The stability of axisymmetric liquid bridges held between non-equal circular supporting disks, and subjected to an axial acceleration, has been analyzed both theoretically and experimentally. Some characteristics of the breaking process which takes place when the stability limit of minimum volume is reached (mainly the dependence with the disks separation of the volume of the liquid drops resulting after the liquid bridge breakage) have been theoretically studied by using standard asymptotic expansion techniques. From the analysis of the nature of the unstable equilibrium shapes of minimum volume at the stability limit it is concluded that the relative volume of the main drops resulting from the liquid bridge rupture drastically change as the disks separation grows. Theoretical predictions have been experimentally checked by working with very small size liquid bridges (supporting disks being some 1 millimeter in diameter), the agreement between theoretical predictions and experimental results being remarkable.
An experimental apparatus to study the breaking process of axisymmetric liquid bridges has been developed, and the breaking sequences of a large number of liquid bridge configurations at minimum-volume stability limit have been analyzed. Experimental results show that very close to the breaking moment the neck radius of the liquid bridge varies as t 1/3 , where t is the time to breakage, irrespective of the value of the distance between the solid disks that support the liquid column.
The stability limit of minimum volume and the breaking dynamics of liquid bridges between nonequal, noncoaxial, circular supporting disks subject to a lateral acceleration were experimentally analyzed by working with liquid bridges of very small dimensions. Experimental results are compared with asymptotic theoretical predictions, with the agreement between experimental results and asymptotic ones being satisfactory. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2107747͔In the simplest configuration a liquid bridge consists of an isothermal drop of liquid held by surface tension forces between two parallel, solid disks as shown in Fig. 1. Disregarding electric and magnetic fields effects, the equilibrium interface shapes and hydrostatic stability limits of liquid bridges are determined by the slenderness, ⌳ = L / ͑2R 0 ͒, where L is the distance between the supporting disks and the characteristic length R 0 is the mean radius, R 0 = ͑R 1 + R 2 ͒ /2; the ratio of the radius of the smaller disk, R 1 , to the radius of the larger one, R 2 , that is K = R 1 / R 2 , or the equivalent parameter h = ͑1−K͒ / ͑1+K͒ = ͑R 2 − R 1 ͒ / ͑R 2 + R 1 ͒; the dimensionless eccentricity, e = E / R 0 , 2E being the distance between the disks axes; the dimensionless volume, defined as the ratio of the actual volume V to the volume of a cylinder of the same length L and diameter 2R 0 : V = V / ͑R 0 2 L͒; and the lateral Bond number, B = ⌬gR 0 2 / , where ⌬ is the difference between the density of the liquid and the density of the surrounding medium, g is the lateral acceleration acting on the liquid drop, and is the surface tension.The stability limit of the minimum volume of long axisymmetric liquid bridges held between unequal, noncoaxial parallel circular supporting disks subject to lateral acceleration can be theoretically analyzed by using an analytical approximation based on the standard bifurcation theory ͑Lyapunov-Schmidt technique 1 ͒. This problem was first analyzed a decade ago, both analytically and experimentally, 2 with the following asymptotic expression for the stability limit of minimum volume obtained:where the eccentricity e is assumed to be positive when the relative position of the disks is as indicated in Fig. 1 ͑the smaller disk axis over the larger disk one͒. According to expression ͑1͒ the combined effect of lateral acceleration and eccentricity becomes maximum when the angle  vanishes; this case is the only one considered in this Brief Communication. The variation of the minimum volume with the eccentricity for a lateral Bond number B = 0.05 and different values of the parameter h ͑assuming  =0͒ of liquid bridges with slenderness ⌳ = 2.7 is shown in Fig. 2. Expression ͑1͒ is only valid when the liquid bridge configuration is close enough to the reference one ͑defined by the Rayleigh stability limit, ⌳ = , V =1, B = h = e =0͒, and far from this configuration of reference, Eq. ͑1͒ gives only a rough approximation of the influence on the stability limit of the different parameters considered. However, ...
A numerical method has been developed to determine the stability limits for liquid bridges held between noncircular supporting disks, and the application to a configuration with a circular and an elliptical disk subjected to axial acceleration has been made. The numerical method led to results very different from the available analytical solution, which has been revisited and a better approximation has been obtained. It has been found that just retaining one more term in the asymptotic analysis the solution reproduces the real behavior of the configuration and the numerical results.
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