, due to the internal friction within the fluid and is known as the viscous dissipation term. The last term on the left-hand side of (2 52) is related to the work required for compressing the fluid. Although this term is identically zero only for constant-pressure conditions (that is, the material is a solid or it is stationary so that Dp jDt = 0), it is frequently small compared with other terms in (2-52) because the density at constant pressure is only weakly dependent on the temperature, and we shall generally adopt this approximation in the analyses of nonisothermal systems in later chapters. 

It is not easy to measure internal friction processes. For example, the contributions of eqs. (VI. 103, VI. 104) do not show up in the static viscosity for weak flows. This can be understood as follows. To discuss the viscosity increment 5t) due to our dilute coils, we may choose any type of (weak) shear flow. It is then convenient (as noted first hy Kramers ) to choose a longitudinal shear flow, such as the one shown in eq. (VI.6S). In this situation the molecule does not rotate but simply stretches to a certain equilibrium length r (for a given shear rate s). Internal friction is involved only if the chain varies its length (or, equivalently, its conformations). In the present case the length is constant, and there is no dissipation associated with internal friction. 

A torsion pendulum is a particular useful device for examining the modulus and internal friction of polymers. When the sample geometry is in the form of a cone-and-plate or concentric cylinders, the pendulum can be used for very weak gels, which are hard to characterize in conventional testing machines. Commercial models are available which give a complete record of amplitude versus time. However, even mannal estimation of the frequency of oscillation and the number of cycles to decrease the amplitude by some factor can be quite useful. 

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

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