Biomedical subjects

Jun-ichi Fukuda

Publications and source records attributed to Jun-ichi Fukuda.

8 recordsLinked to original sources

PubMed2006

Numerical treatment of the dynamics of a conserved order parameter in the presence of walls.

We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing Delta z, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit Delta z --> 0, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.

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PubMed2005

Friction drag of a spherical particle in a liquid crystal above the isotropic-nematic transition.

We study the friction drag of a spherical particle in the isotropic phase of a nematic liquid crystal close to the isotropic-nematic transition point. To describe the orientational order in the liquid crystal, the second-rank tensor order parameter Qalphabeta is employed. We solve the hydrodynamic equations for Qalphabeta and the fluid velocity nu in order to determine the friction drag. In our discussion of the friction drag, we concentrate on four parameters: the temperature, the surface order parameter, the particle radius, and the Ericksen number Er (characterizing the ratio of the viscous force to the elastic force). The temperature dependence of the friction drag agrees well with experiments that show an increasing friction drag when the isotropic-nematic phase transition is approached from above. Furthermore the friction drag increases with the surface order parameter due to the more pronounced surface nematic layer, and for larger particles it is less affected by this layer. Finally, we observe that in the range of Er we study, the friction drag is almost independent of Er although flow-induced order occurs for sufficiently large Er and surface order parameter.

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PubMed2004

Numerical investigation of liquid crystal colloids using a continuum description.

We investigate numerically the configuration of a nematic liquid crystal around two spherical particles. For the description of the orientational order of a nematic liquid crystal, we adopt a Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) together with the use of bispherical coordinates to describe the geometry of the system with two spherical particles. Above but close to the nematic-isotropic transition point, we observe capillary condensation of a nematic liquid crystal between the two particles under appropriate conditions. Below the transition point where liquid crystals possess nematic order, a point-like defect called a hyperbolic hedgehog appears close to a particle when strong normal anchoring is imposed. With the aid of an adaptive mesh refinement scheme to achieve sufficient numerical resolution to describe topological defects, we present our numerical results showing how the orientation profile of a nematic liquid crystal is distorted when the distance between two particles is small enough.

Crystallization↗

PubMed2004

Capillary condensation in liquid-crystal colloids.

We study capillary condensation between two spherical particles dispersed in the isotropic phase of a nematic liquid crystal. Within the Landau-de Gennes theory, we calculate interaction energies due to the formation of capillary bridges that reproduce experimental observations. Close to the critical point of the transition line separating the no-bridge from the bridge configuration, fluctuations in the particle cluster might be described by an effective two-state system. We show that the transition line vanishes for small particles and that the shape of the interaction potential depends on particle size.

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PubMed2004

Interaction between two spherical particles in a nematic liquid crystal.

We numerically investigate the interaction between two spherical particles in a nematic liquid crystal mediated by elastic distortions in the orientational order. We pay attention to the cases where two particles with equal radii R0 impose rigid normal anchoring on their surfaces and carry a pointlike topological defect referred to as a hyperbolic hedgehog. To describe the geometry of our system, we use bispherical coordinates, which prove useful in the implementation of boundary conditions at the particle surfaces and at infinity. We adopt the Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) for the description of the orientational order of a nematic liquid crystal. We also utilize an adaptive mesh refinement scheme that has proven to be an efficient way of dealing with topological defects whose core size is much smaller than the particle size. When the two "dipoles," composed of a particle and a hyperbolic hedgehog, are in parallel directions, the two-particle interaction potential is attractive for large interparticle distances D and proportional to D-3 as expected from the form of the dipole-dipole interaction, until the well-defined potential minimum at D approximately 2.46 R0 is reached. For the antiparallel configuration with no hedgehogs between the two particles, the interaction potential is repulsive and behaves as D-2 for D less than or approximately equal 10R0, which is stronger than the dipole-dipole repulsion (approximately D-3 ) expected theoretically as an asymptotic behavior for large D.

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PubMed2004

Wetting of a spherical particle by a nematic liquid crystal.

We discuss how the curvature of a substrate influences wetting by a nematic liquid crystal concentrating on the surface of a spherical particle. Our investigation is based on Landau-de Gennes free energy formulated in terms of second-rank nematic order parameter Q(ij). We review the method to treat wetting transitions in curved geometries and calculate the wetting phase diagram in terms of the temperature and a surface coupling parameter. We find that the length of the prewetting line which corresponds to the boundary-layer transitions introduced by Sheng [Phys. Rev. A 26, 1610 (1982)] gradually decreases with a decrease in particle radius until it vanishes completely below a critical radius of about 100 nm. The prewetting line ends at a critical point which we study in detail. By interpreting the effect of curvature as an effective shift in temperature in Landau-de Gennes theory, we are able to formulate a good estimate for the critical temperature as a function of the inverse particle radius. It demonstrates that splay deformations around the particle significantly influence nematic wetting of curved surfaces.

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PubMed2002

Stability of a hyperbolic disclination ring in a nematic liquid crystal.

The stability of a hyperbolic disclination ring in a nematic liquid crystal is considered by extending the argument for a radial disclination ring due to Mori and Nakanishi. The ring configuration is indeed stable in the presence of the saddle-splay elasticity (characterized by K24). The ring radius is estimated to be a approximately 2.9r(c), with r(c) being the core radius when K24 approximately K/2, where K is the Frank elastic constant in the one-constant approximation.

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PubMed2002

Defect structure of a nematic liquid crystal around a spherical particle: adaptive mesh refinement approach.

We investigate numerically the structure of topological defects close to a spherical particle immersed in a uniformly aligned nematic liquid crystal. To this end we have implemented an adaptive mesh refinement scheme in an axi-symmetric three-dimensional system, which makes it feasible to take into account properly the large length scale difference between the particle and the topological defects. The adaptive mesh refinement scheme proves to be quite efficient and useful in the investigation of not only the macroscopic properties such as the defect position but also the fine structure of defects. It can be shown that a hyperbolic hedgehog that accompanies a particle with strong homeotropic anchoring takes the structure of a ring.

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