Viscous froth model for a bubble staircase structure under rapid applied shear: An analysis of fast flowing foam

Response of a two-dimensional liquid foam to air injection: Influence of surfactants, critical velocities and branched fracture

“…For such bubbles, the Plateau rules of equilibrium at clearly violated: the curvature along a given edge is not constant and can even revert, and three bubble edges do not meet at 120 • . Interestingly, all these observations corroborate recent numerical studies [22,23,24,25], that evidenced that non-quasistatic effects delay the occurrence of bubble rearrangements and enhance bubble deformation. More precisely, the way bubble edges meet suggests that edges perpendicular to the tip motion have a much larger tension than the short edges parallel to it (Fig.…”

Remarks on the accuracy of algorithms for motion by mean curvature in bounded domains

“…All four indicators suggest that the equidistant distribution of the tessellation points is much better than the standard algorithm, regardless of the chosen strategy, as recommended in [Green et al 2006]. Moreover, even near the symmetry point, y = 0, where the value of the indicators all tend to zero and have a large influence on the relative errors, the accuracy of the computations for the second algorithm is extremely high.…”

“…The obvious route of decreasing t but fixing L min , to ameliorate this effect, leads to greater error in the solution (see again Figure 6, right). The accuracy of the solution can be improved internally by making the line segments of equal length [Green et al 2006]; although this doesn't affect the error at the boundary, it does make the calculations faster (see Figure 4). Possible sources of internal error include: (a) nonoptimal distribution of the tessellation points along the interface after some time; (b) imperfections in the correction procedure (which adds and eliminates points from the interface at some prescribed time); and (c) point-to-point error variation related to the fact that the diffusion-type coefficient changes from point to point along the interface (recall that (2-1) is a nonlinear parabolic equation which is solved by a direct FD scheme with a fixed time step).…”

“…This indicates the further possibility of optimizing this algorithm by redistributing points every M T time steps. It is clear that M T = M T (V ) and this needs further investigation [Green et al 2006]. Note that the function F from (2-24) can be used as an indicator of the accuracy of the computation only for the Mullins' solution.…”

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“…However, if it is required that the position of each material point along the interface is controlled, as in the case of numerical computation, then both equations are equally important. Note that there has previously been an attempt to control both the velocity components in a specific way [Green et al 2006]. Equation (2-7) allows us to find a relation between the two unknown components of the velocity vector v and the normal vector n in the form…”