On the similarities between the resonance behaviors of water balloons and water drops

Abstract

In this study, the resonance of water balloons is examined, and an understanding of their dynamics in terms of our knowledge about resonating sessile drops is reported. The focus is the regime in which the competition between surface and inertial forces dominates the dynamics of the balloon. In experiments, water balloons are mechanically oscillated along their axes of symmetry, and their responses are observed through optical imaging. The observations are compared to the resonance of sessile drops. Balloons differ from drops for having elasticity in place of surface tension. Different as balloons and drops may seem, this study reveals great similarities between them: a resemblance of their normalized pressure–volume curves, a one-to-one shape correspondence between their eigenmodes, and a close approximation of their normalized resonance frequencies. Based on these, turning a drop into a balloon preserves the drop’s mechanical response to a large extent. In fact, as a first approximation, the water balloons respond mechanically as water drops with a much higher surface tension.

Droplet motion on sonically excited hydrophobic meshes

“…In this case, the first term on the right side of Eq. ( 6 ) resembles gravity, the second term is the surface force, and the third term is bending force; hence, the gravity and surface tension forces generally define the wave dynamics in the fluid as the drop is located on the stationary and stiff surface 37 . The Capillary waves are the results of the interaction due to the surface and inertial forces.…”

“…These are 38 : here, is the effective flexural stiffness of the plate, is the gravity-capillary wavelength, is the flexural-capillary wavelength, and is the flexural-gravity wavelength. As the wavelength becomes longer the influence of the forces creating the wave becomes dominant in the fluid 37 . After knowing that the mesh vertical and horizontal displacements are small as compared to droplet fluid during the oscillations, the oscillation wavelengths, which are greater than the gravity-capillary wavelength ( ), governs the droplet oscillatory behavior during the excitation.…”

Droplet Motion on Sonically Excited Hydrophobic Meshes

“…6 resembles gravity, the second term is the surface force, and the third term is bending force; hence, the gravity and surface tension forces generally define the wave dynamics in the fluid as the drop is located on the stationary and stiff surface. 35 The Capillary waves are the results of the interaction due to the surface and inertial forces. The gravity waves are generated as the gravitational force (first term in Eq.…”

A Water Balloon as an Innovative Energy Storage Medium

“…This property enables a rubber membrane to form a balloon and enclose a fluid with several hundred times its volume. In fact, a balloon formed by a flat membrane is known to possess a non-monotonic relation between its pressure P and its volume V [1][2][3][4]. The non-monotonicity of the pressure-volume (P-V) curve incurs snap-through and snapback instabilities [5][6][7].…”