Low-Gravity Fluid Mechanics

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

“…which can be found elsewhere 35,39 . We apply the variational method of Myshkis et al 39 to determine the stability of equilibrium surfaces with respect to arbitrary volume-preserving perturbations.…”

“…The cylindrical volume V = v/(πR 2 0 h), scaled volume v * = v/(4πR 3 0 /3), scaled pressure (mean curvature) Q = qR 0 , and slenderness Λ = h/R 0 are the dimensionless parameters with which the liquid bridges are specified. Note that q = (p g − p l )/γ gl measures the nonhydrostatic pressure differential 39 . We adopt θ c to denote the angle between the tangent to the bridge surface at the contact line ℓ and plate.…”

“…We apply the variational method of Myshkis et al 39 to determine the stability of equilibrium surfaces with respect to arbitrary volume-preserving perturbations. This method associates the second variation of the potential energy with the eigenvalues of the corresponding Sturm-Liouville problem where critical states satisfy…”

Experimental analysis of stability limits of capillary liquid bridges

“…In an early paper published by Da Riva and Martinez 4 concerning liquid bridges between equal disks in gravitationless conditions (B = 0), the maximum volume stability limit is calculated under the assumption that such a limit is reached when the contact angle at the edges of the disks becomes greater than some specified value (they assumed this maximum value of the contact angle was ir), and that if this value is exceeded, the liquid spreads over the lateral surfaces of the supporting disks. On the other hand, as far as we know, there are two works dealing with the same problem, liquid bridges between equal disks in gravitationless conditions, in which a more conservative stability limit of maximum volume was independently found (in one of them, first published in Russian 8 and later in English, 9 the problem is studied from a theoretical point of view, whereas in the other 11 the stability limit of maximum volume is analyzed both theoretically and experimentally). According to these papers, the maximum volume of a liquid bridge is limited by a nonaxisymmetric instability that occurs before the above-quoted V FIG.…”

Physical Mechanisms and Mathematical Models of Bead Defects Formation During Arc Welding

“…From four basic driving forces of a fluid flow: gravity, pressure, friction and inertia remain only two: gravity and pressure which allow describing the phenomena in a weld pool under the hydrostatic law as the pressure created by a column of a liquid. Thus, three known conditions of a hydrostatics should be satisfied according Myshkis et al, 1987:  the Euler's condition in a weld pool volume,  the Laplace law (condition) on a melted free surface  the Dupre-Yuong condition on a contact line of three environments: a liquid -gas -solid body. At balance the equation of continuity (6) (7) where z is the height of a liquid column, we receive where is the arbitrary constant.…”