Lev A. Slobozhanin

Capillary pressure of a liquid in a layer of close-packed uniform spheres

The capillary pressure in liquid partially filling the pore space in a layer of equidimensional close-packed spheres has been calculated numerically and studied experimentally. The case of square packing when the centers of the spheres are in the same plane and lie at the corners of a square receives primary consideration for zero gravity. In the absence of gravity, the menisci shapes of a liquid that occupies some fraction of the pore space are constructed using the Surface Evolver code. The mean curvature (and, hence, the capillary pressure) of the liquid surface is calculated. The dependence of capillary pressure on the liquid volume is obtained for selected contact angles in the range 0⩽θ⩽π. The evolution of the shape of the liquid’s free surface and the capillary pressure under quasistatic infiltration and drainage can be deduced from these results. The maximum pressure difference between liquid and gas required for a meniscus passing through a pore is calculated and compared with that for hexagonal ...

Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

The equilibrium and stability of a liquid that partially fills a cylindrical container with planar ends are examined. It is assumed that the free surface is axisymmetric and does not cross the symmetry axis of the container. Particular attention is given to the case where gravity is parallel to the cylinder’s axis, and where the free surface has one contact line on the lateral cylindrical wall and the other on one of the planar ends. The equilibrium configuration of such a surface is determined by the wetting angle, α, the Bond number, B, and the relative volume, V, of the annular region bounded by the free surface and the solid container. Shapes of stable and critical surfaces have been analyzed, and the stability regions for arbitrary Bond numbers have been obtained in the α–V plane. The shape and stability problems for a zero gravity configuration with both contact lines on the lateral wall of the cylinder are also studied. In addition, the stability of a free surface with at least one contact line coinciding with the edge formed by the lateral wall and a planar end is discussed.

Stability diagrams for disconnected capillary surfaces

Disconnected free surfaces (or interfaces) of a connected liquid volume (or liquid volumes) occur when the boundary of the liquid volume consists of two or more separate surface components Γi (i=1,…,m) that correspond to liquid–gas (or liquid–liquid) interfaces. We consider disconnected surfaces for which each component Γi is axisymmetric and crosses its own symmetry axis. In most cases, the stability problem for an entire disconnected equilibrium capillary surface subject to perturbations that conserve the total liquid volume reduces to the same set of problems obtained when separately considering the stability of each Γi to perturbations that satisfy a fixed pressure constraint. For fixed pressure perturbations, the stability of a given axisymmetric Γi can be found through comparison of actual and critical values of a particular boundary parameter. For zero gravity, these critical values are found analytically. For non-zero gravity, an analytical representation of the critical values is not generally po...

The stability margin for stable weightless liquid bridges

The stability of weightless axisymmetric liquid bridge equilibrium configurations to “large” disturbances is examined by calculating the stability margin. For bridges held between coaxial equidimensional circular disks (radius R0) separated by a distance H, the stability to infinitesimal perturbations (linear stability) has been thoroughly investigated and the stability region is constructed in the (Λ,V) plane. Here, the slenderness Λ (=H/2R0) and the relative volume V (ratio of the actual liquid volume to that of a cylinder with radius R0 and height H) are the parameters that define the system. To assess stability with respect to finite amplitude disturbances we use a potential energy analysis based on the concepts of a potential energy well and the equilibrium stability margin introduced by Myshkis [USSR Comput. Math. Math. Phys. 5, 193 (1965); Math. Notes Acad. Sci. USSR 33, 131 (1983); Introduction to the Dynamics of a Body Containing a Liquid Under Zero-Gravity Conditions (Vychisl. Tsentr Akad. Nauk ...

The stability of two connected drops suspended from the edges of circular holes

The stability of an equilibrium system of two drops suspended from circular holes in a horizontal plate is examined. The drop surfaces are the disconnected axisymmetric surfaces pinned to the edges of the holes. The holes lie in the same horizontal plane and the two drops are connected by a liquid layer that lies above the plate. The total liquid volume is constant. For identical pendant drops pinned to holes of equal radii, axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a solitary pendant drop. A bifurcation analysis shows that the loss of stability leads to a continuous transition from a critical system of identical drops to a stable system of axisymmetric non-identical drops. With increasing total protruded liquid volume this system of non-identical drops reaches its own collective stability limit (to axisymmetric perturbations) which gives rise to dripping or streaming from the holes. Critical volumes and heights for non-identical drops have been calculated as functions of the dimensionless hole radius (associated with the Bond number). For unequal hole radii, there are three intervals of the larger dimensionless hole radius, R 0 1 , with qualitatively different bifurcation patterns which in turn can depend on the smaller dimensionless hole radius, R 0 2 . Loss of stability may occur when the drop suspended from the larger hole reaches its stability limit (to non-axisymmetric perturbations) as a solitary drop or when the system reaches the collective stability limit (to axisymmetric perturbations). Typical situations are illustrated for selected values of R 0 1 , and then the basic characteristics of the stability for a dense set of R 0 1 are presented.

A review of the stability of disconnected equilibrium capillary surfaces

A disconnected free surface consists of several separate pieces (connectivity components). The connectivity components and solid walls bound a connected liquid region. Generally, the stability problem for such equilibrium configurations cannot be simply reduced to a set of independent problems for each connectivity component. Rather, the set of connectivity components, the solid walls and the connected liquid region must be considered simultaneously. In this review, we outline particular properties of the stability of mechanical equilibrium of systems with disconnected free surfaces and summarize the results of previous work. Several open problems are also discussed.

Stability of disconnected free surfaces in a cylindrical container under zero gravity: Simple cases

The stability of equilibrium configurations of a capillary liquid in a circular cylindrical container with planar ends is investigated. The liquid is under zero gravity conditions, and its wetting angle is constant over the entire solid surface. Attention is focused on the case for which the free surface consists of two disconnected pieces (connectivity components) that bound the connected liquid domain. First we outline the method used to determine critical states with disconnected free surfaces when each connectivity component is axisymmetric. Then we examine the stability of disconnected surfaces for the simple cases that arise when each connectivity component represents a closed sphere or a part of a sphere. Ten configurations were considered that represent all possible combinations of the following connectivity components: A closed sphere (that bounds a gas bubble), a spherical cap in contact with the lateral wall of a cylinder; a spherical cap in contact with a cylinder endwall, and a portion of a sphere (that does not cross the cylinder’s axis of symmetry) bounded by a cylindrical wall and a flat endwall.