Stick condition

Equation (7.11) is for the stick condition, i.e. when the solvent immediately adjacent to the spherical particle wets it and so moves along with it. Equation (7.12), on the other hand, is for the slip condition, i.e. when the spherical particle is completely slippery and does not drag along any liquid with it. When the spherical particle is an ion with charge z e and it is in the liquid under a potential gradient X (Vein ), a force/expressed by Eq. (7.13) operates on the particle ... 

Figure 3 Sticking condition of the lOM-layer with the thickness of 1 mm impacted by a copper ball with a diameter of I cm.

Mechanisms of heat generation between the pin tool and the workpiece are also due to friction or plastic dissipation, depending on whether slide or stick conditions prevail at the interface. The amount of heat input from deformational heating around the pin tool has been estimated to range from 2% (Ref 5) to 20% (Ref 6). 

Figure 1 Transverse shear viscosity versus engineering strain for various cross-head speeds (full-stick condition).

Keywords squeeze flow, Plytron , full-slip condition, full-stick condition, unidirectional continuous-fiber reinforced composites, shear thinning fluid, Carreau fluid, APC-2, composite laminate, UD laminate. 

The fundamental rate expression to be considered is the Smoluchowski relation k = 4n iVDAB AB (Equation (2.1)). The derived expression ART/r] (Equation (2.3a)), is a useful approximation, but deviations from it are observed, because the Stokes-Einstein equation which is involved is derived by hydrodynamic theory for spherical particles moving in a continuous fluid, and does not accurately represent the measured values of translational diffusion coefficients in real systems. Although the proportionality Da 1 /rj is indeed a reasonable approximation for many solutes in common solvents, the numeral coefficient 1 /4 is subject to uncertainty. In the first place, this theoretical value derives from the assumption that in translational motion there is no friction between a solute molecule and the first layer of solvent molecules surrounding it, i.e., that slip conditions hold. If, however, one assumes instead that there is no slipping ( stick conditions), so that momentum is... 

Table 3.2 Reorientational rotation times in solution, compared with theoretical values for diffusion with slip or stick conditions. Experimental plots for solutes in various low-polar solvents (as in Figure 3.10) show that the rotational relaxation time r is linearly related to the viscosity (r = Zq +Ct], where Tq is small), and depends on no other solvent property. The table compares experimental values of C with values calculated (a) for slip conditions and (b) for stick conditions, the solute molecules being approximated to ellipsoids, with axial ratio a/b. Data from Ref. [16]. See text and Figure 3.11...

A velocity gradient exists between the surface of the sphere and the bulk of the liquid which is at rest. Here it is assumed that a liquid layer adjacent to the surface sticks to the sphere (sticking condition). The sphere is attaining the constant velocity Vq and the sum of the forces on the sphere has to cancel, such that... 

The results from the coarse mesh from the presented above algorithm are presented in Figure 5. The directions of the horizontal reactions and the horizontal displacements axe are in the directly oposite directions and small in the left lower corner (Figure 5, left) what means that the block is kept in place by the frictional forces concentrated in the lower left part of the surface where the stick conditions occurs. 

As with the case for the impenetrability constraint, the tangential (stick-slip) constraints are also gradually enforced. The frictional slip is determined from a line search along the steepest descent direction M (Gr) (Pxr ), and the rate constraints are active during the Newton iterations while assuming sticking conditions, that is. 

For the sliding speed of the linear part of the micro-slip phase, the flow of the strongly adhesive third strongly is activated - internal flow activated -according to 4.1. This activation physically represents the theoretical stick condition as defined by Kalker s models [7]. 

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