Multi-Domain Boundary Element Method for Sound Scattering on a Partly Perturbed Water Surface

2020 ◽  
Vol 28 (03) ◽  
pp. 2050006
Author(s):  
Mikhail Salin ◽  
Dmitrii Razumov
Keyword(s):  
Boundary Condition ◽  
Water Surface ◽  
Domain Boundary ◽  
Separation Of Variables ◽  
Artificial Boundary ◽  
Integral Boundary ◽  
Air Interface ◽  
Outer Domain ◽  
Rough Water ◽  
Plane Sound

The problem is the scattering of a plane sound wave at a rough water-air interface. The purpose of this paper is to describe in detail the method and demonstrate its work with simple examples. The main advantage of this approach is that there are no limits on the relation between the shape of the surface and the incident wave, so we can consider large Rayleigh parameter, shading, multiple scattering. The solution of the Helmholtz equation in the form of an integral over the boundary is used only in the inner domain, in the outer domain the separation of variables is used to obtain a nonlocal integral boundary condition on the artificial boundary.

scholarly journals Adsorption Properties of Hydrocarbon and Fluorocarbon Surfactants Ternary Mixture at the Water-Air Interface

Molecules ◽  
2021 ◽  
Vol 26 (14) ◽  
pp. 4313
Author(s):  
Bronisław Jańczuk ◽  
Katarzyna Szymczyk ◽  
Anna Zdziennicka
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Standard Free Energy ◽  
Ternary Mixtures ◽  
Free Energy Of Adsorption ◽  
Interface Tension ◽  
Air Interface ◽  
Surface Excess Concentration ◽  
Tail Water ◽  
Triton X

Measurements were made of the surface tension of the aqueous solutions of p-(1,1,3,3-tetramethylbutyl) phenoxypoly(ethylene glycols) having 10 oxyethylene groups in the molecule (Triton X-100, TX100) and cetyltrimethylammonium bromide (CTAB) with Zonyl FSN-100 (FC6EO14, FC1) as well as with Zonyl FSO-100 (FC5EO10, FC2) ternary mixtures. The obtained results were compared to those provided by the Fainerman and Miller equation and to the values of the solution surface tension calculated, based on the contribution of a particular surfactant in the mixture to the reduction of water surface tension. The changes of the aqueous solution ternary surfactants mixture surface tension at the constant concentration of TX100 and CTAB mixture at which the water surface tension was reduced to 60 and 50 mN/m as a function of fluorocarbon surfactant concentration, were considered with regard to the composition of the mixed monolayer at the water-air interface. Next, this composition was applied for the calculation of the concentration of the particular surfactants in the monolayer using the Frumkin equation. On the other hand, the Gibbs surface excess concentration was determined only for the fluorocarbon surfactants. The tendency of the particular surfactants to adsorb at the water-air interface was discussed, based on the Gibbs standard free energy of adsorption which was determined using different methods. This energy was also deduced, based on the surfactant tail surface tension and tail-water interface tension.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

On an approximate model for the shape of a liquid–air interface receding in a capillary tube

1997 ◽  
Vol 342 ◽  
pp. 87-96 ◽  
Author(s):  
E. RAMÉ
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Static Pressure ◽  
Capillary Tube ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Approximate Model ◽  
Viscous Stress ◽  
Air Interface ◽  
Constant Static Pressure

A good approximation to modelling the shape of a liquid–air meniscus advancing or receding in a capillary tube of radius a can be constructed by balancing the curvature of the interface with the sum of a viscous stress valid near the contact line and a constant static pressure. This model has unique solutions for each value of the boundary condition, i.e. the dynamic contact angle. When the meniscus recedes at very small capillary numbers, the model predicts a critical receding velocity beyond which a liquid layer of the receding fluid (a liquid tail) develops along the solid (see figure 4). The length of the layer increases as the receding speed and the contact angle decrease. This layer regime is characterized by menisci whose macroscopic curvature is >1/a.

scholarly journals On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 264
Author(s):  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integral Boundary Condition ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

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