Nematic Liquid Crystal Flows Research Articles

Global existence of weak solutions to the two‐dimensional nematic liquid crystal flow with partially free boundary

AbstractWe consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.

Global existence of strong solutions to the isentropic compressible nematic liquid crystal equations in a cuboid domain

In this paper, we study the initial-boundary value problem of three-dimensional compressible nematic liquid crystal equations in a cuboid domain. We prove that the strong solution exists globally in the time provided that both the initial L1-norm of the density ‖ρ0‖L1 and the initial L3-norm of the gradient of orientation field ‖∇d0‖L3 for nematic liquid crystal flow are small enough. The main tools of proving the global well-posedness are some time-weighted a priori estimates designed for the compressible nematic liquid crystal equations.

Global existence and exponential decay of strong solutions to the 3D nonhomogeneous nematic liquid crystal flows with density-dependent viscosity

Global existence and exponential decay of strong solutions to the 3D nonhomogeneous nematic liquid crystal flows with density-dependent viscosity

Global well-posedness of strong solutions to the two-dimensional inhomogeneous biaxial nematic liquid crystal flow with vacuum

This paper considers the inhomogeneous biaxial nematic liquid crystal flow in a smooth bounded domain Ω⊂R2, where the velocity u and the orthogonal unit vector fields (m,n) admit the Dirichlet and Neumann boundary condition, respectively. By applying piecewise estimate and continuity method, we get the global existence of strong solutions, provided that the basic energy is suitably small. Our result may be regarded as an extension and improvement of Gong-Lin (2022) and Li-Liu-Zhong (2017) to the Neumann boundary condition, where the initial vacuum is allowed. Some new techniques are developed in order to deal with integral estimates caused by the boundary condition, and more complicated model.

A new regularity criterion for the 3D nematic liquid crystal flows

The aim of this study was to establish a new regularity criterion for local-in-time smooth solutions for the 3D nematic liquid crystal flows in terms of the horizontal gradient of two horizontal velocity components in the framework of the homogeneous Besov [Formula: see text] space and one directional derivative of molecular orientations in the framework of the homogeneous Morrey–Campanato [Formula: see text] space. More precisely, we show that the smooth solution [Formula: see text] can be extended beyond [Formula: see text], provided that [Formula: see text]

Singularity Formation for Full Ericksen–Leslie System of Nematic Liquid Crystal Flows in Dimension Two

Singularity Formation for Full Ericksen–Leslie System of Nematic Liquid Crystal Flows in Dimension Two

Notes on Liouville‐type theorems for the 3D compressible nematic liquid crystal equations

In this note, we investigate steady compressible nematic liquid crystal flows in . We establish Liouville‐type theorems for smooth solutions that fulfill specific conditions within Lorentz spaces.

Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow

Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow

Hydrodynamic cavitation in Stokes flow of nematic liquid crystal

The impact of hydrodynamic cavitation is one of the key factors in the fabrication and application of metal materials. The hydrodynamic cavitation in anisotropic fluids can be much different from common fluids due to the unique fluid dynamics characteristics related to the director field. In this paper, the hydrodynamic cavitation of nematic liquid crystal 5CB flowing around a cylindrical pillar in a microchannel in the Stokes flow regime is studied at various Reynolds numbers and blockage ratios by experiments. Once the Reynolds number rises over a threshold value, the hydrodynamic cavitation of nematic liquid crystal is generated in the stokes flow in the microchannel, which is the unique phenomenon for anisotropic fluids. The critical Reynolds number of cavitation inception decreases with the increase of the blockage ratio. The Strouhal number is induced to describe this unsteady oscillating cavitation flow, while the Strouhal number increases and decreases with the increase of the blockage ratio and Reynolds number, respectively. Dynamics characteristics of the cavitation including cavity volume, oscillation frequency, and pressure difference are analyzed at different Reynolds numbers and blockage ratios by image binarization treatment and Fast Fourier Transformation analysis. The results of this study are useful for the application of microfluidic chips based on nematic liquid crystals and protection of devices in the environment of similar anisotropic fluids.

Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum

Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum

Hydrodynamic cavitation of nematic liquid crystal in Stokes flow behind bluff body with different shapes in microchannel

Hydrodynamic cavitation, which occurs when the local pressure is below the saturated vapor pressure in hydrodynamic flow, is ubiquitous in fluid dynamics and implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. In this paper, the hydrodynamic cavitation in the bluff body bypass flow of nematic liquid crystal 5CB in the microchannel is experimentally investigated. By 5CB, we mean the thermotropic liquid crystal 4′-pentyl-4-biphenylcarbonitrile. When the Reynolds number is in the range of 3 × 10−4 < Re < 1.2 × 10−3, a special flow phenomenon behind the bluff body is observed, namely, the disclination loop. The critical Reynolds number of cavitation inception varies with the shape of the bluff body, while the lowest value corresponds to the triangular bluff body. The hydrodynamic cavitation occurs in the Stokes flow regime with the Reynolds number significantly lower than 0.1 for all bluff bodies. There is a close relation between the oscillation behavior of cavitation domains and the structure of the bluff body. In addition, the pressure difference between the inlet and outlet of the microchannel shows linear relation with the Reynolds number rather than the quadratic relation for isotropic fluids, which proves the presence of shear thinning in the flow of nematic liquid crystals. The study in this paper on the hydrodynamic cavitation of nematic liquid crystal can broaden the research on providing new approaches for the enhancement of fluid mixing and heat transfer in microfluidic chips.

The Large Time Behavior for Compressible Non-Isothermal Nematic Liquid Crystal Flows with Vacuum at Infinity

The Large Time Behavior for Compressible Non-Isothermal Nematic Liquid Crystal Flows with Vacuum at Infinity

Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in 3D bounded domains

Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in 3D bounded domains

A blow‐up criterion for the compressible nematic liquid crystal flows in three dimensions

In this paper, we consider the strong solutions under three different types of boundary problems to a compressible nematic liquid crystals system in three dimensions. We establish the blow‐up criterion in terms of the density and the gradient of direction field, provided the shear viscosity and bulk viscosity coefficients of the fluid satisfy an additional relation (i.e., ). In particular, the initial vacuum is allowed.

A new blowup criterion of strong solutions to the two‐dimensional equations of compressible nematic liquid crystal flows

In this paper, we concern the Cauchy problem of two‐dimensional (2D) compressible nematic liquid crystal flows with vacuum as far‐field density. Under a geometric condition for the initial orientation field, we establish a blowup criterion in terms of the integrability of the density for strong solutions to the compressible nematic liquid crystal flows. This criterion generalizes previous results of compressible nematic liquid crystal flows with vacuum, which concludes the initial boundary problem and Cauchy problem.

Global strong solutions for compressible nematic liquid crystal flows

We investigate a simplified compressible isentropic nematic liquid crystal flow in R3. We show the existence and uniqueness of global solutions belonging to a new class of functions provided that the initial energy is properly small. Our result may be regarded as a generalization of Li–Xu–Zhang’s work (Li et al., 2018) in the sense that the lower regularities of initial data are required.

Global Strong Solutions to the Compressible Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 2D Bounded Domains

Global Strong Solutions to the Compressible Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 2D Bounded Domains

On the blow up criterion for the 3D nematic liquid crystal flows involving the second eigenvalue of the deformation tensor

On the blow up criterion for the 3D nematic liquid crystal flows involving the second eigenvalue of the deformation tensor

A stabilized divergence-free virtual element scheme for the nematic liquid crystal flows

In this work, we propose and analyze a stabilized divergence-free virtual element method (VEM) for approximating the hydrodynamics system of nematic liquid crystal flows. By adding appropriate stabilization term so that the nonlinear potential function can be treated explicitly, and using the implicit-explicit (IMEX) approach to handle the nonlinear coupling terms, we develop a linear and energy-stable fully discrete virtual element scheme. We further prove that the fully discrete scheme is uniquely solvable and energy stable in discrete sense, moreover, we obtain the optimal error estimates rigorously. Finally, numerical examples are provided to demonstrate the accuracy, stability and efficiency of the proposed scheme.

Number of Singular Points and Energy Equality for the Co-rotational Beris–Edwards System Modeling Nematic Liquid Crystal Flow

Number of Singular Points and Energy Equality for the Co-rotational Beris–Edwards System Modeling Nematic Liquid Crystal Flow