Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials

Sui, Yubing; Jiang, Jingzhou; Jin, Guigen; Yang, Xiaofeng

doi:10.1007/s10444-021-09865-8

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…the first line of Figure 4, which shows the discrete concentration φ n at different time step). This fact is in accordance with the simulations obtained in [44,53]. In addition, a second interesting aspect concerns the direction of the vector field d. As expected from the modeling viewpoint, the module of the polarization |d| becomes smaller inside the drop (φ ≈ 0) as shown in the second line of Figure 4.…”

Section: Ensupporting

confidence: 89%

“…To the best of our knowledge, no theoretical results have been discussed yet regarding system (1.11)- (1.16). On the contrary, numerical simulations have been presented in [12,44,53].…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Such number of elements is necessary to capture phenomena at the interface which is assumed to be of size ε 1. We study the benchmark example concerning the shape deformation of a drop of polymer immersed in a liquid crystal (see also [42,44,53]. To this end, we consider the following initial data…”

Section: Enmentioning

confidence: 99%

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Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics

Bevilacqua¹,

Giorgini²

2023

Preprint

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We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in a polar liquid crystal immersed in a Newtonian fluid. Such composite material is a paradigmatic example of complex fluids arising in Soft Matter which exhibits multiscale interplay. Beyond the Ginzburg-Landau and Frank elastic energies for the concentration and the polarization, the free energy of the system is characterized by a quadratic anchoring term which tunes the orientation of the polarization at the interface. This leads to several quasi-linear nonlinear couplings in the resulting system describing the macroscopic dynamics. In this work, we establish the first mathematical results concerning the global dynamics of two-phase complex fluids with interfacial anchoring mechanism. First, we determine a set of sufficient conditions on the parameters of the system and the initial conditions which guarantee the existence of global weak solutions in two and three dimensions. Secondly, we show that weak solutions are unique and globally regular in the two dimensional case. Finally, we complement our analysis with some numerical simulations to display polarization and interfacial anchoring.

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Section: Ensupporting

confidence: 89%

“…To the best of our knowledge, no theoretical results have been discussed yet regarding system (1.11)- (1.16). On the contrary, numerical simulations have been presented in [12,44,53].…”

Section: Mathematical Formulationmentioning

confidence: 99%