Figure 1

(Color online) Example rearrangement events in a coarsening foam, illustrated by time traces of (a) raw pixel grayscale levels, (b) variance ratios computed from video data, and (c) bubble speeds computed from variance ratios. The foam age is $t_0=332\min$, and the camera exposure time is $T=10\mathrm{ms}$. The inset of (c) shows the bubble speed distribution, averaged over age range $326–334\min$, with the peak fit to a Gaussian. The threshold speed for discriminating events from noise is computed from the mode and standard deviation of the Gaussian fit as $v_{\mathrm{TH}}=v_{\text{mode}}+3\sigma$. This threshold is indicated by vertical and horizontal dotted lines in the inset and main plot of (c), respectively. The duration of the events is denoted by ${\tau }_d$, and the rest time between successive rearrangements is denoted by ${\tau }_r$, as shown.Reuse & Permissions

Figure 2

(Color online) Autocorrelation of the velocity time trace for a coarsening foam over the age range $326–334\min$. The expected short and long time values based on the event and noise statistics of Fig. 3 are show by dotted lines, as labeled. The expected intermediate time value, labeled $1000{(\mathrm{nm}∕\mathrm{s})}^2$, is given by $f_1^2{⟨v_1⟩}^2+f_1(1-f_1)⟨v_1⟩⟨v_0⟩+{(1-f_1)}^2⟨v_0{}^2⟩$.Reuse & Permissions

Figure 3

(Color online) Characteristic time and speed scales vs foam age. In (a) the solid diamonds represent the rest time between successive rearrangement events in the whole scattering volume and the solid squares represent the event durations, both averaged over $30\min$ runs; the fraction of time the bubbles in the whole scattering volume are in motion is shown by the dashed curve $f_1$. The time ${\tau }_0$ between successive events at one scattering site was previously measured by DWS and is shown by the solid curve. In (b) statistics for event speeds are shown by solid squares for the average, open squares for the standard deviation, and open pluses for the average of the maxima. Statistics for noise speeds are shown by solid diamonds for the average, open diamonds for the standard deviation, solid triangles for the mode, and dotted curve for the threshold; the latter two are from Gaussian fits to the full speed distribution as shown in the inset of Fig. 1c. The rate of change of the average bubble diameter, due to coarsening, was previously measured and is shown by the solid curve labeled “coarsening.”Reuse & Permissions

Figure 4

(Color online) Ratio of average rearrangement event diameter to bubble diameter vs foam age, based on SVS data for the average time $⟨{\tau }_r⟩$ between events in the scattering volume and DWS data for the time ${\tau }_0$ between events at a given scattering site. The average event size is 8.6 bubble diameters across for all foam ages (horizontal line). Error bars represent the range of results taking the scattering volume as aperture area times $(2.5\pm 1.5)l^{*}$.Reuse & Permissions

Figure 5

(Color online) Probability distribution for the rest time between successive bubble rearrangements in the scattering volume, averaged over all ages. For all events combined, the average is indicated by $⟨⟨{\tau }_r⟩⟩=2.9\mathrm{s}$. The dashed line represents an exponential distribution with this average.Reuse & Permissions

Figure 6

(Color online) Probability distribution for the duration of individual events, averaged over all ages. The dashed curve represents the best fit to the sum of two Gaussians, with respective peaks at 0.29 and $0.54\mathrm{s}$, with widths of 0.11 and $0.28\mathrm{s}$, and with weights of 0.55 and 0.45. For all events combined, the average is indicated by $⟨⟨{\tau }_d⟩⟩=0.44\mathrm{s}$.Reuse & Permissions

Figure 7

(Color online) Probability distribution for the event displacements $v_{\max }{\tau }_d$ averaged over all foam ages. The dashed line represents fit to a power-law tail with exponent as labeled. For all events combined the average is indicated by $⟨⟨v_{\max }{\tau }_d⟩⟩$.Reuse & Permissions

Figure 8

(Color online) Probability distribution for peak event speeds, averaged over all ages. The dashed line represents fit to a power-law tail with exponent –5/2 as labeled. For all events combined the average is indicated.Reuse & Permissions

Figure 9

(Color online) Probability density map for the speed vs time during an event; the color code for most to least probable is yellow, orange, red, maroon, brown, black (light gray to black, if viewed in black and white). The speed axis is offset by the mode of the speed distribution and normalized by peak speed for each event; the time axis is offset by the time at which the speed is maximum and normalized by the event duration of each event. Only events in the power-law tail of the peak speed distribution of Fig. 8 are included.Reuse & Permissions