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AuthorDuffy, B. R. (3)Wilson, S. K. (3)Erban, Radek (2)Paterson, C. (2)Shikhmurzaev, Y. D. (2)View MoreJournalPhysics of Fluids (10)The Journal of Chemical Physics (5)Applied Physics Letters (3)Journal of Applied Physics (1)KAUST Grant Number

KUK-C1-013-04 (19)

Publisher
AIP Publishing (19)

TypeArticle (19)Year (Issue Date)2015 (1)2014 (3)2013 (5)2012 (6)2011 (3)View MoreItem AvailabilityMetadata Only (18)Open Access (1)

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Control and optimization of solute transport in a thin porous tube

Griffiths, I. M.; Howell, P. D.; Shipley, R. J. (Physics of Fluids, AIP Publishing, 2013-03) [Article]

Predicting the distribution of solutes or particles in flows within porous-walled tubes is essential to inform the design of devices that rely on cross-flow filtration, such as those used in water purification, irrigation devices, field-flow fractionation, and hollow-fibre bioreactors for tissue-engineering applications. Motivated by these applications, a radially averaged model for fluid and solute transport in a tube with thin porous walls is derived by developing the classical ideas of Taylor dispersion. The model includes solute diffusion and advection via both radial and axial flow components, and the advection, diffusion, and uptake coefficients in the averaged equation are explicitly derived. The effect of wall permeability, slip, and pressure differentials upon the dispersive solute behaviour are investigated. The model is used to explore the control of solute transport across the membrane walls via the membrane permeability, and a parametric expression for the permeability required to generate a given solute distribution is derived. The theory is applied to the specific example of a hollow-fibre membrane bioreactor, where a uniform delivery of nutrient across the membrane walls to the extra-capillary space is required to promote spatially uniform cell growth. © 2013 American Institute of Physics.

Controlling coverage of solution cast materials with unfavourable surface interactions

Burlakov, V. M.; Eperon, G. E.; Snaith, H. J.; Chapman, S. J.; Goriely, A. (Applied Physics Letters, AIP Publishing, 2014-03-03) [Article]

Creating uniform coatings of a solution-cast material is of central importance to a broad range of applications. Here, a robust and generic theoretical framework for calculating surface coverage by a solid film of material de-wetting a substrate is presented. Using experimental data from semiconductor thin films as an example, we calculate surface coverage for a wide range of annealing temperatures and film thicknesses. The model generally predicts that for each value of the annealing temperature there is a range of film thicknesses leading to poor surface coverage. The model accurately reproduces solution-cast thin film coverage for organometal halide perovskites, key modern photovoltaic materials, and identifies processing windows for both high and low levels of surface coverage. © 2014 AIP Publishing LLC.

Free-boundary models of a meltwater conduit

Dallaston, Michael C.; Hewitt, Ian J. (Physics of Fluids, AIP Publishing, 2014-08) [Article]

© 2014 AIP Publishing LLC. We analyse the cross-sectional evolution of an englacial meltwater conduit that contracts due to inward creep of the surrounding ice and expands due to melting. Making use of theoretical methods from free-boundary problems in Stokes flow and Hele-Shaw squeeze flow we construct an exact solution to the coupled problem of external viscous creep and internal heating, in which we adopt a Newtonian approximation for ice flow and an idealized uniform heat source in the conduit. This problem provides an interesting variant on standard free-boundary problems, coupling different internal and external problems through the kinematic condition at the interface. The boundary in the exact solution takes the form of an ellipse that may contract or expand (depending on the magnitudes of effective pressure and heating rate) around fixed focal points. Linear stability analysis reveals that without the melting this solution is unstable to perturbations in the shape. Melting can stabilize the interface unless the aspect ratio is too small; in that case, instabilities grow largest at the thin ends of the ellipse. The predictions are corroborated with numerical solutions using boundary integral techniques. Finally, a number of extensions to the idealized model are considered, showing that a contracting circular conduit is unstable to all modes of perturbation if melting occurs at a uniform rate around the boundary, or if the ice is modelled as a shear-thinning fluid.

Strongly coupled interaction between a ridge of fluid and an inviscid airflow

Paterson, C.; Wilson, S. K.; Duffy, B. R. (Physics of Fluids, AIP Publishing, 2015-07) [Article]

© 2015 AIP Publishing LLC. The behaviour of a steady thin sessile or pendent ridge of fluid on an inclined planar substrate which is strongly coupled to the external pressure gradient arising from an inviscid airflow parallel to the substrate far from the ridge is described. When the substrate is nearly horizontal, a very wide ridge can be supported against gravity by capillary and/or external pressure forces; otherwise, only a narrower (but still wide) ridge can be supported. Classical thin-aerofoil theory is adapted to obtain the governing singular integro-differential equation for the profile of the ridge in each case. Attention is focused mainly on the case of a very wide sessile ridge. The effect of strengthening the airflow is to push a pinned ridge down near to its edges and to pull it up near to its middle. At a critical airflow strength, the upslope contact angle reaches the receding contact angle at which the upslope contact line de-pins, and continuing to increase the airflow strength beyond this critical value results in the de-pinned ridge becoming narrower, thicker, and closer to being symmetric in the limit of a strong airflow. The effect of tilting the substrate is to skew a pinned ridge in the downslope direction. Depending on the values of the advancing and receding contact angles, the ridge may first de-pin at either the upslope or the downslope contact line but, in general, eventually both contact lines de-pin. The special cases in which only one of the contact lines de-pins are also considered. It is also shown that the behaviour of a very wide pendent ridge is qualitatively similar to that of a very wide sessile ridge, while the important qualitative difference between the behaviour of a very wide ridge and a narrower ridge is that, in general, for the latter one or both of the contact lines may never de-pin.

Particle capture efficiency in a multi-wire model for high gradient magnetic separation

Eisenträger, Almut; Vella, Dominic; Griffiths, Ian M. (Applied Physics Letters, AIP Publishing, 2014-07-21) [Article]

High gradient magnetic separation (HGMS) is an efficient way to remove magnetic and paramagnetic particles, such as heavy metals, from waste water. As the suspension flows through a magnetized filter mesh, high magnetic gradients around the wires attract and capture the particles removing them from the fluid. We model such a system by considering the motion of a paramagnetic tracer particle through a periodic array of magnetized cylinders. We show that there is a critical Mason number (ratio of viscous to magnetic forces) below which the particle is captured irrespective of its initial position in the array. Above this threshold, particle capture is only partially successful and depends on the particle's entry position. We determine the relationship between the critical Mason number and the system geometry using numerical and asymptotic calculations. If a capture efficiency below 100% is sufficient, our results demonstrate how operating the HGMS system above the critical Mason number but with multiple separation cycles may increase efficiency. © 2014 AIP Publishing LLC.

A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

Sullivan, J. M.; Paterson, C.; Wilson, S. K.; Duffy, B. R. (Physics of Fluids, AIP Publishing, 2012-08-24) [Article]

We use the lubrication approximation to analyze three closely related problems involving a thin rivulet or ridge (i.e., a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical "yield" value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In the Appendix, we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations. © 2012 American Institute of Physics.

Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release

Flegg, Mark B.; Rüdiger, Sten; Erban, Radek (The Journal of Chemical Physics, AIP Publishing, 2013-04-17) [Article]

The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration and high cooperativity. © 2013 American Institute of Physics.

Diffusion of multiple species with excluded-volume effects

Bruna, Maria; Chapman, S. Jonathan (The Journal of Chemical Physics, AIP Publishing, 2012-11-28) [Article]

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results. © 2012 American Institute of Physics.

Asymptotic and numerical prediction of current-voltage curves for an organic bilayer solar cell under varying illumination and comparison to the Shockley equivalent circuit

Foster, J. M.; Kirkpatrick, J.; Richardson, G. (Journal of Applied Physics, AIP Publishing, 2013-09-09) [Article]

In this study, a drift-diffusion model is used to derive the current-voltage curves of an organic bilayer solar cell consisting of slabs of electron acceptor and electron donor materials sandwiched together between current collectors. A simplified version of the standard drift-diffusion equations is employed in which minority carrier densities are neglected. This is justified by the large disparities in electron affinity and ionisation potential between the two materials. The resulting equations are solved (via both asymptotic and numerical techniques) in conjunction with (i) Ohmic boundary conditions on the contacts and (ii) an internal boundary condition, imposed on the interface between the two materials, that accounts for charge pair generation (resulting from the dissociation of excitons) and charge pair recombination. Current-voltage curves are calculated from the solution to this model as a function of the strength of the solar charge generation. In the physically relevant power generating regime, it is shown that these current-voltage curves are well-approximated by a Shockley equivalent circuit model. Furthermore, since our drift-diffusion model is predictive, it can be used to directly calculate equivalent circuit parameters from the material parameters of the device. © 2013 AIP Publishing LLC.

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C. (The Journal of Chemical Physics, AIP Publishing, 2010-04-26) [Article]

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.

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