Nonlinear dynamics of capillary bridges: theory (original) (raw)

Nonlinear dynamics of capillary bridges: experiments

Journal of Fluid Mechanics, 1993

An experimental investigation of forced and free oscillations of liquid bridges positioned between two rods of equal diameter is presented. Both the resonance frequencies and damping rates for different aspect ratios of the bridge are reported. The damping rate data of the liquid bridges are obtained by high-speed videography and are the first ever reported. Resonance frequencies for the three modified Reynolds numbers of 14, 295 and 1654, and damping rates for the two modified Reynolds numbers of 14 and 295 are reported. These values of modified Reynolds numbers are generated by using ethylene glycol, distilled water, and mercury in small bridges. Gravitational effects are kept small by reducing the size of the capillary bridge. The internal flow fields of several bridges for different modified Reynolds numbers are described based on high-speed visualization. Experimental results show good agreement with results of linear and nonlinear theory.

Viscous oscillations of capillary bridges

Journal of Fluid Mechanics, 1992

Small-amplitude oscillations of viscous, capillary bridges are characterized by their frequency and rate of damping. In turn, these depend on the surface tension and viscosity of the liquid, the dimensions of the bridge, the axial and azimuthal wavenumbers of each excited mode and the relative magnitude of gravity. Both analytical and numerical methods have been employed in studying these effects. Increasing the gravitational Bond number decreases the eigenvalues in addition to modifying the well-known Rayleigh stability limit for meniscus breakup. At high Reynolds numbers results from inviscid and boundary-layer theories are recovered. At very low Reynolds numbers oscillations become overdamped. The analysis is applicable in measuring properties of semiconductor and ceramic materials at high temperatures under well-controlled conditions. Such data are quite scarce. Appl. M a t h . 34, 247-285. ZHANQ, Y. t ALEXANDER, J. 1990 Sensitivity of liquid bridges subject to axial residual acceleration. Phys. Fluids A 2, 1966-1974. Experiment and theory. J. Colloid Interface Sci. 113, 154-163.

Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

Physics of Fluids, 2002

Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit of small viscosity. The supporting disks of the liquid bridge are subjected to small amplitude mechanical vibrations with a frequency that is close to a natural frequency. A set of equations is derived for accounting the slow dynamics of the capillary bridge. These equations describe the coupled evolution of two counter-rotating capillary waves and an associated streaming flow. Our derivation shows that the effect of the streaming flow on the capillary waves cannot be a priori ignored because it arises at the same order as the leading (cubic) nonlinearity. The system obtained is simplified, then analyzed both analytically and numerically to provide qualitative predictions of both the relevant large time dynamics and the role of the streaming flow. The case of parametric forcing at a frequency near twice a natural frequency is also considered.

Statics and dynamics of capillary bridges

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2014

The present theoretical and experimental investigations concern static and dynamic properties of capillary bridges (CB) without gravity deformations. Central to their theoretical treatment is the capillary bridge definition domain, i.e. the determination of the permitted limits of the bridge parameters. Concave and convex bridges exhibit significant differences in these limits. The numerical calculations, presented as isogones (lines connecting points, characterizing constant contact angle) reveal some unexpected features in the behaviour of the bridges. The experimental observations on static bridges confirm certain numerical results, while raising new problems of interest related to the stability of the equilibrium forms. The dynamic aspects of the investigation comprise the capillary attraction (thinning) of concave bridge. The thinning velocities at the onset of the process were determined. The capillary attraction, weight of the plates and viscous forces were shown to be the governing factors, while the inertia forces turned to be negligible.

Boundary-layer analysis of the dynamics of axisymmetric capillary bridges

Physics of Fluids A: Fluid Dynamics, 1991

Small-amplitude oscillations 6f bapillary bridges are examined in the limit of large modified Reynolds. numb&r, The contact line between the free surface of the bridge and the upper and Iower supporting walls is allowed to undergo a restrained motion by taking its velocity to be proportional to the sltrpe ofthe free surface there. It is found that the oscillation frequency and damping rate depend on the aspect ratB of the bridge, the mode being excited, the motion of the contact line, and the modified Revnolds number. Very good agreement with other-studies is obtained for Re > 100. _ f. ~~T~~C~CTfO~

Linear oscillations of weakly dissipative axisymmetric liquid bridges

Physics of Fluids, 1994

Linear oscillations of axisyrnmetric capillary bridges are analyzed for large valúes of the modified Reynolds number C~l. There are two kinds of oscillating modes. For nearly inviscid modes (the flow being potential, except in boundary layers), it is seen that the damping rate -íl R and the frequency íl, are of the form a. R =cú 1 C 1/2 +co 2 C+<?(C in ) and íl I =a> 0 +ú) 1 C 1/2 +#(C 3/2 ), where the coeflicients <a 0 >0, co l <0, and ÍO 2 <0 depend on the aspect ratio of the bridge and the mode being excited. This result compares well with numerical results if C^O.Ol, while the leading term in the expansión of the damping rate (that was already known) gives a bad approximation, except for unrealistically large valúes of the modified Reynolds number (C;S 10 -6 ). Viscous modes (involving a nonvanishing vorticity distribution everywhere in the liquid bridge), providing damping rates of the order of C, are also considered.

Capillary bridge: Transition from equilibrium to hydrodynamic state

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2016

The present study is focused on the capillary bridge (CB) behaviour in the vicinity of its critical state. As is known, a critical state is an extreme, unstable point, by crossing which а system passes from one state to another. In our case, this passage is from equilibrium (static) to a hydrodynamic state. The hydrodynamic process, called here hydrodynamic regime occurring in concave CB is characterized by local deformations in the region of its neck, registered via a high speed camera (~1000 fps). The information obtained from the experiment is interpreted on the basis of a lubrication model. The theoretical evaluations correlate satisfactorily with the experimental data.

Non-axisymmetric oscillations of liquid bridges

Journal of Fluid Mechanics, 1989

The main characteristics of the non-axisymmetric oscillations of a liquid bridge have been considered: free frequencies, deformation modes and the influence of an outer liquid. Oscillations of this kind do not show stability changes. The Plateau technique has been used to obtain the resonant frequencies of the bridge when lateral perturbations are imposed. The results obtained are in good agreement with the theoretical ones when the influence of the outer liquid is considered. Moreover, lateral oscillations observed in experiments performed with liquid bridges in space can be explained with this model.

On the steady streaming flow due to high-frequency vibration in nearly inviscid liquid bridges

Journal of Fluid Mechanics, 1998

The steady streaming flow due to vibration in capillary bridges is considered in the limiting case when both the capillary Reynolds number and the non-dimensional vibration frequency (based on the capillary time) are large. An asymptotic model is obtained that provides the streaming flow in the bulk, outside the thin oscillatory boundary layers near the disks and the interface. Numerical integration of this model shows that several symmetric and non-symmetric streaming flow patterns are obtained for varying values of the vibration parameters. As a by-product, the quantitative response of the liquid bridge to high-frequency axial vibrations of the disks is also obtained.