Viscosity geometry

Spurk (1997) derived closed-form solutions for the average flow velocity v between parallel plates and in full ducts. For laminar flow between parallel plates relationships between viscosity, geometry, pressure gradient and mean flow velocity are given as ... 

It is important at the outset to define more closely the effective film thickness 5m. In any electrolyte solution in contact with a metal surface there is a static layer of solution next to the surface whose thickness will decrease as the solution velocity increases. The way in which this velocity changes the hydrodynamic thickness (6h) is complex and depends on such factors as viscosity, geometry, temperature and surface roughness. ... 

Other SFA studies complicate the picture. Chan and Horn [107] and Horn and Israelachvili [108] could explain anomalous viscosities in thin layers if the first layer or two of molecules were immobile and the remaining intervening liquid were of normal viscosity. Other inteipretations are possible and the hydrodynamics not clear, since as Granick points out [109] the measurements average over a wide range of surface separations, thus confusing the definition of a layer thickness. McKenna and co-workers [110] point out that compliance effects can introduce serious corrections in constrained geometry systems. 

Since we have parallel-plate geometry, the viscosity of the liquid layer is given by... 

In all of these derivations concerning rigid bodies, no other walls are considered except the particle surfaces. Before we turn to the question of the intrinsic viscosity of flexible polymers, let us consider the relationship between the viscosity of a fluid and the geometry and dimensions of the container in which it is measured. 

To solve a flow problem or characterize a given fluid, an instmment must be carefully selected. Many commercial viscometers are available with a variety of geometries for wide viscosity ranges and shear rates (10,21,49). Rarely is it necessary to constmct an instmment. However, in choosing a commercial viscometer a number of criteria must be considered. Of great importance is the nature of the material to be tested, its viscosity, its elasticity, the temperature dependence of its viscosity, and other variables. The degree of accuracy and precision required, and whether the measurements are for quaUty control or research, must be considered. The viscometer must be matched to the materials and processes of interest otherwise, the results may be misleading. 

The speed at which a sphere roUs down a cylindrical tube filled with a fluid or down an angled plate covered with a film of the fluid also gives a measure of viscosity. For the cylindrical tube geometry, equation 35, a generalized form of the Stokes equation is used for any given instmment, where p is the translational velocity of the rolling sphere and k is the instmment constant determined by caUbration with standard fluids. 

Effect of Physical Properties on Drop Size Because of the extreme variety of available geometries, no attempt to encompass this variable is made here. The suggested predictive route starts with air-water droplet size data from the manulac turer at the chosen flow rate. This drop size is then corrected by Eq. (14-195) for different viscosity and surface tension ... 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

The flow process in an injection mould is complicated by the fact that the mould cavity walls are below the freezing point of the polymer melt. In these circumstances the technologist is generally more concerned with the ability to fill the cavity rather than with the magnitude of the melt viscosity. In one analysis made of the injection moulding situation, Barrie showed that it was possible to calculate a mouldability index (p.) for a melt which was a function of the flow parameters K and the thermal diffusivity and the relevant processing temperatures (melt temperature and mould temperature) but which was independent of the geometry of the cavity and the flow pattern within the cavity. 

Universal SEC calibration reflects differences in the excluded volume of polymer molecules with identical molecular weight caused by varying coil conformation, coil geometry, and interactive propenies. Intrinsic viscosity, in the notation of Staudinger/ Mark/Houwink power law ([77]=fC.M ), summarizes these phenom-... 

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