Interfacial slip

The effects of wall slip, interfacial properties, drop size distribution, and drop deformability in emulsions have been discussed in References [134,140-143]. The performance of bio-emulsions was considered by Stokes et al. [144] and Danker et al. [145]. 

Yoshizawa FI and Israelaohvili J N 1993 Fundamental mechanisms of interfacial friction. 2. Stick-slip friction of spherical and chain molecules J. Phys. Chem. 97 11 300-13... 

The dependence of release force on the flexibility of the release layers is noted in systems other than silicones. Recent work in olefin release shows that release is a strong function of the density or crystallinity of the layer [44], At a density above 0.9 g/cm release for an acrylate PSA is greater than 270 g/cm. However, when the density of PE is dropped to 0.865 g/cm-, the release force of the same adhesive construction drops to 35 g/cm. An investigation of interfacial friction and slip in these systems has not yet been reported, but again the manipulation of release rheology greatly impacts the measured peel force. 

Fig. 14—Interfacial slip revealed by the velocity profile from simulations of confine liquid decane the step in the profile at location f indicating a velocity discontinuity between the wall and the molecules adjacent to the wall [26].

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

Wang, H. and Hu, Y. Z., Molecular Dynamics Study on Interfacial Slip Phenomenon of Ultra-thin Lubricating Films," presented 2XITC2000, Nagasaki, Japan, Oct. 2000. 

In summary, sliding can be regarded as a process during which interfacial atoms would experience a series of stick-slip motions, similar to the jump in and out in the adhesion case, and it is the energy loss in this approach/separation cycle that determines the level of friction. 

From the point of view of system d5mamics, the transition from rest to sliding observed in static friction originates from the same mechanism as the stick-slip transition in kinetic friction, which is schematically shown in Fig. 31. The surfaces at rest are in stable equilibrium where interfacial atoms sit in energy minima. As lateral force on one of the surfaces increases (loading), the system experiences a similar process as to what happens in the stick phase that the surface... 

As shown in Section I, very little is known about predicting liquid-liquid flow patterns and calculating pressure drops, holdups, and interfacial areas however, some estimates can be made by assuming no slip between the phases, using... 

This latter case is the same result as Einstein calculated for the situation where slip occurred at the rigid particle-liquid interface. Cox15 has extended the analysis of drop shape and orientation to a wider range of conditions, but for typical colloidal systems the deformation remains small at shear rates normally accessible in the rheometer. The data shown in Figure 3.11 was calculated from Cox s analysis. His results have been confirmed by Torza et al.16 with optical measurements. The ratio of the viscous to interfacial tension forces, Rf, was given as ... 

This ratio implies that slip will increase as the bulk viscosity increases relative to the interfacial viscosity, or as the liquid self-cohesiveness increases and the liquid-surface affinity decreases. 

The dependence of slip on the interaction strength of the surface and liquid was studied early on by Tolstoi [3], later revisited by Blake [12], a model that is linked to interfacial viscosity. Tolstoi modeled the surface using Frenkel s model for the bulk mobility of a liquid molecule [38],... 

Tj is the slip relaxation time, or sliptime, which is the relaxation time for the monolayer slip velocity as it decays. For a rigidly bound monolayer, the velocity will decay very rapidly, at a rate comparable to the relaxation of the surface itself and will be near zero, yielding large interfacial friction and no slip. However, if the surface-monolayer bonds are highly dissipative, the time constant will be large and appreciable slip will occur. Reauanging Eq. (10) and equating to Eq. (14), we arrive at... 

The authors noted that when their friction parameter M= (pG/,) 8/G is real, it is equivalent to the real slip parameter s = fe used by McHale et al. [14]. From this analysis, a real interfacial energy G /8 is related to the slip length b, for a purely viscous fluid, by... 

The presence of a low-viscosity interfacial layer makes the determination of the boundary condition even more difficult because the location of a slip plane becomes blurred. Transitional layers have been discussed in the previous section, but this is an approximate picture, since it stiU requires the definition of boundary conditions between the interfacial layers. A more accurate picture, at least from a mesoscopic standpoint, would include a continuous gradient of material properties, in the form of a viscoelastic transition from the sohd surface to the purely viscous liquid. Due to limitations of time and space, models of transitional gradient layers will be left for a future article. 

In most problems involving boundary conditions, the boundary is assigned a specific empirical or deterministic behavior, such as the no-slip case or an empirically determined slip value. The condition is defined based on an averaged value that assumes a mean flow profile. This is convenient and simple for a macroscopic system, where random fluctuations in the interfacial properties are small enough so as to produce little noise in the system. However, random fluctuations in the interfacial conditions of microscopic systems may not be so simple to average out, due to the size of the fluctuations with respect to the size of the signal itself. To address this problem, we consider the use of stochastic boundary conditions that account for random fluctuations and focus on the statistical variability of the system. Also, this may allow for better predictions of interfacial properties and boundary conditions. 

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