Effects of Variable Viscosity

The methodology to this point has assumed the parabolic velocity profile of Equation 

Variable viscosity in laminar tube flows is an example of the coupling of mass, energy, and momentum transport in a reactor design problem of practical significance. 

Elaborate computer codes that recognize this coupling in complex flow geometries have been devised and verified. The present examples are representative of a general class of single-phase, variable-viscosity, variable-density problems yet avoid undue complications in mathematical or numerical analysis. 

Consider axisymmetric flow in a circular tube so that Vg = 0. Two additional assumptions are needed to treat the variable-viscosity problem in its simplest form  

The first of these assumptions drops the momentum terms from the equations of motion, giving a situation known as creeping flow. This leaves and coupled through a pair of simultaneous PDEs. The pair can be solved when circumstances warrant, but the second assumption allows much greater simplification. It allows an uncoupling of the two equations so that is given by a single ODE  

---

To consider the effect of variable viscosity, the viscosity ratio (p /p )014 is applied. The use of Eqs. 5.269 and 5.272 with their right sides multiplied by (p /p, )014 is recommended. The density change of fluids leads to natural convection consequently, heat transfer is normally enhanced. 

It is noted in Fig. 6.37 that the effects of variable viscosity cause the velocity distributions outside the buffer layer to displace while remaining essentially parallel, so that... 

Prasad, KV. Pal, D. Umesh, V. Prasanna Rao, N. S. (2010). The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet. Comm. Nonlinear Sci. and Num. Simulation, 15, pp. 331-344, ISSN 1007-5704. 

Sahin, A. Z. (1999). Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux. Heat Mass Transfer, 35, pp. 499 506, ISSN 0947-7411. 

Sometimes, the relationship between two variables is obscured by the presence of a third variable which may of may not be related to the other two. In order to clarify the relationship, we may want to remove or account for the effect of the third variable. For example, we may want to find the effect of plasticizer viscosity on the hardness of a resin-plasticizer mix. But some plasticizers are more efficient than others, and this factor may obscure the relationship. What we are really looking for is some way of separating out these effects. For example, in the simpler linear correlation study, we Came up with an equation of the form... 

These five nontheoretical correlations are sufficient to show the difficulty of selecting a satisfactory empirical correlation. The various authors do not agree on the quantitative effects of such important variables as the temperature difference and surface tension they fail even to agree on the qualitative effects of variables such as the liquid viscosity and the vapor density. 

The stomach empties liquids faster than solids. The rate of transfer of gastric contents to the small intestine is retarded by the activity of receptors sensitive to acid, fat, osmotic pressure and amino acids in the duodenum and the small intestine and stimulated by material that has arrived from the stomach. Gastric emptying is a simple exponential or square-root function of the volume of a test meal - a pattern that holds for meals of variable viscosity. To explain the effect of a large range of substances on emptying, an osmoreceptor has been postulated which, like a red blood cell, shrinks in hypertonic solutions and swells in hypotonic solutions. 

Viscosity of Liquids with Dispersed Phases. When a small amount of a dispersed phase is present, there is only a small effect on viscosity as the volume of dispersed phase increases, there is a sharply increasing effect. When the system becomes closely packed with particles, viscosity approaches infinity. Equation (4) shows the effects of variables on viscosity, where rje is the viscosity of the continuous or external phase, is a shape constant, Vi is the volume fraction... 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

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 ... 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

---