Rheology of ordered foams—on the way to Discrete Microfluidics

The mixing of bubbles in two-dimensional bidisperse foams under extensional shear

“…Then each bubble can be seen, and its position tracked over time. Indeed, a large part of the recent literature attests to the profitability of such an approach, both experimentally [5,6,7,8,9], theoretically [10,11] and computationally [12,13,14,15].…”

Foam as a geometer

“…Ideally one would like to be able to feed different reactants through the same channel(s) in such a way that they would not react until reaching some specified locations at specified times. Recent work [14] suggests that this might be achievable by encapsulating the chemicals in the bubbles of ordered foam structures that are then pushed through appropriately designed channel geometries. At low flow rates where viscous dissipation is negligible, whether bubbles mix or sort is governed by surface tension minimisation.…”

Diffusion of curvature on a sheared semi-infinite film

“…Figure 7 shows data for the angle ψ at which the film meets the line along which its endpoint is dragged (see also the definition sketch figure 1). This is initially π/2-the film meets the line at 3 One quantitative measure of the degree of symmetry in the y versus x plot (figure 5) is to consider the ratio between the value of |y| dx (in the domain above the line y = −x), and that of x dy (in the domain below the line y = x). For our data, this ratio turns out to be 4.1 for t = 40, falling to 2.1 for t = 70 and to 1.5 for t = 120, and would asymptote to unity if the plot became perfectly symmetric in the t → ∞ limit.…”

“…In this geometry, a foam film can be represented mathematically by a curve in the 'two-dimensional' plane. The viscous froth model [3,[8][9][10][11][12][13][14] applied to such 'two-dimensional' systems is based on a force balance between the pressure difference across the two sides of the film ( P), the film tensions (γ ) and the viscous drag on each film element (the drag being associated with moving the films over the confining upper and lower plates): λv = Pn − cγ n, (1.1) where λ is the viscous drag coefficient per unit length of film, v is the velocity of a film element, n is the unit vector normal to the film element and c is the 'two-dimensional' film curvature. One particularly attractive feature of the viscous froth model over others is its capability to account for film curvatures which are not simply arcs of circles.…”

“…Flowing foams occur in a variety of applications such as oil recovery, froth flotation and microfluidics, making them of research interest [1][2][3]. A detailed understanding of foam rheology would entail a description of foam structure on the bubble scale [4].…”