Wall friction and Janssen effect in the solidification of suspensions

Abstract

We address the mechanical effect of rigid boundaries on freezing suspensions. For this we perform the directional solidification of monodispersed suspensions in thin samples and we document the thickness h of the dense particle layer that builds up at the solidification front. We evidence a change of regime in the evolution of h with the solidification velocity V with, at large velocity, an inverse proportionality and, at low velocity, a much weaker trend. By modelling the force balance in the critical state for particle trapping and the dissipation phenomena in the whole layer, we link the former evolution to viscous dissipation and the latter evolution to solid friction at the rigid sample plates. Solid friction is shown to induce an analog of the Janssen effect on the whole layer. We determine its dependence on the friction coefficient between particles and plates, on the Janssen's redirection coefficient in the particle layer, and on the sample depth. Fits of the resulting relationship to data confirm its relevance at all sample depths and provide quantitative determinations of the main parameters, especially the Janssen's characteristic length and the transition thickness h between the above regimes. Altogether, this study thus clarifies the mechanical implication of boundaries on freezing suspensions and, on a general viewpoint, provides a bridge between the issues of freezing suspensions and of granular materials.

Boundary-induced inhomogeneity of particle layers in the solidification of suspensions

“…Here, in the present context of suspension freezing, we have shown in a companion paper [41] that viscous friction plays the role of gravity and that solid friction induces a similar exponential amplification of the particle pressure at the solidification front. Both result in a universal relationship between h and U that remains the same independently of the nature of the dominant dissipation mechanism.…”

“…In reference [41], we already studied the evolution of the layer thickness h in the same experiment and with the same data as those considered here. We first noticed that a relevant common value of the critical velocity U c was U c = 15µm.s −1 , close to the value U c = 12µm.s −1 [28] expected from trapping models [21][22][23].…”

“…Following the Hele-Shaw geometry of the sample, the sample width is large enough compared to the sample depth for allowing the stress σp zz to be uniform in the x-direction, so that σp zz ≡ σp zz (z) here. The stress relation completed by the frictional boundary conditions then yields, under usual assumptions invoked in granular materials [40,46], the mean stress equation [41] :…”

“…This stress applies on a surface of the suspension normal to the front. However, as particles occupy only a proportion φ l of it, the mean pressure Pp on particles adjacent to the front reads as [28,41] :…”