Sliding friction in the hydrodynamic lubrication regime for a power-law fluid.

A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n < 1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.

Flux networks in metabolic graphs.

A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms.

Miscibility gap in the microbial fitness landscape.

It is shown from molecular statistical considerations that a demixing instability exists in the moment space of a microbial protein expression profile. Although avoidance of demixing is generally requisite for biological function, a comparison with proteomic and genomic data suggests that many microbes lie close to the onset of this instability. Over evolutionary time scales, straying too close or into the immiscible domain may be associated with intracellular compartmentalization.

Statistical analysis of the spatial distribution of operons in the transcriptional regulation network of Escherichia coli.

We have performed a statistical analysis of the spatial distribution of operons along the DNA in the transcriptional regulation network of Escherichia coli. The analysis reveals that pairs of operons that regulate each other and those that are co-regulated tend to lie much closer to one another than would be expected for a random network. Moreover, these pairs of operons tend to be transcribed in diverging directions. This spatial arrangement of operons allows the upstream regulatory domains to overlap and interfere with each other and our analysis also demonstrates the statistical significance of this motif of overlapping operons. Overlapping operons afford additional regulatory control, such as the correlated or anticorrelated expression of operons. We show by a mean-field analysis of a feed-forward loop that overlapping operons can drastically enhance the performance of gene regulatory networks. Our results suggest that regulatory control can provide a selective pressure that drives operons together in the course of evolution.

The physics of surfactant dissolution.

We have examined the early stages of surfactant dissolution and mesophase formation using a dimer-solvent model with phase behaviour representative of surfactant-water systems. We use an orientational order parameter to characterize systematically the appearance of mesophases. We find the process is diffusion controlled, and the appearance of mesophases is governed adiabatically by the equilibrium phase diagram from the earliest point at which the orientational order parameter can reliably distinguish between mesophases, when only a few repeat spacings of the mesophase microstructures are present. In real systems, such a stage would correspond to times of the order of a few microseconds after the initial contact.

Vapor-liquid coexistence in many-body dissipative particle dynamics.

Many-body dissipative particle dynamics is constructed to exhibit vapor-liquid coexistence, with a sharp interface, and a vapor phase of vanishingly small density. The application to fluid mechanics problems involving free surfaces is illustrated by simulation of a pendant drop. The model is an unusual example of a soft-sphere liquid with a potential energy built out of local-density-dependent one-particle self-energies.

Mesoscale simulations of surfactant dissolution and mesophase formation.

The evolution of the contact zone between pure surfactant and solvent has been studied by mesoscale simulation. It is found that mesophase formation becomes diffusion controlled and follows the equilibrium phase diagram adiabatically almost as soon as individual mesophases can be identified, corresponding to times in real systems of order 10 micros.

Hydrodynamic bubble coarsening in off-critical vapor-liquid phase separation.

Late-stage coarsening in off-critical vapor-liquid phase separation is reexamined. In the limit of bubbles of vapor distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft-sphere fluid.

Characterisation of fluid flow through porous media using three-dimensional microimaging and pulsed gradient stimulated echo NMR.

Pulsed gradient stimulated echo (PGSTE) and microimaging nuclear magnetic resonance (NMR) are used to probe correlations between structure and flow in the void space of a model porous system formed from a packing of 1-mm diameter glass spheres. The pulsed gradient stimulated echo data determine the average propagator and permit the dispersion of the flow to be studied as a function of delay time. Microimaging yields structural information and, specifically, a reduced radial distribution function (rdf) for the structure of the void space. Transition to fully developed dispersive flow is shown to occur on a scale size for which no further correlations in the structure of the void space are observed.

A mathematical model of potassium ion diffusion in dentinal tubules.

Desensitizing agents containing potassium ions (K+) are believed to inactivate intradental nerves by raising extracellular [K+]. A mathematical model was used to investigate factors affecting [K+] in dentinal tubules. The most important factors affecting the steady-state tubular [K+] were the tubular fluid-flow velocity, salivary [K+] and the permeability to potassium (k) of the barrier between the tubule and the pulp. Tubular [K+] decreased with increasing outward flow velocity and increasing k. whereas the dimensions of the tubule and odontoblast process had little effect. Following a 1 min simulated application of 500 mmol/1 K+ to the dentine surface, [K+] at the inner end of the tubule increased above steady-state levels for 20-30 min. The maximum [K+] attained at the inner end of the tubule was around 30 mmol/l for an impermeable barrier (k = 0) and flow velocity of 1.4 microns/s, but lower maximum tubular [K+] were achieved when either the outward flow velocity or k was increased. The model suggests that applying potassium-containing preparations to dentine may increase [K+] at the inner ends of dentinal tubules to levels sufficient to inactivate intradental nerves. However, the localized increase in [K+] is transient, and the concentration change will be lessened by conditions that increase the tubular fluid-flow velocity or the permeability of the barrier between the tubule and pulp.