Viscous flow, correlation with

In Fig.la a lower slope ((j)=2.25) and higher Intercept (g=1.32) Is obtained for the low pressure region as compared to the slope (((>=2.60) and Intercept (g=1.09) for high pressure region. Since from Eq(13), a value of g close to 1 implies adherence to the solution-diffusion model. It appears that at low pressures where g = 1.32>1.0, a combined model of viscous and diffusive flow Is operative. This correlates with previous SEM studies In our laboratory (unpublished), where mlcro-pln holes were postulated to exist In the skin. The presence of such m-LcAO-p-Ln hoZ 6 In the surface can be used to explain the high g-value. Above 10 atm, the DDS-990 membrane Is compressed or compacted and the mlcro-pln holes filled. Thus g = l.O l.O implies adherence to the solution-diffusion model. 

Viscous flow permeametry measured near atmospheric pressure offers the advantages of experimental simplicity and a means of measuring the external or envelope area of a powder sample which is otherwise not readily available by any adsorption method. The usefulness of measuring the external surface area rather than the BET or total surface area becomes evident if the data is to be correlated with fluid flow through a powder bed or with the average particle size. 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

The frequency correlation time xm corresponds to the time it takes for a single vibrator to sample all different cavity sizes. The fluctuation-dissipation theorem (144) shows that this time can be found by calculating the time for a vertically excited v = 0 vibrator to reach the minimum in v = 1. This calculation is carried out by assuming that the solvent responds as a viscoelastic continuum to the outward push of the vibrator. At early times, the solvent behaves elastically with a modulus Goo. The push of the vibrator launches sound waves (acoustic phonons) into the solvent, allowing partial expansion of the cavity. This process corresponds to a rapid, inertial solvent motion. At later times, viscous flow of the solvent allows the remaining expansion to occur. The time for this diffusive motion is related to the viscosity rj by Geo and the net force constant at the cavity... 

In both the cases, the activation energy of the infiltration process (Fig. 1) is practically the same ( 40 kJ/mol) and close to that of the cobalt viscous flow (37.3 kJ/mol) [8], i.e. the observed variations in kinetics of the infiltration are caused by the difference between viscosities of cobalt and its alloys. According to [8] y= Aq exp(Ea/RT), where y is the kinematic viscosity, Aq is the constant, Ea is the activation energy of viscous flow, R is the universal gas constant, T is the absolute temperature. Correlating this formula with Eq. (2) and considering that q = py, where p is the density of the liquid, we have for k ... 

Hard sphere systems are characterized by viscous flow and for low solids loading (less than 5%) they can be described as Newtonian fluid. At higher loadings, cluster formation takes place and the fluid cau acquire shear thinning or thickening behavior. The viscosity and solids loading are correlated with the... 

Some correlations of multipliers are listed in Table 6.7. Lockhart and Martinelli distinguish between the various combinations of turbulent and laminar (viscous) flows of the individual phases in this work the transition Reynolds number is taken as 1000 instead of the usual 2000 or so because the phases are recognized to disturb each other. Item 1 of Table 6.7 is a guide to the applicability of the Lockhart-Martinelli method, which is the oldest, and two more recent methods. An indication of the attention that has been devoted to experimentation with two phase flow is the fact that Friedel (1979) based his correlation on some 25,000 data points. 

The past 5 years have seen considerable progress in the development of whole-earth mantle convection models that show excellent correlations with subduction and mid-ocean ridge patterns, allowing us to begin to model the interactions between asthenospheric flow and the heterogeneous plates moving in response to this flow. Doin et al. (1997) examined controls of asthenospheric flow on plate thickness, and considered thick cratonic roots. Their 3D simulations indicate that cratonic roots are stable only if the root is buoyant and more viscous than normal continental lithosphere. Sleep (1994, 1997) has used these 3D models to parameterize a numerical model of plume-lithosphere interactions... 

However, if convective transport of heat and species mass in porous catalyst pellets have to be taken into account simulating catal3dic reactor processes, either the Maxwell-Stefan mass flux equations (2.394) or dusty gas model for the mass fluxes (2.427) have to be used with a variable pressure driving force expressed in terms of mass fractions (2.426). The reason for this demand is that any viscous flow in the catalyst pores is driven by a pressure gradient induced by the potential non-uniform spatial species composition and temperature evolution created by the chemical reactions. The pressure gradient in porous media is usually related to the consistent viscous gas velocity through a correlation inspired by the Darcy s law [21] (see e.g., [5] [49] [89], p 197) ... 

Pusher -700 and xanthan gum have larger molecular sizes in solution than Colloid and hydroxy ethyl cellulose. The dimensions in solution decrease with increasing salt concentration. Polyacrylamides are affected most severely by the presence of electrolytes. Polysaccharides are also affected by salt, but not to the same extent as polyacrylamides. Hydroxy ethyl cellulose is the most insensitive polymer to salt. Temprature can be inversely correlated with viscosity. Polyacrylamides have low activation energies for viscous flow. In order of decreasing temperature dependency are xanthan gum, Colloid , and hydroxy ethyl cellulose. 

Experimental data associated with gases, water, and viscous oils may be correlated with Eq. (5.150) as shown in Fig 5.22(a), where Rec denotes the critical Reynolds number at which the laminar flow is unstable. Beyond Rec the forced convection eventually becomes turbulent. Equation (5.150) does not correlate the liquid metal data. For liquid metals, viscous forces are small, the momentum equation degenerates to a limit of uniform velocity, and the importance of the Reynolds number diminishes. Consequently, as shown in Fig. 522(b),... 

Effect of nonseparating flow. The effect of nonseparating viscous flow on the barrier separation efficiency depends on the detailed structure of the barrier. Because the theoretical derivation of this effect for the viscous leak model can be worked out simply and completely, this model will be dealt with first. Then results for the mixed flow model derived by Present and de Bethune [P3] will be summarized and both models will be compared with empirical correlations of separation performance suggested by experimental investigators of barrier performance. 

Figure 23-2 Dimensionless correlations between reactant molar density and channel length for viscous flow in square ducts, plug flow in square ducts, and viscous flow in tubes with the same effective diameter for first-order irreversible chemical kinetics and uniform catalyst activity when the Damkohler number is 1.

It is possible to avoid the contact of Cl with the heated surface of the mandrel if it, or its solution in PI, is poured off on the inner surface of the hose at a velocity similar to the extrusion rate from the height of the polymer setting line [78]. It appears that the hydrostatic pressure of the draining liquid is much less than the hose strength at any height of its feeding, so the liquid will not break the hose. The Cl flow velocity correlated with the extrusion depends on its viscosity, density and adhesion to the hose in the viscous-flow state. 

---