C. M. Care

Computer simulation of liquid crystals

A review is presented of molecular and mesoscopic computer simulations of liquid crystalline systems. Molecular simulation approaches applied to such systems are described, and the key findings for bulk phase behaviour are reported. Following this, recently developed lattice Boltzmann approaches to the mesoscale modelling of nemato-dynamics are reviewed. This paper concludes with a discussion of possible areas for future development in this field.

A lattice spring model of heterogeneous materials with plasticity

A three-dimensional lattice spring model of a heterogeneous material is presented. For small deformations, the model is shown to recover the governing equations for an isotropic elastic medium. The model gives reasonable agreement with theoretical predictions for the elastic fields generated by a spherical inclusion, although for small particle sizes the discretization of the underlying lattice causes some departures from the predicted values. Plasticity is introduced by decreasing the elastic moduli locally whilst maintaining stress continuity. Results are presented for a spherical inclusion in a plastic matrix and are found to be in good agreement with the predictions of Wilner (1988 J. Mech. Phys. Solids 36 141-65).

Lattice Boltzmann modelling of blood cell dynamics

Many diseases are a result of, or are associated with, abnormal blood flow. Usually, these abnormalities are caused by unhealthy red blood cells with modified shape which have difficulty traversing the microvessels. Unfortunately, experimental approaches to these problems are limited due to difficulties in isolating the critical determinants of flow in vivo or in vitro. Computer models overcome these problems, but most strive only to reproduce the macroscopic, continuum aspect of blood flow by making many simplifying assumptions. Unfortunately, these models cannot address the relationship between microscopic, cellular flow dynamics and macroscopic, bulk blood rheology. Here, we demonstrate the wide applicability of a novel, computational model for simulating blood flow that includes each blood cell explicitly. This fully 3D model accounts for cell membrane dynamics and reproduces rest shapes accurately. This model allows us to: (i) extract empirical relationships for use in macroscopic models and (ii) simulate various disease states to identify potential targets for therapy. We show here that the model accurately reproduces the well-documented flow relationships for healthy blood, and also predicts the abnormalities in blood rheology exhibited by malaria and sickle cell patients.

Multi-component lattice Boltzmann equation for mesoscale blood flow

We present an improved lattice Boltzmann model of multi-component flow which permits practical, hydrodynamic modelling of multiple immiscible fluids. The model is robust and significantly reduces the interface anisotropy and micro-currents, which are artefacts observed in many schemes. Our new scheme is used on a particular regime of blood flow: that of the veinule mesoscale, where it is necessary to resolve significant numbers of deformable, interacting cells, which we model as incompressible liquid drops. We demonstrate the models ability to recover the complex flow phenomena typical of the veinule scale.

A MONTE CARLO SIMULATION OF THE MICELLAR PHASE OF AN AMPHIPHILE AND SOLVENT MIXTURE

Results are presented from Monte Carlo simulations of a three-dimensional lattice model of a binary mixture of solvent and amphiphile chains in which free self-assembly of the chains is allowed. The use of a lattice model allows good statistics to be collected for clusters containing up to 100 chains. The model exhibits a critical micelle concentration and a cluster size distribution with a minimum and maximum in the micellar region. The dependence of the weight average aggregation number on the total amphiphile concentration is found to obey theoretical predictions. The dilute solution excess chemical potential μ0 n - μ0 1 is determined from the cluster size distribution, where n is the number of monomers in a cluster. A single analytical expression is found to describe the cluster size distribution and the behaviour of the monomer concentration with total amphiphile concentration in the concentration range from 0 to 10 vol%. The excess chemical potential is found to be a monotonically decreasing functio...

In silico multi-scale model of transport and dynamic seeding in a bone tissue engineering perfusion bioreactor†

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. Biotechnol. Bioeng. 2013; 110: 1221–1230.

A Monte Carlo Simulation of Cyclic Polymeric Liquid Crystals

Abstract A cyclic polymeric liquid crystal system is simulated using the Metropolis Monte Carlo method in the NVT ensemble. The polymeric system consists of mesogenic moieties attached to siloxane ring polymers and is simulated with two different mathematical models. In one model, the polymer molecules are represented as objects with disc-like symmetry, and columnar stacking of these molecules has been observed for simulations in two dimensions. In the other model the mesogenic moieties are represented individually by an anisotropic Lennard-Jones potential. The ring is represented solely as a constraint on the relative motions of the attached mesogens. If the ring-mesogen link is sufficiently flexible the mesogens are found to order at low temperatures.

Phase diagram for the lattice model of amphiphile and solvent mixtures by Monte Carlo simulation

Results are presented from a Metropolis Monte Carlo simulation in the NVT ensemble of a three-dimensional lattice model of an amphiphile and solvent mixture. In this model the amphiphiles are represented as flexible chains of adjacent sites with one site at the end of the chain representing the solvophobic head site.The simulation exhibits self-assembly of micelles, vesicles and bilayers from random starting configurations. A temperature–concentration phase diagram is obtained for chains of length four with a fixed value of head–solvent interaction. At low concentrations the model exhibits a sharp critical micelle concentration despite a high cluster size polydispersity and a weak minimum in the cluster size distribution. The micelles grow with increasing concentration and form cylindrical structures. At high concentrations the system exhibits a transition from a bicontinuous phase at high temperatures to a lamellar phase at low temperatures.

Enhanced closure scheme for lattice boltzmann equation hydrodynamics

A simple and adaptable closure algorithm for the edge nodes of a lattice Boltzmann fluid simulation space is presented. Its rules are designed to be correct at every instant, to maintain local mass and to produce a specified fluid velocity and, crucially, the correct strain rate tensor at the resulting fluid boundary. Further, our algorithm models the fluid on boundary nodes to the same accuracy as on the bulk nodes and in a demonstrably equivalent manner, requiring only a specified boundary velocity, the fluid boundary pressure emerging. Illustrative results for steady and time-dependent flows, together with outline generalizations, are presented.

A computer simulation study of tilted smectic mesophases

We present comprehensive results from constant NVT and constant NPT Monte Carlo simulations of particles interacting via a biaxial variant of the Gay–Berne potential which we term the Internally Rotated Gay–Berne (IRGB) potential. The IRGB potential may be considered to be a single-site approximation to the interaction between two zig–zag shaped molecules, the extent of this molecular biaxiality being characterized by an internal rotation angle δ. We find that increasing the value of δ frustrates the formation of orientationally ordered phases, all phase transitions being shifted to lower temperatures and higher densities. Additionally, for δ⩾30 degrees, the smectic B phase is replaced by the tilted smectic J phase. The smectic A phase, in contrast, is destabilized completely for sufficiently large δ, with neither smectic A nor its tilted equivalent, smectic C, being observed. This suggests that models for smectic C-formation which are based on biaxial intermolecular attractions may not offer the best rou...