Viscosity, critical kinematic

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

Because of the strong effects of plate rotations on the rector performance for both RE and PC electrolyzers, the critical design parameters for these reactors are the Taylor number (a2w/4v)0 5 and the Reynolds number (aVf/v). Here a is the gap width between the plate, w the angular velocity of rotation (in radians per second), v the kinematic viscosity of the fluid, and V the velocity in the feed pipe. Since no asymptotic velocity profile is reached for PC, the length of the cell will be an important design parameter in a pump-cell electrolyzer. Detailed mathematical models for RE and PC electrolyzers are given by Thomas et al. (1988), Jansson (1978), Jansson et al. (1978) and Simek and Rousar (1984). 

Note 1 Kinematic viscosity v and ttieimal ditfusivily o can be calculated from their defmlbons, v = pJp and o = Wpc, = vtPi. The temperatures O.Ol C, lOOfC, and 374.14 C are the triple-, boiling-, and critical-point temperatures of vraler. respectively. The properties listed abc/e (exccptUie vapor density) can be used a any pressure v/llh negligible error except at temperatures near the critical-point value. 

These two bulk properties (TBP data/°API) are then used to calculate other constants such as molecular weight (MW), the pseudo-critical temperature (T ) and pressure (P ), respectively, and the pseudo-acentric factor (m). The other properties generally measured are the kinematic viscosities at 100°F (—311 K) and 200°F (—366 K), respectively, and the Reid Vapor Pressure (RVP) (mainly for the gasoline range cut, defined as the vapor pressure exerted by the cut at 100 °F (—311 K)). All of the above-measured properties and the calculated constants are generally... 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

For liquid viscosity, theory is lacking and correlations are largely empirical. The main variation is with temperature the effect of pressure is small for liquids well removed from the critical point. It is common to correlate the viscosity (or sometimes the kinematic viscosity, v = 11/p) with a logarithmic dependence in reciprocal temperatnre ... 

Although these eddy diffusivities act in the same manner as the kinematic viscosity and thermal diffusivity in laminar flow, the critical difference is that the eddy diffusivities are not properties of the fluid but are dependent largely on the dynamic behavior of the fluid motion. In this section the fluid dynamic bases for evaluating these eddy diffusivities are given. They will then be used in a variety of convective heating situations to yield formulas useful in engineering computations. 

Ye and co-workers exploited the shear stability of highly branched, high molecular weight polyethylenes (PEs) as lubricant viscosity index improvers [252, 253]. Viscosity index of a lubricant is a critical parameter which defines its quality and application temperature range. They synthesized PEs with controllable chain topologies ranging from linear to a hyperbranched dendritic structure by chain walking polymerization [254]. The PE samples were blended into a base paraffinic oil (density 0.8659 g mL at 15 °C, kinematic viscosity 30.06 cST at 40 °C) to form lubricants. The lubricants were subjected to the Kurt Orbahn (KO) test to measure the shear stability index, which is expressed by... 

For a rotating-disc electrode with a radius r = 1 cm in an aqueous electrolyte (kinematic viscosity of water 0.01 cm s at 20 °C) the critical rotation rate is 10,000 rot min. ... 

A rise in the trifunctional unit content from 0 to 1.4 mol% in oligomethylethylsiloxanes leads to sharp growth of the kinematic viscosity. There is a great probability therewith of formation of star-like compounds, and lateral branch lengths exceed a definite critical point, thus resulting in a viscosity increase. A further rise in the trifunctional unit content up to 16.9 mol% results in a kinematic viscosity drop. 

Viscosity is a fluid s resistance to flow, so advection models must account for viscosity either as an explicit term or in a scaling constant. The dynamic viscosity (tj, kg/m sec) equals the kinematic viscosity (v, mVsec) divided by the density (p, kg/m ). The dynamic viscosity of liquid water in equilibrium with the vapor phase for temperatures between the freezing and critical points can be computed from an equation given by Watson et al. (1980). 

On the basis of these standard requirements, an appropriate equation for kinematic viscosity should be able to yield good or at least reasonable results in the widest operative temperature range in the limits between the triple point up to the critical point for most liquid compounds. Furthermore, the functional form must describe as best as possible all experimental trends, whether linear or more complex. 

Removal of the corrosion product or oxide layer by excessive flow velocities leads to increased corrosion rates of the metallic material. Corrosion rates 2ire often dependent on fluid flow and the availability of appropriate species required to drive electrochemical reactions. Surface shear stress is a measure of the force applied by fluid flow to the corrosion product film. For seawater, this takes into account changes in seawater density and kinematic viscosity with temperature and salinity [33]. Accelerated corrosion of copper-based alloys under velocity conditions occurs when the shear surface stress exceeds the binding force of the corrosion product film. Alloying elements such as chromium improve the adherence of the corrosion product film on copper alloys in seawater based on measurements of the surface shear stress. The critical shear stress for C72200 (297 N/m, 6.2 Ibf/ft ) far exceeds the critical shear stresses of both C70600 (43 N/m, 0.9 Ibf/ft ) and C71500 (48 N/m, 1.0 Ibf/ft ) copper-nickel alloys [33]. 

---