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The emergence of new techniques for the fabrication of nematic droplets with nontrivial topology provides new routes for the assembly of responsive devices. Here we perform a numerical study of spherical nematic droplets on fibres. We analyse the equilibrium textures and find that, under certain conditions,the nematic can avoid the nucleation of topological defects. We consider in detail a homeotropic nematic droplet wrapped around a fibre with planar anchoring. We investigate the effect of an electric field on the texture of this droplet such type of system. In the presence of a DC field, the system undergoes a Freederickzs-like transition above a given threshold $E_c$. We also consider AC fields, at high and low frequencies, and find that the textures are similar to those observed for static fields, in contrast with recently reported experiments., Comment: 8 pages, 5 figures, submitted

Understanding the flow of liquid crystals in microfluidic environments plays an important role in many fields, including device design and microbiology. We perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal flowing under an applied pressure gradient in two-dimensional channels with various anchoring boundary conditions at the substrate walls. We investigate the relation between flow rate and pressure gradient and the corresponding profile of the nematic director, and find significant departures from the linear Poiseuille relation. We also identify a morphological transition in the director profile and explain this in terms of an instability in the dynamical equations. We examine the qualitative and quantitative effects of changing the type and strength of the anchoring. Understanding such effects may provide a useful means of quantifying the anchoring of a substrate by measuring its flow properties.