Accepted Paper

Inserted: 29 jan 2021
Last Updated: 29 jan 2021

Journal: Mathematics in Engineering
Volume: 2
Number: 2
Pages: 290-312
Year: 2020
Doi: 10.3934/MINE.2020015

Abstract:

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the effective free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an effective free energy functional with an additional linear term, which may be interpreted as an "effective field" induced by the inclusions. Moreover, we compute the effective free energy in a regime of "very strong anchoring", that is, when the surface energy effects dominate over the volume free energy.