Viscosity thin-film model

The traditional, essentially phenomenological modeling of boundary lubrication should retain its value. It seems clear, however, that newer results such as those discussed here will lead to spectacular modification of explanations at the molecular level. Note, incidentally, that the tenor of recent results was anticipated in much earlier work using the blow-off method for estimating the viscosity of thin films [68]. 

The theory of seaweed formation does not only apply to solidification processes but in fact to the completely different phenomenon of a wettingdewetting transition. To be precise, this applies to the so-called partial wetting scenario, where a thin liquid film may coexist with a dry surface on the same substrate. These equations are equivalent to the one-sided model of diffusional growth with an effective diffusion coefficient which depends on the viscosity and on the thermodynamical properties of the thin film. 

This work shows that high shear rates are required before viscous effects make a significant contribution to the shear stress at low rates of shear the effects are minimal. However, Princen claims that, experimentally, this does not apply. Shear stress was observed to increase at moderate rates of shear [64]. This difference was attributed to the use of the dubious model of all continuous phase liquid being present in the thin films between the cells, with Plateau borders of no, or negligible, liquid content [65]. The opposite is more realistic i.e. most of the liquid continuous phase is confined to the Plateau borders. Princen used this model to determine the viscous contribution to the overall foam or emulsion viscosity, for extensional strain up to the elastic limit. The results indicate that significant contributions to the effective viscosity were observed at moderate strain, and that the foam viscosity could be several orders of magnitude higher than the continuous phase viscosity. 

The first milestone in modeling the process is credited to Pearson and Petrie (42—44). who laid the mathematical foundation of the thin-film, steady-state, isothermal Newtonian analysis presented below. Petrie (45) simulated the process using either a Newtonian fluid model or an elastic solid model in the Newtonian case, he inserted the temperature profile obtained experimentally by Ast (46), who was the first to deal with nonisothermal effects and solve the energy equation to account for the temperature-dependent viscosity. Petrie (47) and Pearson (48) provide reviews of these early stages of mathematical foundation for the analysis of film blowing. 

Thin solid films of polymeric materials used in various microelectronic applications are usually commercially produced the spin coating deposition (SCD) process. This paper reports on a comprehensive theoretical study of the fundamental physical mechanisms of polymer thin film formation onto substrates by the SCD process. A mathematical model was used to predict the film thickness and film thickness uniformity as well as the effects of rheological properties, solvent evaporation, substrate surface topography and planarization phenomena. A theoretical expression is shown to provide a universal dimensionless correlation of dry film thickness data in terms of initial viscosity, angular speed, initial volume dispensed, time and two solvent evaporation parameters. 

In this chapter we review molecular dynamics simulations of thin films confined between two surfaces under shear. Potential models, temperature regulation methods, and simulation techniques are presented. Three properties (friction, shear viscosity, and flow boundary condition) that relate the dynamic response of confined thin films to the imposed shear velocity are presented in detail. 

Problem 6-7. Coating Flows The Drag-Out Problem A very important model problem in coating theory is sometimes called the drag-out problem. In this problem, a flat plate is pulled through an interface separating a liquid and a gas at a prescribed velocity U. The primary question is to relate the pull velocity U to the thickness // of the thin film that is deposited on the moving plate. We consider the simplest case in which the plate is perpendicular to the horizontal interface that exists far from the plate. The density of the liquid is p, the viscosity //, and the surface tension y. 

The above observations can be explained as follows. Once the tip of the gaseous phase enters the orifice, it fills almost the entire cross-section of this microchannel. This is because the value of the capillary number is low the interfacial forces dominate the shear stress, the tip assumes a compact, and area-minimizing shape, and restricts the flow of the continuous liquid to thin films between the interface and the walls of the orifice. As the flow in thin films is subject to an increased viscous dissipation (and resistance) the liquid inflowing from the inlet channels cannot pass through the orifice. Instead, the pressure upstream of the orifice rises and the liquid squeezes the neck of the stream of gas. As the rate of inflow of the continuous liquid is externally fixed to a constant value, this squeezing proceeds at a rate that is strictly proportional to Q and independent of all the other parameters (pressure, viscosity of the liquid, the value of interfacial tension). This model has been confirmed in detailed experiments by Marmottant et al. [22],... 

The coefficients of viscosity (fy) and the modulus of elasticity (Y,) for the Maxwell (i = 1) and Kelvin units (i = 2) according to the Burgers Model, had the same behavior (Figures 1-4), increasing with thickness of all the films, according to a power law model, with important variation in the thin films, excepting the Y, that present a low value of regression coefficient (R2 = 0.33). 

The theoretical findings of thin-film drainage models clearly suggest the important role that surface viscosities and elasticities play in foam sta-... 

FIGURE 12.4. Film drainage in foams can be modeled as a thin film of liquid of thickness, 8, between two parallel vertical plates of width, w. The rate of hydraulic (gravity-driven) drainage will depend on the viscosity of the liquid as well as other factors, as is found in real foams [Eq. (12.3)]. 

The coefficients of friction for these mlcro-elasto-hydrodynamlc models are still small compared with experimental values. If allowance is made for an Increase In the effective viscosity as the films become small, according to the methods adopted earlier In boosted lubrication analysis, the maximum coefficient of friction rises to about 0.004. It appears that a more complete analysis of friction in synovial joints must await further clarification of the rheological behaviour of synovial fluid In thin films at very high shear rates. 

Abstract The structure and mechanics of very thin hquid crystal films depend on the intermolecular interactions in confined dimensions. The rheology of such films has been investigated by a shear force apparatus constructed as an attachment to the surface forces apparatus. The novelty of this method is that the rheological parameters are extracted from the amplitude and the phase of the output signal as a function of the resonance frequency. The apparent viscosity of the liquid crystal film is calculated from the damping coefficient by using a simple theoretical model. The viscosity of nanometer thin films of 4-cyano-4-... 

A theoretical framework is developed to predict curvature of sintering thin film deposited on presintered substrate for three different heating rates as a way for validating a constrained sintering model developed recently. Using universal expression for free sintering rate and viscosity and estimating... 

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