Modeling and Analysis of Cooling Induced Isotropic Nematic Transitions in Pharmaceutical Liquid Crystals
Abstract
This paper studies the phase transition from an isotropic to a nematic liquid crystal driven by controlled cooling, motivated by the manufacturing of next-generation pharmaceutical drugs. Using the non-isothermal Ericksen model for liquid crystals with a variable degree of orientation, we formulate the problem as a stiff, quasilinear system of parabolic partial differential equations. We establish a consistent thermodynamic framework, prove the well-posedness of the system, and conduct a rigorous asymptotic and numerical scaling analysis of the moving phase boundary in a cylindrical cell subjected to bottom-wall convective cooling. Our analysis identifies a critical sample thickness that separates two distinct physical regimes. Below this threshold, the transition follows the cooling dynamics and the material remains quasi-isothermal. Above the thickness threshold, bulk thermal diffusion governs the dynamics, imposing a dominant thermal delay characterized by a concave quadratic propagation front. These results demonstrate that scaling from laboratory characterization to industrial production fundamentally alters the spatial thermal history of the material, providing a predictive mathematical framework to optimize cooling protocols for kinetic arrest.
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BibTeX
@misc{liu2026modeling,
title = {{Modeling and Analysis of Cooling Induced Isotropic Nematic Transitions in Pharmaceutical Liquid Crystals}},
author = {Pei Liu and Debanjan Banerjee and Daniel Siebel-Cortopassi and Sichen Song and Maria-Carme Calderer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00273},
eprint = {2611.00273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00273},
}
RIS
TY - UNPB
TI - Modeling and Analysis of Cooling Induced Isotropic Nematic Transitions in Pharmaceutical Liquid Crystals
AU - Pei Liu
AU - Debanjan Banerjee
AU - Daniel Siebel-Cortopassi
AU - Sichen Song
AU - Maria-Carme Calderer
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00273
UR - https://arxiv.org/abs/2611.00273
AB - This paper studies the phase transition from an isotropic to a nematic liquid crystal driven by controlled cooling, motivated by the manufacturing of next-generation pharmaceutical drugs. Using the non-isothermal Ericksen model for liquid crystals with a variable degree of orientation, we formulate the problem as a stiff, quasilinear system of parabolic partial differential equations. We establish a consistent thermodynamic framework, prove the well-posedness of the system, and conduct a rigorous asymptotic and numerical scaling analysis of the moving phase boundary in a cylindrical cell subjected to bottom-wall convective cooling. Our analysis identifies a critical sample thickness that separates two distinct physical regimes. Below this threshold, the transition follows the cooling dynamics and the material remains quasi-isothermal. Above the thickness threshold, bulk thermal diffusion governs the dynamics, imposing a dominant thermal delay characterized by a concave quadratic propagation front. These results demonstrate that scaling from laboratory characterization to industrial production fundamentally alters the spatial thermal history of the material, providing a predictive mathematical framework to optimize cooling protocols for kinetic arrest.
ER -