No description available.

No description available.

No description available.

In this thesis we investigate the equilibrium and dynamic correlations in a number of model fluids. We make extensive use of the bulk Ornstein-Zernike (OZ) framework for determining two-body correlation functions, and equilibrium density functional theory (DFT) for determining equilibrium one-body density profiles.

Control over particle positioning is of particular importance in microfluidic systems. Acoustic techniques offer a low- power, minimally invasive method of achieving such control. This thesis discusses such control using surface acoustic waves. Mathematical models are first developed to describe the control over particles in liquids using acoustic radiation forces , which highlight the influence of acoustic power and particle size. The formation of both one and two dimensional particle arrays in fluidic channels are t hen demonstrated experimentally in a range of fluidic channels. Particle acceleration during array formation is shown by experiment to be directly proportional to the acoustic power level, indicating both fast and slow regimes of operation for this technique. Additionally, the time taken for particle arrays to form is shown to follow an inverse square relationship with particle size, allowing the possibility of sorting particles according to their size. A method of transporting particle arrays is reported, by sequential increments in the acoustic frequency. This is a cyclic process and the controlled transport of arrays of micron-sized particles by distances greater than 100 11m is demonstrated. A biocompatible microfluidic device is presented, which enables the use of the techniques presented here with biologically relevant samples. A significant biological application is demonstrated by the formation and transportation of arrays of microbubbles. This could allow the characterisation of individual micro bubbles in targeted drug delivery studies, for example.

This thesis is motivated by the observation in the magnetorotational Taylor-Couette flow that, for certain configurations of an externally applied magnetic field, there is competition between two different wavelengths at the thresh• old of instability. Moreover, for a particular magnetic field configuration the two critical wavelengths coalesce, such that the marginal stability curve has a quartic minimum. By perturbing about this quartic minimum, we recover competition between two similar wavelengths. This competition suggests the possibility that the secondary flow may exhibit localised patches of Taylor vortices of one wavelength embedded in a background of Taylor vortices with the other wavelength. In this thesis we develop a model equation that displays qualitatively the aforementioned behaviour, based on the Swift- Hohenberg equation [75]. A weakly nonlinear analysis is performed, in the manner of the Ginzburg-Landau derivation from the Swift- Hohenberg equation [41]. The resultant amplitude equation is, under certain restrictions on the parameters, the complex SwiftHohenberg equation [32J. We next extend the recently developed [24] techniques for finding localised solutions of the Swift- Hohenberg equation to the model equation; in particular the use of a conserved quantity to identify the constituent wavelengths of the localised solutions, and numerical continuation to compute the bifurcation diagrams for the model equation. We also compute the normal form for the bifurcation at the quartic minimum, following the similar analysis of the Hamiltonian-Hopf bifurcation relevant to the Swift- Hohenberg equation. The extension does not carry forward the integrals we might expect, however. Finally, we present preliminary numerical simulations of the nonlinear Taylor-Couette system in the appropriate parameter regime. The derivation and analysis of the model equation in this thesis represents a significant advance in the development of a framework for understanding localised solutions consisting of regions of two similar wavelengths.

Confined fluids occur naturally in nature in the form of fluids in porous rocks, soil formation and even in our bodies, our bones being porous. The behavior of fluids changes when in porous media, as it has been reported in the case of water. For instance, the boiling and freezing points of water differ in porous rocks than when in a bowl. Understanding these changes in not just water but in other fluids is of importance in several industries.

No description available.

In this thesis the instability of two viscous incompressible flows is discussed by using numerical and analytical methods. The first problem concerns the steady streaming flow, that is contained within a hollow stationary cylinder and induced by the transverse oscillation of a solid inner cylinder. The small gap limit is taken so that a series solution in odd powers of the angular variable is possible. From the studies by Hall & Papageorgiou [37] and Watson et al. [97], it is known that the leading order equation has solutions that are steady, quasi-periodic and chaotic (period doubling). Since all the higher order equations are driven by the solution at leading order; the series solution for the steady streaming flow is investigated with an interest to determine any chaotic structures. The second problem concerns the flow in a horizontal circular pipe, that is subject to torsional oscillations about a vertical axis that passes symmetrically through the pipe. The onset of a new axisymmetric roll-type instability, as observed experimentally by Bolton & Maurer [10] for the corresponding rectangular tank problem (of small width), is sought in the high-frequency (Phi >> 1) and small-amplitude limit (alpha << 1). A perturbation of the WKBJ type is imposed upon the basic state, so that the slow angular variation of the disturbance is accounted for in the linear stability equations. Accordingly, a dispersion relation for the dimensionless frequency parameter Phi is derived. In order to identify the most dangerous disturbance, it is necessary to minimise the eigenvalue B = alpha/Phi^(1/4). The theory of Soward & Jones [82] is used to show that an acceptable solution of the governing eigenvalue problem, cannot be obtained for real values of the latitudinal variable theta; instead, the correct minimum is found in the complex theta-plane.

Rotating bodies of finite size in the context of general relativity remain very poorly understood; one of the issues is in establishing the precise nature of the conditions that must be satisfied in order to match with a suitable vacuum solution. Several well-known fluid solutions exist, but so far only one of them describes a bounded matter distribution. This is the Wahlquist solution, which happens to possess an unusual shape to its boundary, and because of this many consider it not to describe an isolated rotating body. So far, this claim is yet to be decisively proved. Recent work has suggested that this may well be the case, but it did not consider the issue of the exterior appearance of the boundary. An attempt is made to follow up the investigations regarding the apparent non-asymptotic flatness of the Wahlquist solution to second order, and to eventually arrive at a physical interpretation for the shape of the fluid. The slow rotation matching conditions are developed from first principles, and we demonstrate that by perturbing the boundary of the Wahlquist solution, it is possible to generate invariant Cauchy boundary data as viewed in the exterior Weyl coordinates. The exterior metric is then obtained to first and second order in the rotation speed using the Ernst potential method, where we show that it is possible to perform up to second order Cauchy matching of the interior and exterior fields. It is shown that while the first order solution is asymptotically flat, the second order solution is not so, and we show that the non-asymptotic flatness is due to the interior multipole expansion of a field originating from two-point masses present outside the fluid.