We have studied the two-dimensional axisymmetric Ericksen–Leslie equations with the non-zero inertial constant. The existence and uniqueness of the global weak solution is proved under certain ...assumptions. In the neighborhood of the solid surface we derived the boundary layer equations and show that the effective viscosity of the liquid in the boundary layer decreases as the inertial constant grows. Under the assumption that the Reynolds number is large enough we prove the solution to the boundary layer equations to be close to the solution of the original problem in the Sobolev space.
•Axisymmetric Ericksen–Leslie equations have a unique global solution.•The effective viscosity near the boundary decreases as the inertial constant grows.•The boundary layer equations are valid if Reynolds number is large enough.
Biomechanical ordering of dense cell populations Volfson, Dmitri; Cookson, Scott; Hasty, Jeff ...
Proceedings of the National Academy of Sciences - PNAS,
10/2008, Letnik:
105, Številka:
40
Journal Article
Recenzirano
Odprti dostop
The structure of bacterial populations is governed by the interplay of many physical and biological factors, ranging from properties of surrounding aqueous media and substrates to cell-cell ...communication and gene expression in individual cells. The biomechanical interactions arising from the growth and division of individual cells in confined environments are ubiquitous, yet little work has focused on this fundamental aspect of colony formation. We analyze the spatial organization of Escherichia coli growing in a microfluidic chemostat. We find that growth and expansion of a dense colony of cells leads to a dynamical transition from an isotropic disordered phase to a nematic phase characterized by orientational alignment of rod-like cells. We develop a continuum model of collective cell dynamics based on equations for local cell density, velocity, and the tensor order parameter. We use this model and discrete element simulations to elucidate the mechanism of cell ordering and quantify the relationship between the dynamics of cell proliferation and the spatial structure of the population.
The use of nematics in microfluidic devices offers methods of flow control that are inaccessible to isotropic fluids. While nematics have been used in channel flows found in lab on chip devices, ...their flow and microstructure formation still needs to be fully understood in geometries with a cylindrical cross-section. This paper investigates liquid crystal flows through capillaries via 1) the Beris-Edwards (BE) model and 2) the Leslie-Ericksen (LE) model, which emerges as a limiting case (uniaxial, constant order parameter) of the BE model. We show that the microstructure distribution is controlled by the Ericksen (
) and Deborah (
) numbers in the Beris-Edwards model. Defects at low Ericksen numbers arise when the elastic energy dominates the thermotropic energy. Defect destruction provides a new shear-thinning mechanism, which cannot be observed in the Leslie-Ericksen theory.
We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state ...of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.
We analyzed hydrodynamic fluctuations in nematic liquid crystals simulated by Multi-particle Collision Dynamics. Velocity effects on orientation were incorporated by allowing mesoscopic velocity ...gradients to exert torques on nematic particles. Backflow was included through an explicit application of angular momentum conservation during the collision events. We measured the spectra of hydrodynamic fluctuations and compared them with those derived from a linearized hydrodynamic scheme. Numerical results were found to reproduce the expected coupling between hydrodynamic modes, thus showing that the implementation simulates proper nematodynamic effects at the mesoscopic level.
Nematodynamics and random homogenization Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S. ...
Applicable analysis,
10/2016, Letnik:
95, Številka:
10
Journal Article
Recenzirano
Odprti dostop
We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen-Leslie equations for ...an incompressible medium with inhomogeneous density with random structure. Under the assumption that randomness is statistically homogeneous and ergodic, we construct the limit problem and prove almost sure convergence of solutions of the original problem to the solution of the limit (homogenized) problem.
In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence ...and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.
In this paper, we study the full three-dimensional Ericksen–Leslie system of equations for the nematodynamics of liquid crystals. We announce the short-time existence and uniqueness of strong ...solutions for the initial value problem in the periodic case and in a bounded domain with Dirichlet- and Neumann-type boundary conditions.
Dans cet article, nous étudions le système tridimensionnel complet des équations d'Ericksen–Leslie decrivant la nématodynamique des cristaux liquides. Nous donnons la formulation des théorèmes d'existence en temps court et d'unicité des solutions fortes pour le problème de valeur initiale dans le cas périodique et dans un domaine borné avec conditions au bord de types Dirichlet et Neumann.
Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincaré reduction produces a unifying framework for various theories, including Ericksen-Leslie, ...Luhiller-Rey, and Eringen’s micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing disclination density. All results are also extended to flowing liquid crystals.
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