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Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model…
We are concerned with the asymptotics and perturbation analysis of a singular second-order nonlinear ODE that models capillary rise of a fluid inside a narrow vertical tube. We prove the convergence of the exact solution to a unperturbed…
The aim of this paper is to extend Washburn's capillary rise equation by incorporating a slip condition at the pipe wall. The governing equation is derived using fundamental principles from continuum mechanics. A new scaling is introduced,…
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy solutions to the evolution, in the sense used in the…
We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for…
This study proposes a new fundamental formula that describes in a more coherent way, the rise and fall of liquids in capillaries. The variation of the contact angle classically associated with these phenomena appears to be the indirect…
Four different numerical approaches are compared for the rise of liquid between two parallel plates. These are an Arbitrary Lagrangian-Eulerian method (OpenFOAM solver interTrackFoam), a geometric volume of fluid code (FS3D), an algebraic…
In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method. In the…
The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth.…
A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting…
In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle,…
We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques,…
We compare and discuss the respective efficiency of three methods (with two variants for each of them), based respectively on Taylor (Maclaurin) series, Pad\'{e} approximants and conformal mappings, for solving quasi-analytically a…
We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the…
We provide an analytical approximation of a periodic solution of the three body problem in celestial mechanics, the so-called figure eight solution, discovered 1993 by C. Moore. This approximation has the form of a Fourier series whose…
The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid…
Axisymmetric steady solutions of Taylor-Couette flow at high Taylor numbers are studied numerically and theoretically. As the axial period of the solution shortens from about one gap length, the Nusselt number goes through two peaks before…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
Capillary rise occurs when a thin tube contacts a liquid, which rises against gravity due to the capillary force. This phenomenon is present in a wide range of everyday and industrial settings and provides the means to measure the physical…