Related papers: Characteristic Angles in the Wetting of an Angular…
When a capillary channel with corners is wetted by a fluid, there are regions where the fluid fills the whole cross-section and regions where only the corners are filled by the fluid. The fluid fraction of the partially-filled region,…
The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface…
In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the…
Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption…
We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
Recent studies of cooled oil emulsion droplets uncovered transformations into a host of flattened shapes with straight edges and sharp corners, driven by a partial phase transition of the bulk liquid phase. Here, we explore theoretically…
In this work we study the affine principal lines of surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic…
Practical methods for quantitative analysis of radial and angular coordinates of leafy organs of vascular plants are presented and applied to published phyllotactic patterns of various real systems from young leaves on a shoot tip to…
We give criteria for which a principal curvature becomes a bounded $C^\infty$-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended…
Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We consider…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
In this paper, we systematically investigate the wetting behavior of a liquid ring in a cylindrical capillary tube. We obtain analytical solutions of the axisymmetric Young-Laplace equation for arbitrary contact angles. We find that, for…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
Measuring the rheology of liquids typically requires precise control over shear rates and stresses. Here, we describe an alternative route for predicting the characteristic features of a power-law fluid by simply observing the capillary…
A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory…
In this article we study surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$ for which the $\mathbb{R}$-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature…
A transformation based on mean curvature is introduced which morphs triangulated surfaces into round spheres.
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
The analytical expressions of liquid-vapor macroscopic contact angles are analyzed for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of…