Boundary Viscosity

8 BLOW-OFF METHOD FOR INVESTIGATION OF BOUNDARY VISCOSITY OF VOLATILE LIQUIDS 

A blow-off method allows determining the boundary viscosity as a function of the distance to a solid substrate. A theory is suggested, taking into account not only the flow of a liquid film but also its evaporation, with gas being blown through a plane-parallel channel over the film. The theory allows one to find the dependence of the dynanuc viscosity, q, on the distance to the substrate, h, with q being a continuous function of h. A procedure is outlined for calculation of the viscosity, q, on dependency based on experimental data. The theory is applied to the calculation of the boundary viscosity of hexadecane. It turns out that the viscosity in thin layers (40-200 A) is lower than that in the bulk [35,57]. 

The measurements of the boundary viscosity are of substantial interest. Attanpts have been made to apply the conventional methods adapted to the measurement of boundary viscosity. These methods may be divided into three groups  

These methods afford the possibility of determining only the mean value of viscosity for a sufficiently thick layer. 

If the liquid viscosity over the whole distance to the wall is invariable, the slope remains constant until the wetting boundary is reached. In the case of an increased viscosity close to the wall, the slope increases in the case of a decreased viscosity, the slope decreases. The viscosity is calculated from the slope at a given point of the profile. 

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The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries. Viscosity is the fluid resistance to shear or flow and is a measure of the adhesive/cohesive or frictional fluid property. The resistance is caused by intermolecular friction exerted when layers of fluids attempt to slide by one another. 

The blow-off method was used to examine the boundary viscosity of some organic liquids [31]. It has been established that the profile of a film of very pure... 

Up to now, a limitation of the blow-off method has been its inapplicabiUty to the measurement of the boundary viscosity of volatile liquids. In this section, the blow-off method has been modified so as to be applicable to studies of the boundary viscosity of volatile Uquids. It is necessary to take into account the fact that when gas is blown through a plane-parallel channel, the flow of a film of liquid occurs (as in the usual variant of the blow-off method) simultaneously with its evaporation. 

The theory of the blow-off method, allowing determining the boundary viscosity of volatile liquids, is developed in the following text. 

Consider conseqnences of the solution obtained. If there is no special boundary viscosity, i.e., ti(/j) = r = const, then... 

The experimental device used for studying the boundary viscosity of volatile substances was substantially the same as that for nonvolatile liquids (Figure 3.20). 

FIGURE 3.20 Schematic diagram of the experimental device for investigations of the boundary viscosity of liquids. 

The experimental data were processed according to Equation 3.298, which gives the dependence of the boundary viscosity on film thickness. 

Figure 3.22 represents the deduced dependences of the boundary viscosity on film thickness. Figure 3.22 shows that in the thickness range from 50 to 200 A, the viscosity of hexadecane is lower than the bulk viscosity of liquid. 

FIGURE 3.22 Calculated dependencies of the boundary viscosity of hexadecane on the film thickness. Curves from 1 to 4 corresponds to curves from 1 to 4 in Figure 3.21. 

The theory thus developed allows us to determine the boundary viscosity as a function of the distance to the substrate, r (h). The dependency is determined according to Equation 3.298, using the extension procedure set forth in (iii). 

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability (k) and reservoir thickness (h), by the oil properties viscosity (p) and formation volume factor (BJ and by any change in the resistance to flow near the wellbore which is represented by the dimensionless term called skin (S). For semisteady state f/owbehaviour (when the effect of the producing well is seen at all boundaries of the reservoir) the radial inflow for oil into a vertical wellbore is represented by the equation ... 

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]. 

In the Smoluchowski limit, one usually assumes that the Stokes-Einstein relation (Dq//r7)a = C holds, which fonns the basis of taking the solvent viscosity as a measure for the zero-frequency friction coefficient appearing in Kramers expressions. Here C is a constant whose exact value depends on the type of boundary conditions used in deriving Stokes law. It follows that the diffiision coefficient ratio is given by ... 

K) were investigated. From an equation of state for iron the densities at these temperatures could be predicted to enable the simulations to be performed. A periodic system containing 64 atoms was used and the simulation run for 2 ps after equilibration. The calculated pressure agreed within 10% with the experimental values (330 GPa at the inner core boundary and 135GPa at the core-mantle boundary). Additional parameters could also be calculated, including the viscosity, the values for which were at the low end of previous suggestions. 

Molecular dynamics calculations are more time-consuming than Monte Carlo calculations. This is because energy derivatives must be computed and used to solve the equations of motion. Molecular dynamics simulations are capable of yielding all the same properties as are obtained from Monte Carlo calculations. The advantage of molecular dynamics is that it is capable of modeling time-dependent properties, which can not be computed with Monte Carlo simulations. This is how diffusion coefficients must be computed. It is also possible to use shearing boundaries in order to obtain a viscosity. Molec-... 

It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a flowing liquid with laminar flow. This makes it possible to compute properties not measurable in a static fluid, such as the viscosity. Nonequilibrium simulations give rise to additional technical difficulties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work. 

High Water-Base Fluids. These water-base fluids have very high fire resistance because as Httle as 5% of the fluid is combustible. Water alone, however, lacks several important quaUties as a hydrauHc fluid. The viscosity is so low that it has Httle value as a sealing fluid water has Httle or no abiHty to prevent wear or reduce friction under boundary-lubrication conditions and water cannot prevent mst. These shortcomings can be alleviated in part by use of suitable additives. Several types of high water-based fluids commercially available are soluble oils, ie, od-in-water emulsions microemulsions tme water solutions, called synthetics and thickened microemulsions. These last have viscosity and performance characteristics similar to other types of hydrauHc fluids. 

Because the reaction takes place in the Hquid, the amount of Hquid held in the contacting vessel is important, as are the Hquid physical properties such as viscosity, density, and surface tension. These properties affect gas bubble size and therefore phase boundary area and diffusion properties for rate considerations. Chemically, the oxidation rate is also dependent on the concentration of the anthrahydroquinone, the actual oxygen concentration in the Hquid, and the system temperature (64). The oxidation reaction is also exothermic, releasing the remaining 45% of the heat of formation from the elements. Temperature can be controUed by the various options described under hydrogenation. Added heat release can result from decomposition of hydrogen peroxide or direct reaction of H2O2 and hydroquinone (HQ) at a catalytic site (eq. 19). 

Because EP additives ate effective only by chemical action, their general use should be avoided to minimize possible corrosion difficulties and shortened lubricant life in any appHcation where they ate not necessary. For long-time operation of machines, conversion from boundary to hill-film operation is desirable through changes such as higher oil viscosity, lowered loading, or improved surface finish. 

Sihcate solutions of equivalent composition may exhibit different physical properties and chemical reactivities because of differences in the distributions of polymer sihcate species. This effect is keenly observed in commercial alkah sihcate solutions with compositions that he in the metastable region near the solubihty limit of amorphous sihca. Experimental studies have shown that the precipitation boundaries of sodium sihcate solutions expand as a function of time, depending on the concentration of metal salts (29,58). Apparently, the high viscosity of concentrated alkah sihcate solutions contributes to the slow approach to equihbrium. 

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