Scaling arguments are developed for the load balance in hydrodynamic lubrication, and applied to non-Newtonian lubricants with a shear-thinning rheology typical of a structured liquid. It is argued that the shear thinning regime may be mechanically u
nstable in lubrication flow, and 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 recent theories of shear thickening in non-Brownian particulate suspensions is indicated.
The coarsening kinetics for the beading instability for liquid contained in a groove with convex curved sides (for example between a pair of parallel touching cylinders) is considered as an open channel flow problem. In contrast to a V-shaped wedge o
r U-shaped microchannel, it is argued that droplet coarsening takes place by viscous hydrodynamic transport through a stable column of liquid that coexists with the droplets in the groove at a slightly positive Laplace pressure. With some simplifying assumptions, this leads to a t^(1/7) growth law for the characteristic droplet size as a function of time, and a t^(-3/7) law for the decrease in the droplet line density. Some remarks are also made on the spreading kinetics of an isolated drop deposited in such a groove.
In a recent paper, Dunkel and Hilbert [Nature Physics 10, 67-72 (2014)] use an entropy definition due to Gibbs to provide a consistent thermostatistics which forbids negative absolute temperatures. Here we argue that the Gibbs entropy fails to satisf
y a basic requirement of thermodynamics, namely that when two bodies are in thermal equilibrium, they should be at the same temperature. The entropy definition due to Boltzmann does meet this test, and moreover in the thermodynamic limit can be shown to satisfy Dunkel and Hilberts consistency criterion. Thus, far from being forbidden, negative temperatures are inevitable, in systems with bounded energy spectra.
We extend our previous study [J. Chem. Phys. 138, 204907 (2013)] to quantify the screening properties of four mesoscale smoothed charge models used in dissipative particle dynamics. Using a combination of the hypernetted chain integral equation closu
re and the random phase approximation, we identify regions where the models exhibit a real-valued screening length, and the extent to which this agrees with the Debye length in the physical system. We find that the second moment of the smoothed charge distribution is a good predictor of this behaviour. We are thus able to recommend a consistent set of parameters for the models.
Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the systems dynamics. It applies to systems in or
out of equilibrium, in steady state or time-dependent situations, and has applications in the calculation of response coefficients, parameter sensitivities and Jacobian matrices for gradient-based parameter optimisation algorithms. The implementation of MWS has been described in the specific contexts of kinetic Monte Carlo and Brownian dynamics simulation algorithms. Here, we present a general theoretical framework for deriving the appropriate MWS update rule for any stochastic simulation algorithm. We also provide pedagogical information on its practical implementation.
A metabolic model can be represented as 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 visualisation 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 the other organisms.
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are predicted, conn
ected by smooth crossovers. The first regime is at low primary particle concentrations where the primary particles stick individually to the walls. The second regime is at intermediate concentrations where clusters grow to a certain size, smaller than the pore size, then stick individually to the walls. The third regime is at high concentrations where the final state is a pore-space-filling network.
The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As phi
--> 0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.
Many water soluble polymers are chemically modifi
