This paper generalizes the two-component algorithm of Sec. , extending it, in Sec. , to describe N>2 mutually immiscible fluids in the isothermal continuum regime. Each fluid has an independent interfacial tension. While retaining all its computational advantages, we remove entirely the empiricism associated with contact behavior in our previous multiple immiscible fluid models [M. M. Dupin, Phys. Rev. E 73, 055701(R) (2006); Med. Eng. Phys. 28, 13 (2006)] while solidifying the physical foundations. Moreover, the model relies upon a fluid-fluid segregation which is simpler, computationally faster, more free of artifacts (i.e., the interfacial microcurrent), and upon an interface-inducing force distribution which is analytic. The method is completely symmetric between any numbers of immiscible fluids and stable over a wide range of directly input interfacial tension. We present data on the steady-state properties of multiple interface model, which are in good agreement with theory [R. E. Johnson and S. S. Sadhal, Annu. Rev. Fluid Mech. 17, 289 (1985)], specifically on the shapes of multidrop systems. Section is an analysis of the kinetic and continuum-scale descriptions of the underlying two-component lattice Boltzmann model for immiscible fluids, extendable to more than two immiscible fluids. This extension requires (i) the use of a more local kinetic equation perturbation which is (ii) free from a reliance on measured interfacial curvature. It should be noted that viewed simply as a two-component method, the continuum algorithm is inferior to our previous methods, reported by Lishchuk [Phys. Rev. E 67, 036701 (2003)] and Halliday [Phys. Rev. E 76, 026708 (2007)]. Greater stability and parameter range is achieved in multiple drop simulations by using the forced multi-relaxation-time lattice Boltzmann method developed, along with (for completeness) a forced exactly incompressible Bhatnagar-Gross-Krook lattice Boltzmann model, in the Appendix. These appended schemes closely follow those developed by Guo [Phys. Rev. E 65, 046308 (2002)] for the single-relaxation-time scheme.

A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng [Phys. Rev. E 58, 7475 (1998)] equations for the evolution of the velocity and tensor order-parameter fields. The resulting algorithm is able to include five independent Leslie viscosities, a Landau-deGennes free energy which introduces three or more elastic constants, a temperature dependent order parameter, surface anchoring and viscosity coefficients, flexoelectric and order electricity, and chirality. When combined with a solver for the Maxwell equations associated with the electric field, the algorithm is able to provide a full "device solver" for a liquid crystal display. Coupled lattice Boltzmann schemes are used to capture the evolution of the fast momentum and slow director motions in a computationally efficient way. The method is shown to give results in close agreement with analytical results for a number of validating examples. The use of the method is illustrated through the simulation of the motion of defects in a zenithal bistable liquid crystal device.

AimsStent deployment causes endothelial cells (EC) denudation, which promotes in-stent restenosis and thrombosis. Thus endothelial regrowth in stented arteries is an important therapeutic goal. Stent struts modify local hemodynamics, however the effects of flow perturbation on EC injury and repair are incompletely understood. By studying the effects of stent struts on flow and EC migration, we identified an intervention that promotes endothelial repair in stented arteries.Methods and ResultsIn vitro and in vivo models were developed to monitor endothelialization under flow and the influence of stent struts. A 2D parallel-plate flow chamber with 100 μm ridges arranged perpendicular to the flow was used. Live cell imaging coupled to computational fluid dynamic simulations revealed that EC migrate in the direction of flow upstream from the ridges but subsequently accumulate downstream from ridges at sites of bidirectional flow. The mechanism of EC trapping by bidirectional flow involved reduced migratory polarity associated with altered actin dynamics. Inhibition of Rho-associated protein kinase (ROCK) enhanced endothelialization of ridged surfaces by promoting migratory polarity under bidirectional flow (P < 0.01). To more closely mimic the in vivo situation, we cultured EC on the inner surface of polydimethylsiloxane tubing containing Coroflex Blue stents (65 μm struts) and monitored migration. ROCK inhibition significantly enhanced EC accumulation downstream from struts under flow (P < 0.05). We investigated the effects of ROCK inhibition on re-endothelialization in vivo using a porcine model of EC denudation and stent placement. En face staining and confocal microscopy revealed that inhibition of ROCK using fasudil (30 mg/day via osmotic minipump) significantly increased re-endothelialization of stented carotid arteries (P < 0.05).ConclusionsStent struts delay endothelial repair by generating localized bidirectional flow which traps migrating EC. ROCK inhibitors accelerate endothelial repair of stented arteries by enhancing EC polarity and migration through regions of bidirectional flow.

Computer simulations can potentially be used to design, predict, and inform properties for tissue engineering perfusion bioreactors. In this work, we investigate the flow properties that result from a particular poly-L-lactide porous scaffold and a particular choice of perfusion bioreactor vessel design used in bone tissue engineering. We also propose a model to investigate the dynamic seeding properties such as the homogeneity (or lack of) of the cellular distribution within the scaffold of the perfusion bioreactor: a pre-requisite for the subsequent successful uniform growth of a viable bone tissue engineered construct. Flows inside geometrically complex scaffolds have been investigated previously and results shown at these pore scales. Here, it is our aim to show accurately that through the use of modern high performance computers that the bioreactor device scale that encloses a scaffold can affect the flows and stresses within the pores throughout the scaffold which has implications for bioreactor design, control, and use. Central to this work is that the boundary conditions are derived from micro computed tomography scans of both a device chamber and scaffold in order to avoid generalizations and uncertainties. Dynamic seeding methods have also been shown to provide certain advantages over static seeding methods. We propose here a novel coupled model for dynamic seeding accounting for flow, species mass transport and cell advection-diffusion-attachment tuned for bone tissue engineering. The model highlights the timescale differences between different species suggesting that traditional homogeneous porous flow models of transport must be applied with caution to perfusion bioreactors. Our in silico data illustrate the extent to which these experiments have the potential to contribute to future design and development of large-scale bioreactors.