Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix---ferronematics---as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.


  1. ferronematics
  2. liquid crystal
  3. homogenization

MSC codes

  1. 35B27
  2. 35Q56

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Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 237 - 262
ISSN (online): 1095-712X


Submitted: 20 February 2013
Accepted: 4 December 2013
Published online: 6 March 2014


  1. ferronematics
  2. liquid crystal
  3. homogenization

MSC codes

  1. 35B27
  2. 35Q56



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