Dissipative lateral walls are sufficient to trigger convection in vibrated granular gases

Abstract

Abstract. Buoyancy-driven (thermal) convection in dilute granular media, fluidized by a vibrating base, is known to appear without the need of lateral boundaries in a restricted region of parameters (inelasticity, gravity, intensity of energy injection). We have recently discovered a second buoyancy-driven convection effect which occurs at any value of the parameters, provided that the impact of particles with the lateral walls is inelastic (Pontuale et al., Phys. Rev. Lett. 117, 098006 (2016)). It is understood that this novel convection effect is strictly correlated to the existence of perpendicular energy fluxes: a vertical one, induced by both bulk and wall inelasticity, and a horizontal one, induced only by dissipation at the walls. Here we first review those previous results, and then present new experimental and numerical data concerning the variations of box geometry, intensity of energy injection, number of particles and width of the box. Convection in granular media, from slow dense configurations to dilute gas-like setupsVibration of granular materials frequently leads to convective patterns [1]. However, the particular mechanism for sustaining and control of a convective dynamics depends upon the particular granular phase under scrutiny [2]. At high packing fraction [3] and low fluidization, "dense convection" has been first identified in the 90's [4][5][6][7] and explained through an asymmetric tangential friction at the lateral walls [8][9][10] or the formation of unstable heaps at the free surface [11]. In granular gases [12][13][14], on the contrary, the first discovered mechanism is bulk buoyancydriven thermal convection (BBD-TC), initially observed in simulations [15,16]. As in molecular liquids [17,18], it is driven by the buoyancy force associated to temperature/density gradients: in BBD-TC such gradients appear spontaneously because of the bulk inelasticity of graingrain collisions [19]. This is a bulk effect: indeed, no particular conditions on the lateral or top boundaries are required for its appearance (for instance in [15] and [20] it appears also with elastic lateral walls) and in fact an analytical study of the stability of the granular gas hydrostatic state without lateral walls (lateral periodic boundary conditions) has shown the emergence of BBD-TC in a region of system's parameters [21,22]. When lat- Recently we have demonstrated the existence of a convection mechanism for granular gases which is alternative to BBD-TC and which necessarily appears in all granular gases fluidized by a vibrating base under gravity, with the only necessary condition being the presence of inelastic lateral walls [28]. Such a mechanism has been called dissipative-lateral-wall-induced thermal convection, "DLW-TC". In this recent study we have employed experiments and simulations to isolate DLW-TC from BBD-TC. In Section 2 we review these recent results, while in Section 3 we present new experimental and numerical data. Conclusions are drawn in Section 4. DLW-TCLet us consider (similarly to the setup ske...