Biomedical subjects

P I C Teixeira

Publications and source records attributed to P I C Teixeira.

8 recordsLinked to original sources

PubMed2006

Simple model for biaxial smectic-A liquid-crystal phases.

We have generalized the McMillan theory of liquid crystalline smectic order in uniaxial particle fluids to biaxial particles. Upon varying the control parameter, a uniaxial nematic phase may: (i) order biaxially first, then smectically; (ii) order smectically first, then biaxially; and (iii) simultaneously order biaxially and smectically. We investigate, in the limit of complete orientational order of the molecular major axes, which of these scenarios are realized for a simple model of particles with the symmetry of rectangular parallelepipeds. We also present a generic variational derivation of the theory based on the identification of the dominant order parameters for the most ordered phase.

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PubMed2005

Triple-line decoration and line tension in simple three-dimensional foam clusters.

We show that if the triple line around a three-dimensional double bubble or lens bubble is decorated with another bubble or with a Plateau border, then the film prolongations into the decoration no longer meet at 2pi/3. These deviations can be accounted for in terms of a line tension that equals half the excess surface energy associated with the decoration.

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PubMed2005

Symmetry-breaking transitions and dissociation of two-dimensional Plateau borders.

We have experimentally studied the dissociation/coalescence of internal Plateau borders (PBs) in simple monolayer bubble clusters, as a result of changing the liquid fraction. At large liquid content, the clusters consist of n bubbles of the same size, symmetrically placed around an internal n-sided PB (n-PB). On decreasing the liquid fraction we observed symmetry-breaking transitions in the 4- and 5-bubble clusters (but not in the 3-bubble cluster), followed by dissociation of the PBs. We used the Surface Evolver to determine the various equilibrium configurations of the corresponding two-dimensional wet clusters and their surface energies. The sequence of 4-bubble cluster configurations observed on varying the liquid fraction correlates qualitatively with that predicted on the basis of Surface Evolver calculations. The same is not true of the 5-bubble cluster.

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PubMed2004

Mechanical instabilities of bubble clusters between parallel walls.

We have carried out a systematic study of buckling-like mechanical instabilities in simple two- (2D) and three-dimensional (3D) symmetric foam clusters sandwiched between parallel planar walls. These instabilities occur when the wall separation w is reduced below a critical value, w*, for which the foam surface energy E reaches its minimum, E*. The clusters under investigation consist of either a single bubble, or of "twin bubbles" of fixed equal sizes (areas A in 2D or volumes V in 3D), which are either free to slide or pinned at the confining walls. We have numerically obtained w* for both free and pinned 2D and 3D clusters. Furthermore, we have calculated the buckled configurations of 2D twin bubbles, either free or pinned, and of 3D free twin bubbles, whose energy is independent of w and equal to the minimum energy E* of the unbuckled state. Finally, we have also predicted the critical w(t)* at which the terminal configurations under extension of 2D and 3D single and twin bubbles are realised. Experimental illustrations of these transitions under compression and extension are presented. Our results, together with others from the literature, suggest that a bubble cluster bounded by two parallel walls is stable only if the normal force it exerts on the walls is attractive, i.e., if dE/dw > 0; clusters that cause repulsion between the walls are unstable. We correlate this with the distribution of film orientations: films in a stable cluster cannot be "too parallel" to the confining walls; rather, their average tilt must be larger than for a random distribution of film orientations.

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PubMed2002

Distribution of film orientations in free and strained foams.

We show that the distribution of film orientations in a free (i.e., unstrained) foam cluster, though in general not uniform, has the same second moments as a uniform distribution. This is, however, in general not true of its other moments, which reflects the internal order of film orientations imposed by Plateau's laws. For a strained cluster, we relate the deviations of the second moments of the orientation distribution from their values for an unstrained cluster, to the stresses acting on the cluster. Our predictions are corroborated by experimental results for free and strained two-dimensional clusters, allowing us to find the force on a cluster bounded by two parallel walls.

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PubMed2002

Theoretical and finite-element investigation of the mechanical response of spinodal structures.

In recent years there have been major advances in our understanding of the mechanisms of phase separation in polymer and copolymer blends, to the extent that good control of phase-separated morphology is a real possibility. Many groups are studying the computational simulation of polymer phase separation. In the light of this, we are exploring methods which will give insight into the mechanical response of multiphase polymers. We present preliminary results from a process which allows the production of a two-dimensional finite-element mesh from the contouring of simulated composition data. We examine the stretching of two-phase structures obtained from a simulation of linear Cahn-Hilliard spinodal phase separation. In the simulations, we assume one phase to be hard, and the other soft, such that the shear modulus ratio G is large (>or= 10(3)). We indicate the effect of varying composition on the material modulus and on the distribution of strains through the stretched material. We also examine in some detail the symmetric structures obtained at 50% composition, in which both phases are at a percolation threshold. Inspired by simulation results for the deformation of these structures, we construct a "scaling" theory, which reproduces the main features of the deformation. Of particular interest is the emergence of a lengthscale, below which the deformation is non-affine. This length is proportional to G(1/4), and hence is still quite small for all reasonable values of this ratio. The same theory predicts that the effective composite modulus scales also as G(1/4), , which is supported by the simulations.

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PubMed2002

Mixing and sorting of bidisperse two-dimensional bubbles.

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area lambda (lambda< or =1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of lambda, the minimal configuration for N-->infinity. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in "phase-separated" clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N, lambda). As lambda is varied, this alternates between a circular cluster of one of the mixed tilings, and "partial wetting" of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area lambda.

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PubMed2002

Lower bounds for the surface energy of two-dimensional foams.

Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell boundaries ( i.e., films between bubbles) has a local minimum. For a given set of bubble areas Ai (i=1,..., N), P can be written in the form P=R(SigmaN(i=1) square root Ai)/2, where R is topology dependent. We seek the set of areas Ai and the cluster topology that minimise R, and propose lower bounds for R that set lower bounds for the surface energy of i) individual bubbles, with circular edges meeting at 2pi/3 angles at vertices (Plateau cells), and ii) infinite periodic bubble clusters.

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