De-pinning instability of an evaporating-bounded liquid bridge: Experiments and axisymmetric analysis

In this manuscript we examine the stability of an evaporating-bounded axisymmetric liquid bridge confined between parallel-planar similar substrates by using both theory and experiments. From classical stability analysis appearing in the literature it is now generally understood that a bounded liquid bridge stability diagram contains; a region of low slenderness where instability is caused by de-pinning; a region of low to large slenderness and small liquid bridge volume where axisymmetric minimum volume instabilities occur; and a low to large slenderness region with large liquid bridge volume where non-axisymmetric maximum volume instabilities are present. Under a quasistatic assumption we use hydrostatics via the Young-Laplace equation to estimate the minimum stable volume before either de-pinning or rupture occur for a range of axial and radial Bond numbers. To examine liquid bridge stability from the Young-Laplace equation for bounded-axisymmetric liquid bridges we analyzed zero capillary pressure solutions, and their transition, as stability limits. Observable trends show good agreement for critical behavior when comparing experiments and theory.