Multiphase Fluids

Introduction

Multiphase fluids are ubiquitous - examples of interest here include oil pipeline flows, which are an example of a liquid-liquid flow, flow of fluid-particle suspensions through filters, fluidized beds created by passing a fluid up through an assembly of particles, and dissolved air flotation (DAF) where fine gas bubbles are passed through a liquid to remove suspended fine particulates and drops. We are using various numerical methods and experiment to elucidate the fundamentals of multiphase fluid systems like those mentioned above with a view to designing better materials and processes more rapidly and cheaper. A major part of this endeavour is the development of a general class of methods we term Explicit Numerical Simulation (ENS) in which the system of interest is simulated as faithfully as possible. A well known example of this approach is direct numerical simulation (DNS) of turbulence - we highlight below various examples of our ENS models relevant to multiphase fluids. The second aspect of our work is the experimental study of multiphase systems - we primarily do this through collaboration with others, but in one particular area - dense granular systems - we have developed our own programme of experimental research - this is also summarized below.

ENS of single-phase flow in macroporous media

We have developed an ENS method for predicting the hydrodynamic properties of fluid flows in macroporous media such as packed beds and porous rock. The method involves solving for the flow through a model of the porous solid. The flow is solved for using the lattice-gas automata (LGA) method (see Biggs and Humby (1998) for a review). The model of the porous solid may be obtained by reconstruction using experimental data for the solid as was done in Humby et al. (2002), or by a mimitec method that involved simulating the process by which the solid is produced (e.g. diagenesis; weaving). We have to date applied this methodology to Darcy flow in a packed bed to determine the permeability of the bed (Humby et al., 2002) - comparison with experiment was very good. The traditional LGA approach is limited to slow flow. We are currently addressing this issue with a view to predicting the parameters of hydrodynamic models for higher speed flows such as, for example, the Brinkman and Forchheimer equations - initial results of this work should appear in mid-2008.

ENS of suspension flow in porous media with deposition
We have developed an ENS model for suspension flow in porous media with deposition - this is of direct relevance to filtration and also fines deposition in reserviors amongst other things. The method, which is illustrated in the figure to the right, involves solving for the flow through a model of the porous solid and around the particles that are moving under the influence of their local pressure field, and the depositied particles. We have shown that this ENS model yields very different deposition behaviour compared to the traditional trajectory models, which assume the particles, whether suspended or depositied, do not influence the flow - as the ENS model is closer to reality, this means the traditional trajectory models should NOT be used to estimate collector efficiency except in the very dilute limit.
We have also investigated the variation of the deposition process in complex pore spaces such as that illustrated below. We were able to elucidate how the deposit profile through the solid varies with the Reynolds and Stokes numbers. We also found that the permeability is not a unique function of the amount deposited.
The ENS model and its application are reported in Biggs et al. (2003).

ENS of liquid-liquid flows
We have developed an ENS model for liquid-liquid flows - this is of direct relevance to pipeline flow, suspension polymerization and artificial blood amongst many other things. We have used the method to study the phase inversion process in pipe flow, and binary collision of drops in a linear shear field. In the binary drop collision study, we obtained a range of collision scenarios ranging from coalescence in the compressional and extensional quadrants both with and without secondary drops, to collisions we term ‘kiss-and-break' in which the drops coalesce before separating again to form two or more drops (below left), and non-coalescence. We have generated a Re-Ca map showing where these events occur (below right) - this suggests regions of the parameter space associated with the various collision scenarios are not separated by distinct boundaries but, rather, transition zones in which the probabilities of the two outcomes vary in a complementary fashion from one to the other. More details may be found in Biggs et al. (2007).

 

Measurement of granular temperature in dense particulate systems
In all but the most trivial of particulate systems, the velocity of a particle, u, at any instant in time invariably differs from the average velocity of the particles around it, . This difference, the fluctuating (or peculiar) velocity, δv = u - , is quantified by the so-called granular temperature, θ. The granular temperature was first formally defined by Ogawa in the late 1970s as part of one of the earliest kinetic theory based models for inelastic granular systems (in Proceedings of the US-Japan Seminar on Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials (eds.: Cowin S.C., Satake M.); Gakajutsu Bunken Fukyu-Kai: Tokyo, Japan; 1978: pp. 208-217) and it is now recognised as an important parameter in these theories. It is also playing an increasing role in other contexts including heat transfer, attrition and granulation in particulate systems. Because of its fundamental role in various theories of granular phenomena, it is highly desirable to be able to measure the granular temperature. Whilst this has been done for dilute systems using a variety of techniques (PEPT, NMR, video image analysis, PIV), dense systems have proved more challenging - we have, however, successfully applied diffusing wave spectroscopy (DWS) to such systems. We have to date measured the granular temperature in an air fluidised bed of fine particles that are Geldart type-A like, and a vibrated fluidized bed of 1 mm glass particles, whilst work is currently underway on a number of other fluidized bed configurations.
In the air fluidised bed study, we were able to show that bubbling is not a prerequesite for a finite granular temperature as suggested by previous work of others. Instead, we have shown that the granular temperature increases in a sigmoidal like fashion with superficial velocity as illustrated in the figure right. Although excessive bubbling prevented us from studying superficial velocities, Us, higher than those shown in the figure (some processing of the light intensity data could remove this problem, but has not been done here), we hypothesis that the granular temperature will start to rise again for Us > 10 mm/s. Further discussion on this figure and other results can be found in Xie et al. (Europhysics Letters, 74, 268-274, 2006) and Biggs et al. (Granular Matter, in press).
	In the dense vibro-fluidised bed study, we found that the granular temperature increased with the square of peak vibrational velocity, vp, as illustrated in the figure left. We also observed a glass-transition point, which occurs at vp ~ 18 mm/s. Further discussion on this figure and other results can be found in Zivkovic et al. (2007)