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See EPAPS Document No. E-PLEEE8-80-009909 for supplementary material. For more information on EPAPS
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See EPAPS Document No. E-PLEEE8-80-009909 for supplementary material. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
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A Taylor expansion of the cavity profile around the neck yields r (z) = r0 + (2 r/z2) Δ z2 /2= r0 +(1/ rc) (Δ z2 /2). To collapse these profiles one can rescale the radial length scale with r′ =r/ r0 and the axial length scale with z′ =z/ r0 rc to obtain the time-independent shape r′ =1+Δ z′2 /2.
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A Taylor expansion of the cavity profile around the neck yields r (z) = r0 + (2 r/z2) Δ z2 /2= r0 +(1/ rc) (Δ z2 /2). To collapse these profiles one can rescale the radial length scale with r′ =r/ r0 and the axial length scale with z′ =z/ r0 rc to obtain the time-independent shape r′ =1+Δ z′2 /2.
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In the BI data we verified that | dα/dlnτ | | α-2 α2 |
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In the BI data we verified that | dα/dlnτ | | α-2 α2 |.
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note
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The long duration of the universal regime for the quasistatic case A can be understood as follows: in case A the maximum diameter of the bubble is only slightly larger than the orifice in contrast to the other two situations where the bubble is much larger than the needle exit. Accordingly, the neck in case A possesses already initially a rather symmetrical shape with its upper half being very similar to the lower one, which is prerequisite for the universal solution to be applicable.
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