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Register a new userShear viscosity of a model for confined granular media
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The shear viscosity in the dilute regime of a model for confined granular matter is studied by simulations and kinetic theory. The model consists on projecting into two dimensions the motion of vibrofluidized granular matter in shallow boxes by modifying the collision rule: besides the restitution coefficient that accounts for the energy dissipation, there is a separation velocity that is added in each collision in the normal direction. The two mechanisms balance on average, producing stationary homogeneous states. Molecular dynamics simulations show that in the steady state the distribution function departs from a Maxwellian, with cumulants that remain small in the whole range of inelasticities. The shear viscosity normalized with stationary temperature presents a clear dependence with the inelasticity, taking smaller values compared to the elastic case. A Boltzmann-like equation is built and analyzed using linear response theory. It is found that the predictions show an excellent agreement with the simulations when the correct stationary distribution is used but a Maxwellian approximation fails in predicting the inelasticity dependence of the viscosity. These results confirm that transport coefficients depend strongly on the mechanisms that drive them to stationary states.
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A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.
A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature $T$. As expected, the kinetic partial temperatures $T_i$ of each component are different and hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature $T$ and the ratio of partial kinetic temperatures $T_i/T_j$ are obtained by considering Maxwellian distributions defined at the partial temperatures $T_i$. The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.
We study a simple model of periodic contraction and extension of large intruders in a granular bed to understand the mechanism for swimming in an otherwise solid media. Using an event-driven simulation, we find optimal conditions that idealized swimmers must use to critically fluidize a sand bed so that it is rigid enough to support a load when needed, but fluid enough to permit motion with minimal resistance. Swimmers - or other intruders - that agitate the bed too rapidly produce large voids that prevent traction from being achieved, while swimmers that move too slowly cannot travel before the bed re-solidifies around them i.e., the swimmers locally probe the fundamental time-scale in a granular packing.
We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $eta$, which implies that it diverges algebraically with a critical exponent $kge 2 u-beta$. Here, $ u$ and $beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.
In this paper we present the molecular theory of viscosity of confined fluids in small or nano systems. This theory is also applicable to the interfacial viscosity. The basis of this research work is the Enskog kinetic theory and the Boussinesq constitutive equation. The Enskog kinetic theory is first transformed into a two-dimensional form. Then the potential energy collisional transfer part of the flux vector and the contribution to the surface pressure tensor due to collisional transfer are derived. Then the kinetic energy part of the flux vector and consequently the contribution to the surface pressure tensor due to flow of molecules is obtained. The microscopic expression of total surface pressure tensor is obtained by adding of the potential energy collisional transfer part and the kinetic energy contribution. Then the expression of interfacial shear and dilatational viscosities are concluded by the comparison of corresponding terms of the two microscopic and macroscopic surface pressure tensor equations. Finally the dimensionless forms of interfacial shear viscosity, interfacial dilatational viscosity and the surface tension equations are derived and they are plotted versus the reduced superficial number density.
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