The diffusion coefficient of a swollen microgel particle

The drag on a permeable particle traversing through a Newtonian liquid is calculated. This is in terms of a single dimensionless group, Da, the Darcy number, which relates the particle permeability to the radius. For small values of the Darcy number the solution reverts to the well-known Stokes drag for smooth hard particles. For larger values of the Darcy number the drag is reduced. This drag allows calculation of the diffusion coefficient of such particles, again as a function of the Darcy number. The results are discussed in relation to microgel particles, which display swelling under certain conditions. The size of such particles is typically measured with dynamic light scattering, which measures the diffusion coefficient of particles and as such the analysis presented here shows the conditions under which dynamic light scattering is accurate. The Darcy number for microgel particles is estimated to be on the order of 10(-7).     

A model for surfactant distribution in latex coatings

The presence of surfactants in dried latex films can adversely affect the adhesive, water-resistant, and gloss properties, so investigating the surfactant distribution in latex coatings is of prime industrial relevance. Here we present a model that predicts the distribution of surfactant in a latex coating during the solvent evaporation stage. The conservation equation for surfactant during solvent evaporation is solved in the limit of infinite particle Peclet numbers, a dimensionless quantity giving the measure of relative magnitudes of evaporative to diffusive fluxes. A parametric analysis using the model reveals that the surfactant adsorption isotherm is the determining physical parameter. The model always predicts surfactant excesses at the top surface and either excess or depletion at the bottom surface depending on the isotherm. Uniform distributions are predicted for low surfactant Peclet numbers. Attenuated total reflection Fourier transform infrared spectroscopic probes on film surfaces conform to the behavior predicted by the model.     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Effect of added free polymer on the swelling of neutral microgel particles: a thermodynamic approach

Microgel particles based on poly (N-isopropylacrylamide) have been shown to display an initial swelling behavior, followed by a collapse, with increasing concentration of added poly(ethylene oxide), PEO, chains. This paper considers the thermodynamic reasons for the observed expansion and subsequent shrinkage of the particles. At low concentrations of PEO, the free chains permeate into the microgel particles and cause an increase in osmotic pressure, expanding the particles. At higher concentrations of PEO, the particles are saturated and an increase in osmotic pressure in the external phase causes the particles to collapse again. The calculated magnitude of swelling and the effect of PEO molecular weight are, at least qualitatively, in agreement with the experimental observations reported elsewhere.     

Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkinmethod for mixed periodic/non-periodic convection-diffusionproblems. The scheme is unconditionally stable, independentof the diffusion coefficient, even in the case when numericalquadrature is used. The theoretical predictions are illustratedby a series of numerical experiments. For the periodic case,our results present a significant improvement on those givenby Süli & Ware (1991) SIAM J. Numer.Anal.28, 423-445).     

Why do drying films crack?

Understanding the mechanism by which films fail during drying is the first step in controlling this natural process. Previous studies have examined the spacing between cracks with predictions made by assuming a balance between elastic energy released with a surface energy consumed. We introduce a new scaling for the spacing between cracks in drying dispersions. The scaling relates to the distance that solvent can flow, to relieve capillary stresses, as a film fails. The scaling collapses data for a range of evaporation rates, film thicknesses, particle sizes, and materials. This work identifies capillary pressures, induced by packed particle fronts travelling horizontally across films, as responsible for the failure in dried films.