Biomedical subjects

A J C Ladd

Publications and source records attributed to A J C Ladd.

8 recordsLinked to original sources

PubMed2004

The electroviscous force between charged particles: beyond the thin-double-layer approximation.

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95-112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye-Hückel approximation.

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PubMed2004

Microstructure in a settling suspension of hard spheres.

We report direct observations of the structure factor in a settling suspension, using numerical simulations based on a lattice-Boltzmann model of the fluid. We find that the horizontal density fluctuations in bounded suspensions are strongly suppressed by the settling process, vanishing as k(2) at long wavelengths. Our measurements of the structure factor confirm the qualitative predictions of one of several competing theories, although this theory does not yet explain why container walls are so important. Our results contradict the idea that a settling suspension is inevitably stratified by hydrodynamic dispersion at the suspension-supernatent interface.

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PubMed2004

Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces.

Simulations of heat and mass transport may require complex nonlinear boundary conditions to describe the flow of mass and energy across an interface. Although stochastic methods do not suffer from the numerical diffusion of grid-based methods, they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce ideas and algorithms to account for mass (or energy) transfer at reactive interfaces, with accuracies comparable to the bulk phase. We show how to introduce particles into the system with the correct distribution near the interface, as well as the correct flux through the interface. The algorithms have been tested in a channel flow, for which accurate numerical solutions can be independently calculated.

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PubMed2003

Boundary conditions for stochastic solutions of the convection-diffusion equation.

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection-diffusion equation with accuracies comparable to the bulk phase. The algorithms have been tested in two-dimensional channel flows over a range of Peclet numbers, and compared with independent finite-difference calculations.

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PubMed2002

Lubrication corrections for lattice-Boltzmann simulations of particle suspensions.

The lattice-Boltzmann method has been refined to take account of near-contact interactions between spherical particles. First, we describe a comprehensive solution to the technical problems that arise when two discretized surfaces come into contact. Second, we describe how to incorporate lubrication forces and torques into lattice-Boltzmann simulations, and test our method by calculating the forces and torques between a spherical particle and a plane wall. Third, we describe an efficient update of the particle velocities, taking into account the possibility that some of the differential equations are stiff.

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PubMed2002

Simulation of chemical erosion in rough fractures.

We report on numerical simulations of acid erosion in a fractured specimen of Carrara marble. The simulations combine two recent advances in lattice-Boltzmann methodology to accurately and efficiently calculate the velocity field in the pore space. A tracer diffusion algorithm was then used to calculate the distribution of reactants in the fracture, and the local erosion rate was obtained from the flux of tracer particles across the surfaces. Our results show that at large length scales, erosion leads to increased heterogeneity via channel formation, whereas at small length scales it tends to smooth out the roughness in the local aperture.

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PubMed2002

Effects of container walls on the velocity fluctuations of sedimenting spheres.

Simulations describing the settling of suspensions of solid particles bounded by a rigid container are presented. Results are compared with previous simulations of homogeneous suspensions with periodic boundary conditions. Velocity fluctuations in vertically inhomogeneous suspensions are found to saturate under conditions similar to those found in laboratory experiments, while in vertically homogeneous suspensions, with or without side walls, the velocity fluctuations diverge. A mechanism for the establishment of a correlation length in sedimenting suspensions is proposed.

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PubMed2001

Accuracy and stability of a lattice-Boltzmann model with subgrid scale boundary conditions.

A lattice-Boltzmann method has recently been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a real numbered parameter, specified at each node and representing the fluid volume associated with that node, we were able to accurately simulate arbitrary geometries without the need to specify surface normals. In this paper a detailed description of the rules is presented and the accuracy and stability of the method is discussed, based on numerical results for flow in systems with planar surfaces and for flow through periodic arrays of disks and spheres.

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