Janine E. Galvin

On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures

For rapidly flowing granular mixtures, existing kinetic-theory descriptions based on an assumed form of the velocity distribution function typically contain one of two simplifying assumptions: a Maxwellian velocity distribution or an equipartition of energy. In the current work, the influence of non-equipartition effects is explored in the context of two flow types: flow in which species segregation does not occur (namely, simple shear flow) and a segregating flow. For the former case, a comparison between existing kinetic theories and molecular-dynamics simulations of a binary system indicates that the incorporation of a non-Maxwellian velocity distribution is critical for reliable stress predictions, as is consistent with previous findings. However, the predictions are fairly insensitive to the equipartition versus non-equipartition treatment, despite the presence of a significant non-equipartition of energy. Nevertheless, an analysis of the diffusion equation for a segregating flow indicates that the presence of a non-equipartition of energy gives rise to additional components of the driving forces associated with size segregation. These additional components involve gradients of the species temperature, whereas theories based on an equipartition assumption only involve gradients in the mixture temperature. Molecular-dynamics simulations of the segregating flow, in conjunction with kinetic theory of binary systems, show that the non-equipartition effects are non-negligible for systems characterized by moderate values of mass differences and restitution coefficients. These simulations also reveal that the more massive particle may exhibit a lower species temperature than its lighter counterpart, contrary to previous observations in non-segregating systems. A physical explanation for this behaviour is provided.

On the role of the Knudsen layer in rapid granular flows

A combination of molecular dynamics simulations, theoretical predictions and previous experiments are used in a two-part study to determine the role of the Knudsen layer in rapid granular flows. First, a robust criterion for the identification of the thickness of the Knudsen layer is established: a rapid deterioration in Navier–Stokes order prediction of the heat flux is found to occur in the Knudsen layer. For (experimental) systems in which heat flux measurements are not easily obtained, a rule-of-thumb for estimating the Knudsen layer thickness follows, namely that such effects are evident within 2.5 (local) mean free paths of a given boundary. Secondly, comparisons of simulation and experimental data with Navier–Stokes order theory are used to provide a measure as to when Knudsen-layer effects become non-negligible. Specifically, predictions that do not account for the presence of a Knudsen layer appear reliable for Knudsen layers collectively composing up to 20% of the domain, whereas deterioration of such predictions becomes apparent when the domain is fully comprised of the Knudsen layer.

Evidence of Higher-Order Effects in Thermally-Driven, Rapid Granular Flows

Molecular dynamic (MD) simulations are used to probe the ability of Navier–Stokes-order theories to predict each of the constitutive quantities – heat flux, stress tensor and dissipation rate – associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect).

Breakup of a liquid rivulet falling over an inclined plate: Identification of a critical Weber number

We have numerically investigated the breakup of a rivulet falling over a smooth inclined plate using the volume of fluid method. Rivulet breakup is a complex phenomenon dictated by many factors, such as physical properties (viscosity and surface tension), contact angle, inertia, and plate inclination. An extensive simulation was conducted wherein these factors were systematically investigated. Regimes for a stable rivulet and an unstable rivulet that leads to breakup are examined in terms of a critical value of the Weber number (Wecr) that delineates these regimes. A higher Wecr implies that a higher flow rate is required to maintain a stable rivulet. The impact of liquid properties is characterized by the Kapitza number (Ka). Variation of Wecr with Ka shows two trends depending on the Ka value of the liquid. Liquids with lower Ka values, corresponding to high viscosities and/or low surface tensions, show linear variation and smaller value of the critical Weber number. In other words, the lower the liquid...