Size-topology relations in packings of grains, emulsions, foams, and biological cells.

Particulate packings in 3D are used to study the effects of compression and polydispersity on the geometry of the tiling in these systems. We find that the dependence of the neighbor number on cell size is quasilinear in the monodisperse case and becomes nonlinear above a threshold polydispersity, independent of the method of creation of the tiling. These size-topology relations can be described by a simple analytical theory, which quantifies the effects of positional disorder in the monodisperse case and those of size disorder in the polydisperse case and is applicable in two and three dimensions. The theory thus gives a unifying framework for a wide range of amorphous systems, ranging from biological tissues, foams, and bidisperse disks to compressed emulsions and granular matter.

Epithelial tissue statistics: eliminating bias reveals morphological and morphogenetic features.

Geometric order in quasi-two-dimensional epithelia has been extensively researched in order to identify and classify different tissues to help our understanding of how tissues form (morphogenesis) and how their formation may be influenced (tissue regeneration). However, the significance of published data -such as the distribution of numbers of cell neighbors- has been debatable because of measurement bias. We shown that such bias can be detected and corrected without detailed knowledge of the original samples, using only the biased (measured) distributions. This is true for both of the most important sources of bias: the measurement of apparent four-fold vertices and the selective preference for measuring smaller cells introduced by selecting a finite sampling window. The resulting unbiased data allows for a meaningful comparison of all available data, from different sources, taken with different experimental resolution and methodology. Conclusive evidence is found that the apparent four-fold vertices are neither distributed randomly nor oriented randomly, revealing profound differences in topological correlation between proliferating and remodeling tissues. The method is applied to measurements of Drosophila wing tissue, where it successfully disentangles distributional moments, allowing for an assessment of their relative importance, independence, and significance in tissue identification and classification.

Foam drainage on the microscale II. Imaging flow through single Plateau borders.

The liquid in foam forms an interconnected network, which is composed of Plateau borders, nodes, and films. One of the dominant pathways for foam drainage is flow through Plateau borders, and we use confocal microscopy to obtain experimental results for the flow fields inside individual Plateau borders. For three types of surfactants detailed comparisons are made with a model based upon the influence of surface viscosity at free boundaries between the gas in the bubbles and the liquid in the Plateau borders. The model describes the flows well, and we find good agreement between the surface viscosity predicted by this model and representative values found in the literature. We also give a qualitative description of the flow in the nodes.

Foam drainage on the microscale I. Modeling flow through single Plateau borders.

The drainage of liquid through a foam involves flow in channels, also called Plateau borders, which generally are long and slender. We model this flow by assuming the flow is unidirectional, the shear is transverse to the flow direction, and the liquid/gas interfaces are mobile and characterized by a Newtonian surface viscosity, which does not depend on the shear rate. Numerical finite difference simulations are performed, and analytical approximations for the velocity fields inside the channels and the films that separate the bubbles are given. We compare the liquid flow rates through interior channels, exterior channels (i.e., channels contacting container walls) and films. We find that when the number of exterior channels is comparable to the number of interior channels, i.e., narrow container geometries, the exterior channels can significantly affect the dynamics of the drainage process. Even for highly mobile interfaces, the films do not significantly contribute to the drainage process, unless the amount of liquid in the films is within a factor of ten of the amount of liquid in the channels.

Dynamics of coarsening foams: accelerated and self-limiting drainage.

The evolution of a foam is determined by drainage flow of the continuous (liquid) phase and coarsening (aging) of the dispersed phase (gas bubbles). Free-drainage experiments with slow- and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of the two effects. Strong coarsening leads to drainage times that are shorter (accelerated drainage) and independent of the initial liquid content (self-limiting drainage). A model incorporating the physics of both drainage and diffusive coarsening shows quantitative agreement with experiment.

An accurate von Neumann's law for three-dimensional foams.

The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with detailed simulations and experiments. The average growth rate of a bubble with F faces is shown to be proportional to F1/2 for large F, in contrast to the conjectured linear dependence. Accounting for foam disorder in the model further improves the agreement with data.

Squeezing alcohols into sonoluminescing bubbles: the universal role of surfactants

We conduct an experimental study of the dependence of single bubble sonoluminescence intensity on the concentration of various alcohols. The light intensity is reduced by one-half at a molar fraction of ethanol of approximately 2.5x10(-5); butanol achieves the same reduction at a concentration 10 times smaller. We account for the results by a theoretical model in which the alcohols are assumed to be mechanically forced into the bubble at collapse, modifying the adiabatic exponent of the gas. The increasing hydrophobicities of the alcohols lead to decreasing effective adiabatic exponents, and thus to less heating and therefore less light. Support for this model is obtained by replotting the experimental light intensity values vs the calculated exponents, yielding a collapse of all data onto a universal curve.

The acoustics of diagnostic microbubbles: dissipative effects and heat deposition.

We discuss the effectively detectable scattered intensity of ultrasound from diagnostic microbubble suspensions, taking dissipative mechanisms in the liquid medium into account. In particular, we conclude that neither non-linear wave steepening of the incident (driving) wave nor of the outgoing (scattered) wave has a large effect on the scattered signal from typical bubbles. It is shown that, paradoxically, the far-field solution of the wave field is sufficient to compute the magnitude of expected temperature rises in the medium due to acoustic heat deposition, although appreciable heating is limited to intermediate-field distances from the bubble surface.

Sound scattering and localized heat deposition of pulse-driven microbubbles

The sound scattering of free microbubbles released from strongly driven ultrasound contrast agents with brittle shell (e.g., Sonovist) is studied numerically. At high peak pressure of the driving pulses, the bubbles respond nonlinearly with cross sections pronouncedly larger than in the linear case; a large portion of the energy is radiated into high frequency ultrasound. Subsequent absorption of these high frequencies in the surrounding liquid (blood) diminishes the effective scattering cross section drastically. The absorption results in highly localized heating, with a substantial temperature rise within the first few microm from the bubble surface. The maximum heating in 1 microm distance is strongly dependent on driving pressure. Temperature elevations of more than 100 K can be achieved for amplitudes of Pa approximately 30 atm, which coincides with the highest pressures used in ultrasound diagnostics. The perfectly spherical collapses assumed here occur rarely, and the heating is highly localized and transient (approximately 10 micros). Therefore, a thermal hazard would only be expected at driving pressures beyond the diagnostic range.