Impact of boundaries on velocity profiles in bubble rafts

Abstract

Under conditions of sufficiently slow flow, foams, colloids, granular matter, and various pastes have been observed to exhibit shear localization, i.e., regions of flow coexisting with regions of solidlike behavior. The details of such shear localization can vary depending on the system being studied. A number of the systems of interest are confined so as to be quasi two-dimensional, and an important issue in these systems is the role of the confining boundaries. For foams, three basic systems have been studied with very different boundary conditions: Hele-Shaw cells (bubbles confined between two solid plates); bubble rafts (a single layer of bubbles freely floating on a surface of water); and confined bubble rafts (bubbles confined between the surface of water below and a glass plate on top). Often, it is assumed that the impact of the boundaries is not significant in the "quasistatic limit," i.e., when externally imposed rates of strain are sufficiently smaller than internal kinematic relaxation times. In this paper, we directly test this assumption for rates of strain ranging from 10(-3) to 10(-2) s(-1). This corresponds to the quoted rate of strain that had been used in a number of previous experiments. It is found that the top plate dramatically alters both the velocity profile and the distribution of nonlinear rearrangements, even at these slow rates of strain. When a top is present, the flow is localized to a narrow band near the wall, and without a top, there is flow throughout the system.

Two-Dimensional Foam Rheology with Viscous Drag

“…While quasistatic cellular simulations [9,10] showed some agreement with the results, they continue to excite debate [7], especially in regard to the localization of shear and deformation [6], which is the salient feature of the experiment. Recently, Wang et al have extended shear experiments to the simpler planar geometry [8]. While their experiments using bubbles between a liquid pool and a glass plate showed the formation of shear bands with an exponential velocity profile, a nearly linear velocity profile was obtained for a bubble floating on the liquid (bubble raft or Bragg raft).…”

“…This, or one of its variants, is often invoked in the analysis of bulk foams. However, as in the recent work of Takeshi and Sekimoto [15], we also include an elastic response, so that the model we propose has four key ingredients: elasticity up to a yield stress, plasticity, internal viscosity, and a viscous drag force.While it is amenable to obvious generalization, the model will be defined here for the simple planar shear geometry, as in [8]. Displacement u y; t and the velocity v y; t @u y;t @t are in the x direction only, as when shear takes place between two parallel infinite boundaries in that direction (see Fig.…”

Networklike Propagation of Cell-Level Stress in Sheared Random Foams

“…Experimental studies have addressed shear banding in quasi-2D foams, which consist of bubbles confined to a single layer in various ways [15][16][17][18]. The shear bands appear to be caused by stress inhomogeneities or by viscous drag from confining glass plates [19].…”

Stable small bubble clusters in two-dimensional foams

“…Stress fluctuations are often characterized by periods of increasing stress followed by sudden decreases, referred to as stress drops [15][16][17][18][19] or avalanches 20 . During flow, particle rearrangements can localize, which gives rise to shear banding [21][22][23][24][25] .…”

“…In fact, one event at a given location in the system at a given time can trigger another at a different location later in time. Theoretical descriptions of the mechanical properties of dry foams are typically formulated in terms of the activation of T1 and other topological events 7,9,12,15,17,18,[20][21][22][23]43,44 .…”