Non-Newtonian fluids flows

Townsend, P. and Webster, M. I- ., 1987. An algorithm for the three dimensional transient simulation of non-Newtonian fluid flow. In Pande, G. N. and Middleton, J. (eds). Transient Dynamic Analysis and Constitutive Laws for Engineering Materials Vul. 2, T12, Nijhoff-Holland, Swansea, pp. 1-11. 

Shear stress at the pipe wall against flow characteristic for a non-Newtonian fluid flowing in a pipe... 

Srinivas, B. K. and Chhabra, R.P. Chem. Eng. Processing 29 (1991) 121-131. An experimental study of non-Newtonian fluid flow in fluidised beds minimum fluidisation velocity and bed expansion. 

N. Mai-Duy and R.I. Tanner. Computing non-Newtonian fluid flow with radial basis function networks. International Journal for Numerical Methods in Fluids, 48 1309-1336, 2005. 

The simulation of non-Newtonian fluid flow is significantly more complex in comparison with the simulation of Newtonian fluid flow due to the possible occurrence of sharp stress gradients which necessitates the use of (local) mesh refinement techniques. Also the coupling between momentum and constitutive equations makes the problem extremely stiff and often time-dependent calculations have to be performed due to memory effects and also due to the possible occurrence of bifurcations. These requirements explain the existence of specialized (often FEM-based) CFD packages for non-Newtonian flow such as POLYFLOW. 

Both FVM and FEM based packages have been applied successfully to study non-Newtonian fluid flow. 

The CFD-analysis of non-Newtonian flow has made progress in the last decade but the extension of the calculations to other types of non-Newtonian fluid flow and more complex geometries is highly desirable from the perspective of the chemical engineer. 

Homogeneous Models. The basic assumption in these models is that the emulsion is a continuum, single-phase liquid that is, its microscopic features are unimportant in describing the physical properties or bulk flow characteristics. It ignores interactions between the droplets in the emulsions and the rock surface. The emulsion is considered to be a single-phase homogeneous fluid, and its flow in a porous medium is modeled by using well-documented concepts of Newtonian and non-Newtonian fluid flow in porous media (26, 38). 

T. F. Irvine Jr. and J. Kami, Non-Newtonian Fluid Flow and Heat Transfer, in Handbook of Single-Phase Convective Heat Transfer S. Kakac, R. K. Shah, and W. Aung, eds., John Wiley Sons, New York, 1987. 

In recent years, the SPH methods in particular have gone through major improvements, and their application was expanded into a wider range of engineering problems. These include both more advanced physical models and more advanced engineering processes. For example, SPH was successfully used to simulate non-Newtonian fluid flows and viscoelastic materials. It has been also used for the analysis of fluid-stmcture interaction problems, fluid flow in porous media and fractures, heat transfer, and reacting flow problems. 

The applications related to non-Newtonian fluid flow through microchannels are mostly associated with the transport of biofluids, with blood as the most common example. Utilizing the mathematical model outlined as above, recent efforts have been directed to understand the implications of various rheological characteristics of blood on electrokinetically driven microfluidic transport [9]. The simulation studies based on the above-mentioned mathematical model clearly revealed... 

Polymers are used for mobility control in chemical flooding processes such as micellar-polymer and caustic-polymer flooding and in polymer augmented waterflooding. Selection of a polymer for mobility control is a complex process because it is not possible to predict the behavior of a polymer in porous rock from rheological measurements such as viscosity/ shear rate curves. Polymers used for mobility control are non-Newtonian fluids. Flow characteristics are controlled by the shear field to which the polymer is subjected. Properties of polymers can be measured under steady shear in rheometers. However, in porous rock, it is difficult to define the shear environment a polymer experiences as it flows through tortuous pores. 

Singh, R. P. and P. Mishra, Friction Factor for Newtonian and non-Newtonian Fluid Flow in Curved Pipes, J. Chem. Engg, Japan, 13, 275-280 (1980). 

In the very important case of non-Newtonian fluid flow, the viscosity p, which is defined in this paper, has to be replaced by the apparent viscosity of the generalized Newtonian fluid when it is possible (pseudoplastic, dilatant, or plastic fluids). This apparent viscosity is defined from the flow rheological model representing the fluid by = f(y). 

Hartnett and Kostic [12] studied a number of correlations for predicting the turbulent friction factor of purely viscous non-Newtonian fluids flowing in circular and non-circular geometries. They concluded that the Dodge-Metzner Equation 7 was the best over the entire range of power law value. 

Many concentrated suspensions follow non-Newtonian behavior and considerations ought to be made as the viscosity is not a constant anymore, and such fluids should be characterized properly to use their parameters of characterization instead of viscosity in calculations using some dimensionless groups. Most of the theory developed for non-Newtonian fluid flow through tubes, apply to laminar flow round smooth tubes. The most studied non-Newtonian fluids are the power-law fluids and there are some relationships available for pressure-loss-flow rate in purely viscous and viscoelastics flows principally. Relations for thixotropic and rheopectic systems appear not to be available. 

Hydrodynamie similarity is important for retaining equal influence of two phenomena that ean be important for the reactive extrusion process distributive mixing and non-Newtonian fluid flow. 

Lev que s problem was extracted from the rescaled mass balance in Equation 8.28. As can be seen, this equation is the basis of a perturbation problem and can be decomposed into several subproblems of order 0(5 ). The concentration profile, the flux at the wall, and consequently the mixing-cup concentration (or conversion) can all be written as perturbation series on powers of the dimensionless boundary layer thickness. This series is often called as the extended Leveque solution or Lev jue s series. Worsoe-Schmidt [71] and Newman [72] presented several terms of these series for Dirichlet and Neumann boundary conditions. Gottifredi and Flores [73] and Shih and Tsou [84] considered the same problem for heat transfer in non-Newtonian fluid flow with constant wall temperature boundary condition. Lopes et al. [40] presented approximations to the leading-order problem for all values of Da and calculated higher-order corrections for large and small values of this parameter. 

Hosseini SM, Manzari MT, Hannani SK (2007) A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow. Int J Numer Method Heat and Fluid How 17 715-735... 

Wu B, Chrai S. CFD simulation of non-Newtonian fluid flow in anaerobic digesters. Biotechnol Bioeng 2008 99(3) 700 11. 

The applications related to non-Newtonian fluid flow through microchannels are mostly associated with the transport of biofluids, with blood as the most common... 

Sadhukhan, K., Non-Newtonian fluid Flow in Tapered Geometries, M. Tech, thesis. Department of Chemical Engineering, Indian Institute of Technology, Bombay, 1992. 

Torrance, B. McK. 1963. Friction factors for turbulent non-Newtonian fluid flow in circular pipes. South African Mechanical Engineer, 13, 4, 89-91. 

A non-Newtonian fluid flows at 4.55 kg/min inside a 0.0254-m-diameter tube that is 1.52 m long. The wall is kept at 93.3°C. If the fluid enters at 37.8°C, what is its exit temperature ... 

Solutions exist for a porous channel with two porous walls for laminar channel flow with heat transfer for asymmetric isoflux hoimdaries (Hadim, 1994 Nield et al., 1996, 2003h Kuznetsov and Nield, 2009 Chen and Tso, 2012), with small uniform suction or injection (Doughty, 1971 Raithhy, 1971 Doughty and Perkins, 1972), with arbitrary uniform suction or injection (Lan and Khodadadi, 1993), for non-Newtonian fluid flow (Mahmud and Fraser, 2002), and for internal heat sources included (Vidhya and Kesavan, 2010) with arbitrary uniform suction or injection (Elbashbeshy and Bazid, 2004 Cortell, 2005). 

Chauhan, D.S., Olkha, A., 2011. Entropy generation and heat transfer effects on non-Newtonian fluid flow in annular pipe with naturally permeable boimdaries. Int. J. Energy Technol. 3 (30), 1-9. 

Huang, C.L., 1977. Laminar non-Newtonian fluid flow in a porous annulus. J. Math. Anal. Appl. 59, 130-144. 

Based on capillary bundle model for non-Newtonian fluid flow ... 

Becker, E., Simple non-Newtonian fluid flows, Ada AppL MetA., 20, 177-226 (1980). 

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