Dynamic stability of long axisymmetric liquid bridges

This paper deals with the non-linear forced oscillations of axisymmetric long liquid bridges between equal disks. The dynamics of the liquid bridge has been analyzed by using a self-similar, one-dimensional model already used in similar problems. The influence of the dynamics on the static stability limits, as well as the main characteristics of the non-linear behaviour of long liquid bridges, have been studied with in the range of validity of the mathematical model used here

On the stability limits of long nonaxisymmetric cylindrical liquid bridges

There is a self-similar solution for the stability limits of long, almost cylindrical liquid bridges between equal disks subjected to both axial and lateral accelerations. The stability limits depend on only two variables; the so-called reduced axial, and lateral Bond numbers. A novel experimental setup that involved rotating a horizontal cylindrical liquid bridge about a vertical axis of rotation was designed to test the stability limits predicted by the self-similar solution. Analytical predictions compared well with both numerical and experimental results

A perturbation analysis of the stability of long liquid bridges between non-circular supporting disks

The stability of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart (the so-called liquid bridge model) is considered. For a weightless liquid bridge that is a right circular cylinder, the well-known Rayleigh stability limit holds, and the liquid column becomes unstable when its length is larger than its circumference. Many perturbations from this ideal configuration have been studied in the past, but the supporting disk shape has always been assumed circular. In this Brief Communication the influence of noncircular supports on stability limits of almost cylindrical liquid bridges is analyzed through an asymptotic analysis. Closed form expressions for the stability limits are presente

A summary of new predictive high frequency thermo-vibrational models in porous media

In this chapter, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous media is saturated either by a pure fluid or by a binary mixture. The importance of transport model on stability diagrams are presented and discussed. The stability threshold for the Darcy-Brinkman case in the RaTc-R and kc-R diagrams are presented (where RaTc, kc and R are the critical Rayleigh number, the critical wave number and the vibration parameters respectively). It is shown that there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold of mono-cellular convection is derived. This relation shows how the separation factor Ψ is related to controlling parameters of the problem, Ψ = f (R, ε*, Le) when the wave number k -> 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase components separation