André M. Sonnet

Evolution of vesicles subject to adhesion

We derive the evolution equation for a lipid vesicle in the presence of an adhering wall, under the assumption that the vesicles membrane is permeable to the surrounding fluid that is permanently at rest. For vesicles in two dimensions, we study the asymptotic decay to a circle and the incipient adhesion to a flat wall with a piecewise adhesion potential. We illustrate several computer animations driven by the evolution equation obtained here. They are available in full at http://smmm.unipv.it/vesicles.html.

Flow and reorientation in the dynamics of nematic defects

We propose a simple phenomenological model for hydrodynamic defect dynamics in nematic liquid crystals, inspired by the Ericksen–Leslie theory. We identify the main forces that govern both fluid and defect motion and we comment on their symmetry. As shown for two annihilating disclinations, our model is predictive for arbitrary length scales and topological charges.

Order parameter dependence of the viscosity coefficients of a biaxial nematic liquid crystal

We derive expressions for the order parameter dependence of the viscosity coefficients of a biaxial nematic liquid crystal by comparing its dissipation function expressed in terms of directors with that expressed in terms of order tensors. The results enable us to identify the dominant flow viscosity coefficients and to compare their temperature variation according to their dependence on the dominant scalar order parameters. By considering different orientations of an external field, we identify three characteristic switching times corresponding to three rotational viscosities, and we estimate the ratio of the switching times of the primary and the secondary directors.

Reorientational dynamics of conjugated nematic point defects

To appreciate the universal qualitative features of defect annihilation in nematic liquid crystals, we study how the viscous force of reorientational dynamics behaves under a transformation that reverses the sign of the defects topological charge. As an illustration of our general results, we consider a class of point defects that were first studied by A. Saupe. The reorientational viscous forces acting on them differ dramatically from those acting on line defects.

Lifting ordered surfaces: ellipsoidal nematic shells

When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as pre-image of the physical surface under a suitable height function. This paper proposes a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. To produce a specific application, we specialize this method to nematic shells, for which it also provides a simple, but convincing interpretation of the outcomes of some molecular-dynamics experiments on ellipsoidal shells.When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeler faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as preimage of the physical surface under a suitable height function. This paper applies a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. We specialize this method to nematic shells, for which it also provides a simple but perhaps convincing interpretation of the outcomes of some molecular dynamics experiments on ellipsoidal shells.

Order Tensor Theories

The history of order tensor theories is a long and winding one. Since DE GENNES introduced what he called the tensor order parameter in [57, 58] to phrase a LANDAU- GINZBURG-type theory for the nematic order, many steps have been taken toward a general continuum theory of nematics with tensorial order. Using standard methods of nonequilibrium thermodynamics, HESS [142, 143] and later OLMSTED and GOLDBART [254, 255] obtained constitutive theories for homogeneous alignments, later generalized by HESS and PARDOWITZ to include also spatial variations [145]. All these attempts were impaired by not yielding the full anisotropy of viscosities predicted by the ERICKSEN-LESLIE director theory. An extension using a codeformational model was proposed in [144], and while it recovered the complete anisotropy of viscosities, it failed to be otherwise fully consistent with the phenomenological ERICKSEN-LESLIE theory [267].

Dynamics of Dissipative Fluids

In the first chapter we explored the microscopic origins of orientational order. We now turn to macroscopic continuum theories. These are phenomenological theories that attempt to model real materials. They do not attempt to explain material properties by resorting to the molecular structure of matter, but they can draw inspiration from molecular theories—and the best of modern theories actually do so, in the spirit of a true multiscale approach to materials science. The same continuum theory can describe different materials by means of specific constitutive laws, which being first formulated in accordance with general invariance and symmetry principles, are then corroborated by matching experimental evidence with theoretical predictions, a comparison that eventually determines the phenomenological coefficients of the continuum theory. Often, it is also possible to link microscopic and macroscopic theories by estimating directly on molecular grounds the values of the phenomenological coefficients—for example, through a mean field theory. Whenever this happens, we extract the best from both worlds.