We calculate the long-range pair potential between spherical colloid particles suspended in a uniform liquid crystal. At weak director anchoring on the particle surface the director distortions decay as ␦nϳr Ϫ3 sin2 away from its center. This leads to an anisotropic interaction potential of the form Uϳd Ϫ5 with d the distance between two colloid particles. This interaction also depends on the particle position with respect to the nematic director, giving strong repulsion for particles along the director axis and for particles located in the perpendicular plane, and attraction at oblique angles. We also analyze the system behavior in an external field, when the director decays exponentially away from the particle and, hence, interaction forces are short range. ͓S1063-651X͑97͒02603-2͔PACS number͑s͒: 61.30. Gd, 82.70.Dd, 64.70.Md Colloid suspensions are characteristically mesoscopic systems with structure and time scales such that typical shear rates can bring them out of equilibrium and into some exotic states. Even without a flow the structure and properties of colloids pose a number of theoretical and experimental challenges ͓1,2͔. Of much interest are various novel interactions, for instance, hydrodynamic and polymeric solvent-mediated forces. Many obvious practical applications of colloid systems add to the fundamental interest of this class of objects.Colloid suspensions in a liquid crystal matrix are qualitatively different from their isotropic analogues due to the long-range deformation field n͑r͒ created by particles in the liquid crystal ͓3͔. Perhaps one of the most important applications of liquid crystal colloids is the moulding processing of filled liquid crystalline polymers and the suspension of abrasive particles in lyotropic mesophases. Recently the phase equilibrium of a nematic colloid has been examined experimentally ͓4͔. In that work the authors also explore the theoretical model, accounting for the steric interaction between particles and the concept of ''distortion'' of nematic order by individual particles.Obviously, the effect of a suspended particle on the orientational order in its surrounding will depend on the strength and type of director anchoring on its surface. Colloids with extremely weak anchoring will disturb the static director field very little, although in the flow one must expect a significant effect due to the Leslie-Ericksen coupling ͓5͔. Particles with very strong anchoring create a topological mismatch with the otherwise uniform director field and develop singularities. The resulting director texture can have a quadrupolar symmetry, such as that of the nematic matrix itself. In this case one obtains a pair of polar boojums for planar anchoring, or a (Ϫ1/2) disclination ring for radial ͑homeotropic͒ anchoring. The equilibrium quadrupolar director field around a single spherical particle has been analyzed theoretically ͓3͔, where it has been shown that in all cases the director distortions decay as r Ϫ3 away from the particle. It is possible that large particles with an a...

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We use a Monte Carlo algorithm to simulate the director field around a spherical inclusion in a uniform nematic liquid crystal matrix. The resulting structure crucially depends on the relative strength of the nematic bulk elasticity and the director anchoring on the particle surface. When this anchoring is weak, the director field perturbations are small and have quadrupolar symmetry. With increasing strength of anchoring two topologically nontrivial situations are possible: a dipolar configuration with a satellite point defect ͑hedgehog͒ near the particle pole, or a quadrupolar configuration with a ''Saturn ring'' of disclination around the particle equator.

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules.We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F ⊥ /F = 1.50) for an exactly computed field is in good agreement with experiments (∼ 1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic↔isotropic and for a rod-like and a disc-like liquid crystal will be given.

The flow of a liquid crystal around a body depends not only on the geometry of the body but also on the director field around it. For low-Ericksen number flows, the director distribution largely remains in its static equilibrium texture (along a uniform direction far away from the body and, for instance, perpendicular to its surface). We calculate the velocity and pressure of a cylinder in a nematic flow numerically, taking into account topological defects on the particle surface and find the drag force acting on the moving body. The drag force is, in general, non-central, i.e. not aligned with the direction of motion. The lift component of the drag force is a measure for the anisotropy of the system. We show that due to the realistic director texture the drag force is larger than previously thought and the anisotropy, FII/F^, smaller and decreasing while approaching the nematic clearing point.

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