ORCID Profile
0000-0001-8036-4733
Current Organisation
The University of Auckland
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Publisher: The Royal Society
Date: 08-07-2014
Abstract: In this study, we consider suspensions of swimming microorganisms in situations where we might expect the promotion of two-dimensional flow, such as within thin fluid films. Given that two-dimensional, inertialess flows are notoriously long-ranged (although not afflicted by Stokes paradox in the case of self-motile bodies), this raises interesting questions around the care which must be taken with the semi-dilute assumption in such situations. Adopting the prototype squirmer as a model of a swimming microorganisms of the type previously considered, we find that although the flowfield decays algebraically with the characteristic separation distance between microorganisms, there remains a finite interaction between the squirmers even at asymptotically large distances. This finding is further borne out by asymptotic analysis, which confirms that the limiting form of the far-field interaction depends solely upon the relative orientation between the microorganisms. Those which swim in the same general direction are seen to experience very large lateral displacements (many times the size of the displacements experienced owing to interactions between less well-aligned swimmers). This clearly has potential implications for very dilute suspensions in which squirmers become broadly aligned in their swimming direction (e.g. during chemotaxis). We show that hydrodynamically enhanced cell spreading, previously reported for denser suspensions, can persist even at extreme dilutions. Moreover, we demonstrate that this induced spreading can continue in the presence of potentially decohering Brownian effects.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 13-02-2018
Publisher: Springer Science and Business Media LLC
Date: 10-2014
Publisher: The Royal Society
Date: 07-2015
Abstract: We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic–mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.
Publisher: Cambridge University Press (CUP)
Date: 12-01-2019
DOI: 10.1017/JFM.2017.896
Abstract: We consider pressure-driven flow of an ion-carrying viscous Newtonian fluid through a non-uniformly shaped channel coated with a charged deformable porous layer, as a model for blood flow through microvessels that are lined with an endothelial glycocalyx layer (EGL). The EGL is negatively charged and electrically interacts with ions dissolved in the blood plasma. The focus here is on the interplay between electrochemical effects, and the pressure-driven flow through the microvessel. To analyse these effects we use triphasic mixture theory (TMT) which describes the coupled dynamics of the fluid phase, the elastic EGL, ion transport within the fluid and electric fields within the microvessel. The resulting equations are solved numerically using a coupled boundary–finite element method (BEM-FEM) scheme. However, in the physiological regime considered here, ion concentrations and electric potentials vary rapidly over a thin transitional region (Debye layer) that straddles the lumen–EGL interface, which is difficult to resolve numerically. Accordingly we analyse this region asymptotically, to determine effective jump conditions across the interface for BEM-FEM computations within the bulk EGL/lumen. Our results demonstrate that ion–EGL electrical interactions can influence the near-wall flow, causing it to become reversed. This alters the stresses exerted upon the vessel wall, which has implications for the hypothesised role of the EGL as a transmitter of mechanical signals from the blood flow to the endothelial vessel surface.
Publisher: AIP Publishing
Date: 12-2008
DOI: 10.1063/1.3054146
Abstract: We report the results of an experimental investigation into fluid motion induced by the deceleration to rest of a rigidly rotating fluid-filled torus. Transition to a transient turbulent state is found where the onset of the complicated motion is triggered by a small-scale wavelike instability. The wave forms on a front that propagates from the inner wall of the toroidal container after it is stopped. We reveal the origins of the front through a combination of careful experimental measurements, boundary-layer analysis, and computation of the axisymmetric Navier–Stokes equations.
Publisher: Informa UK Limited
Date: 10-2021
DOI: 10.1080/10255842.2021.1984434
Abstract: The ability of the lymphatic network to absorb large molecules and bypass the first-pass liver metabolism makes it appealing as a delivery system for therapeutic substances. In most cases, the drug is injected into the subcutaneous tissue and must negotiate the tissue space, before being drained via the lymphatics. Tracking the transport of drug molecules through this route is challenging, and computational models of lymphatic drainage can play an important role in assessing the efficacy of a proposed delivery strategy. The three-dimensional computational model we present here of the peripheral lymphatic network and surrounding interstitium is informed by anatomical data, and quantifies the degree to which uptake and transit times are affected by drug particle size, physiological flow rates, and specifics of drug injection.
Publisher: The Royal Society
Date: 08-2018
DOI: 10.1098/RSOS.180456
Abstract: Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of ‘active matter’. Ex les include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely isotropic fluid (Ericksen 1960 Colloid Polym. Sci. 173 , 117–122 ( doi:10.1007/bf01502416 )) treats suspensions of non-motile particles as a continuum with an evolving preferred direction this model describes fibrous materials as erse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified stress tensor with four viscosity-like parameters. By making fundamental connections with recent models for active suspensions, we propose a modification to Ericksen's model, mainly the inclusion of self-motility this can be considered the simplest description of an oriented suspension including transversely isotropic effects. Motivated by the fact that transversely isotropic fluids exhibit modified flow stability, we conduct a linear stability analysis of two distinct cases, aligned and isotropic suspensions of elongated active particles. Novel aspects include the anisotropic rheology and translational diffusion. In general, anisotropic effects increase the instability of small perturbations, while translational diffusion stabilizes a range of wave-directions and, in some cases, a finite range of wavenumbers, thus emphasizing that both anisotropy and translational diffusion can have important effects in these systems.
Publisher: Cambridge University Press (CUP)
Date: 20-10-2011
DOI: 10.1017/JFM.2011.366
Abstract: We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature a problem first investigated by Madden & Mullin ( J. Fluid Mech. , vol. 265, 1994, pp. 265–217). The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container’s rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, on allowing for a change in direction of rotation, there is a (negative) ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to a combination of axisymmetric centrifugal and non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of Madden & Mullin (1994). Throughout our work, detailed quantitative comparisons are made between asymptotic predictions and finite- (but small-) Ekman-number Navier–Stokes computations using a finite-element method. We find that the boundary-layer results correctly capture the (finite-Ekman-number) rotationally symmetric flow and its global stability to linearised perturbations.
Publisher: Springer Science and Business Media LLC
Date: 10-01-2008
No related grants have been discovered for Richard Clarke.