Minimum volume of long liquid bridges between noncoaxial, nonequal diameter circular disks under lateral acceleration

Abstract

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, ...

IDR/UPM facilities for liquid bridge experimentation on Earth under microgravity conditions

“…6, where the variation with the dimensionless eccentricity, e, of the liquid bridge volume at minimum volume stability limit, V, of liquid bridges between unequal disks, h, under lateral gravity acceleration, B,, is presented [27]. In the same plot theoretical predictions according to the asymptotic expression V = 1+ -A + 2 N are shown.…”

“…In the same plot theoretical predictions according to the asymptotic expression V = 1+ -A + 2 N are shown. [27].…”

“…As indicated in Table 1 these experiments deal mainly with liquid bridges between coaxial disks of the same diameter, and they have been oriented to the study of the equilibrium shapes and stability of liquid bridges subject to both axial [4,22,23] and lateral accelerations [24][25][26][27], to the analysis of the breaking dynamics [4,22], and to the analysis of thermal problems related to Marangoni flow [28] and the influence of a temperature gradient along the liquid column span on the stability of long liquid bridges [29].…”

Surface tension and microgravity

“…Since the value of the surface tension, σ, is hard to control on an Earth-based laboratory, in this environment small values of the Bond number can only be reached by decreasing the values of the parameters in the numerator of the Bond number expression. Thus, it could be reduced by using liquids of almost the same density, Δρ → 0, giving rise to the experimental technique known as neutral buoyancy or the Plateau tank technique [19][20][21][22][23], by decreasing the characteristic length l by working with samples of very small size, l → 0 [24][25][26][27][28], or by reducing the global acceleration acting on the sample, a → 0, as it happens in space platforms, in sounding rockets and in drop towers [29][30][31][32].…”