Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Simple shearing flow of dry soap foams with TCP structure[Tetrahedrally Close-Packed]

The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization

Foam Microrheology

The microrheology of liquid foams is discussed for two different regimes: static equilibrium where the capillary number Ca is zero, and the viscous regime where viscosity and surface tension are important and Ca is finite. The Surface Evolver is used to calculate the equilibrium structure of wet Kelvin foams and dry soap froths with random structure, i.e., topological disorder. The distributions of polyhedra and faces are compared with the experimental data of Matzke. Simple shearing flow of a random foam under quasistatic conditions is also described. Viscous phenomena are explored in the context of uniform expansion of 2D and 3D foams at low Reynolds number. Boundary integral methods are used to calculate the influence of Ca on the evolution of foam microstructure, which includes bubble shape and the distribution of liquid between films, Plateau borders, and (in 3D) the nodes where Plateau borders meet. The micromechanical point of view guides the development of structure-property-processing relationships for foams

Bubble shapes in foams: the importance of being isotropic

Foams, and by extension a whole class of random cellular materials are characterized by minimizing total interfacial area between the cells. Both structure and evolution of such materials by aging (coarsening) are ill-understood because of our lack of knowledge of the cell geometry. Combining Plateau's rules and certain symmetry requirements, we analytically determine the geometry of generic polyhedral cells we call Isotropic Plateau Polyhedra (IPPs). Their properties, such as surface area, edge length, or coarsening rate, are exactly known and very close approximations to the corresponding properties of average, random foam bubbles. Certain IPPs can also be found experimentally in soap foam. We show that measuring the coarsening rate of these bubbles allows for the simple computation of the soap film thickness, which is found to vary with foam age

Bubble shapes in foams: the importance of being isotropic

Foams, and by extension a whole class of random cellular materials are characterized by minimizing total interfacial area between the cells. Both structure and evolution of such materials by aging (coarsening) are ill-understood because of our lack of knowledge of the cell geometry. Combining Plateau's rules and certain symmetry requirements, we analytically determine the geometry of generic polyhedral cells we call Isotropic Plateau Polyhedra (IPPs). Their properties, such as surface area, edge length, or coarsening rate, are exactly known and very close approximations to the corresponding properties of average, random foam bubbles. Certain IPPs can also be found experimentally in soap foam. We show that measuring the coarsening rate of these bubbles allows for the simple computation of the soap film thickness, which is found to vary with foam age