Thermal Transients and Convective Particle Motion in Dense Granular Materials

Abstract

The mechanism of dry granular convection within dense granular flows is mostly neglected by current analytical heat equations describing such materials, for example, in geophysical analyses of shear gouge layers of earthquake and landslide rupture planes. In dry granular materials, the common assumption is that conduction by contact overtakes any other mode of heat transfer. Conversely, we discover that transient correlated motion of heated grains can result in a convective heat flux normal to the shear direction up to 3-4 orders magnitude larger than by contact conduction. Such a thermal efficiency, much higher than that of water, is appealing and might be common to other microscopically structured fluids such as granular pastes, emulsions, and living cells. DOI: 10.1103/PhysRevLett.105.218301 PACS numbers: 47.57.Gc, 47.55.pb, 65.20.Àw, 91.32.Jk The temperature evolution within sheared granular layers is balanced by heat production and transfer. Identifying the dominant modes of the heat transfer is therefore critical to temperature predictions. As typical with any classical fluid, the two most important modes of heat transfer during granular flow are those by conduction and convection. Heat conduction is now well understood to rely on the properties controlling the contact network: contact size, anisotropy, and heterogeneity [1][2][3][4]. Various studies examined the effect of convection on the heat transfer between the flowing granular materials and bounding walls [5]. In such cases where the wall interacts with the flow, the heat transfer is affected by the first layer of wall-contacting grains that may or may not recirculate. Moreover, the efficiency of the overall heat transfer depends on the thermal properties of the wall. Here, we examine the heat transfer that is purely intrinsic to the granular media, independent of wall properties. Intrinsic to the flow, the heat is carried by grains as they move. We term this process dry granular convection. Some heat is thus simply flowing along the mass flux. In addition to this obvious advection, in turbulent flow of water vortices develop and induce heat transfer normal to the mass flux [6]. Granular flows exhibit similar turbulent-like patterns of velocity vortices [7], leading to temperature mixing normal to the mass flux [8], but the corresponding heat flux has not been studied. Unlike water, vortice-like motion in granular media results from force chain buckling, leading to high fluctuations in local strain and kinetic energies, and thereafter, as we show, to thermal convection that increases with vertical stresses.In this Letter, we discover that dry granular convection does add a striking contribution to the overall heat transfer budget in dense granular flows. The study is based on a series of numerical experiments using thermal discrete element method [2]; the motion and the temperature evolution of the grains are simulated while they experience a plane shear flow and a temperature gradient in the direction transverse to the shear plane [ Fig. 1(a)]. ...

Partial jamming and non-locality in dense granular flows

“…More generally, correlated motion of particles [20][21][22], and avalanche-like rearrangements have been observed in various glassy materials like sand [23], granular materials [15,24,25], cohesive grains [26], foams [27], suspensions [8,28], colloids [29,30], and Lennard-Jones glass [31,32]. These observations suggest that clusters of particles may exist in many glassy materials.…”

10,000 – A reason to study granular heat convection

“…To our surprise the conductivity we measured showed dependence on particles' heat capacity [8]. Although this appears to be a relatively moderate effect, it triggered our interest to search for a possibly more impressive phenomenon -also reported in [8] related to heat convection due to the internal mixing of the grains. In this paper we will gradually unfold the physics of this phenomenon, its significance, and the reasons behind its overwhelming extent.…”

“…Schematics of Earthquake Fault Gouge. Heat production arises from shear heating, while heat transfer across the gouge was assumed to come only through conduction [9,10]; the current paper explores another mode of heat transfer, convection via internal mixing [8]. We link the latter phenomenon to the possibility of transient vortexlike motions (as shown in Fig.…”

“…Significant research focused on their effective conductivity, as it was assumed to be the most important factor in granular materials [1,2]. More recently this has been studied using discrete element model (DEM) simulations [5][6][7][8].…”

Simulation of current-activated pressure-assisted densification

“…Beside the fundamental timescales specifying the behavior of granular matter during a compaction process like the inertial time t i = m * /(dσ y ) and the collision time t c = m * /K n we need two more timescales: the thermal time t th = C/Λ characterizes the heat transfer from particle to particle [10] and the heating time t he = (CT m G)/I 2 gives an approximation of the time to reach the melting point.…”