Viscosity non-Newtonian flow

Ellis model See viscosity, non-Newtonian flow Ellis model. 

Level of enforcement of the incompressibility condition depends on the magnitude of the penalty parameter. If this parameter is chosen to be excessively large then the working equations of the scheme will be dominated by the incompressibility constraint and may become singular. On the other hand, if the selected penalty parameter is too small then the mass conservation will not be assured. In non-Newtonian flow problems, where shear-dependent viscosity varies locally, to enforce the continuity at the right level it is necessary to maintain a balance between the viscosity and the penalty parameter. To achieve this the penalty parameter should be related to the viscosity as A = Xorj (Nakazawa et al, 1982) where Ao is a large dimensionless parameter and tj is the local viscosity. The recommended value for Ao in typical polymer flow problems is about 10. ... 

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

Dispersion of a soHd or Hquid in a Hquid affects the viscosity. In many cases Newtonian flow behavior is transformed into non-Newtonian flow behavior. Shear thinning results from the abiHty of the soHd particles or Hquid droplets to come together to form network stmctures when at rest or under low shear. With increasing shear the interlinked stmcture gradually breaks down, and the resistance to flow decreases. The viscosity of a dispersed system depends on hydrodynamic interactions between particles or droplets and the Hquid, particle—particle interactions (bumping), and interparticle attractions that promote the formation of aggregates, floes, and networks. 

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

Since non-Newtonian flow is typical for polymer melts, the discussion of a filler s role must explicitly take into account this fundamental fact. Here, spoken above, the total flow curve includes the field of yield stress (the field of creeping flow at x < Y may not be taken into account in the majority of applications). Therefore the total equation for the dependence of efficient viscosity on concentration must take into account the indicated effects. 

Caustic Waterflooding. In caustic waterflooding, the interfacial rheologic properties of a model crude oil-water system were studied in the presence of sodium hydroxide. The interfacial viscosity, the non-Newtonian flow behavior, and the activation energy of viscous flow were determined as a function of shear rate, alkali concentration, and aging time. The interfacial viscosity drastically... 

Non-Newtonian flow may result if the monolayer array consists of molecules that interact by specific Coulombic or dipole interactions to form floating islands , which in turn may interact by van der Waals forces around their peripheries (Joly, 1956). Non-Newtonian flow may also be a property of collapsed films. The resulting differences in viscosity over a range of flow rates may then reflect film-component segregation or partial monolayer collapse. 

In the case of non-Newtonian flow, it is necessary to use an appropriate apparent viscosity. Although the apparent viscosity (ia is defined by equation 1.71 in the same way as for a Newtonian fluid, it no longer has the same fundamental significance and other, equally valid, definitions of apparent viscosities may be made. In flow in a pipe, where the shear stress varies with radial location, the value of fxa varies. As pointed out in Example 3.1, it is the conditions near the pipe wall that are most important. The value of /j.a evaluated at the wall is given by... 

This equation too is solved with the same boundary conditions as Eq. (148). A series of equations results when different combinations of fluids are used. There is no change for the first stage. All the terms of equation of motion remain the same except the force terms arising out of dispersed-phase and continuous-phase viscosities. The main information required for formulating the equations is the drag during the non-Newtonian flow around a sphere, which is available for a number of non-Newtonian models (A3, C6, FI, SI 3, SI 4, T2, W2). Drop formation in fluids of most of the non-Newtonian models still remains to be studied, so that whether the types of equations mentioned above can be applied to all the situations cannot now be determined. 

Ito,Y., Shishida,S. Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane. J. Polymer Sci., Polymer Phys. Ed. 10,2239-2278 (1972). 

Bird et al. (Bll), 1960 Brief theoretical treatments of various cases of film flow (on cone, with variable viscosity, non-Newtonian liquids, etc.) and of heat and mass transfer to films. 

For convenience, this chapter has been divided into three sections in which the viscosity of dilute solutions and dispersions, non-Newtonian flow, and the viscoelastic properties of semi-solid systems are discussed. 

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