We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle... more We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI4/SiCl4, which displays liquid-liquid coexistence below an upper critical solution temperature around 140 °C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 °C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.
Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to til... more Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to tilt or to form piles, an effect studied by Faraday for grains in air. Here, we investigate the physical mechanisms behind Faraday tilting in a bed of vertically vibrated bronze spheres fully immersed in water. Experimental observations of surface tilting and bulk convection are compared with the results of molecular dynamics simulations in which the water is treated as an incompressible fluid. Our simulations reproduce the main features observed experimentally. Most tilt construction is shown to be due to horizontal fluid flow within the bed, principally occurring when the gap between the bed and the supporting platform is close to a maximum. Tilt destruction occurs by granular surface flow and in the bulk of the bed at times during each vibratory cycle close to and just later than bed impact. Destruction becomes more important for higher values of frequency and vibration amplitude, leading to lower tilt angles, partial tilting, or the symmetric domed geometry of Muchowski flow.
We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle... more We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI4/SiCl4, which displays liquid-liquid coexistence below an upper critical solution temperature around 140 °C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 °C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.
Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to til... more Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to tilt or to form piles, an effect studied by Faraday for grains in air. Here, we investigate the physical mechanisms behind Faraday tilting in a bed of vertically vibrated bronze spheres fully immersed in water. Experimental observations of surface tilting and bulk convection are compared with the results of molecular dynamics simulations in which the water is treated as an incompressible fluid. Our simulations reproduce the main features observed experimentally. Most tilt construction is shown to be due to horizontal fluid flow within the bed, principally occurring when the gap between the bed and the supporting platform is close to a maximum. Tilt destruction occurs by granular surface flow and in the bulk of the bed at times during each vibratory cycle close to and just later than bed impact. Destruction becomes more important for higher values of frequency and vibration amplitude, leading to lower tilt angles, partial tilting, or the symmetric domed geometry of Muchowski flow.
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Papers by kevin good