scholarly journals Self-similar solutions to kinetic-type evolution equations: beyond the boundary case

2021 ◽  
Vol 26 (0) ◽  
Author(s):  
Dariusz Buraczewski ◽  
Konrad Kolesko ◽  
Matthias Meiners
Keyword(s):  
Evolution Equations ◽  
Boundary Case ◽  
Self Similar ◽  
Similar Solutions

Dynamics and Stability of Surfactant Coated thin Spreading Films

1996 ◽  
Vol 464 ◽  
Author(s):  
Omar K. Matar ◽  
Sandra M. Troian
Keyword(s):  
Surfactant Concentration ◽  
Evolution Equations ◽  
Third Order ◽  
Small Perturbations ◽  
Insoluble Surfactant ◽  
State Approximation ◽  
Steady State Approximation ◽  
Self Similar ◽  
Similar Solutions ◽  
Air Liquid Interface

ABSTRACTWithin lubrication theory, we investigate the hydrodynamic stability of a thin surfactant coated liquid film spreading strictly by Marangoni stresses. These stresses are generated along the air-liquid interface because of local variations in surfactant concentration. The evolution equations governing the unperturbed film thickness and surface surfactant concentration admit simple self-similar solutions for rectilinear geometry and global conservation of insoluble surfactant. A linear stability analysis of these self-similar flows within a quasi steady-state approximation (QSSA) yields an eigenvalue problem for a single third-order nonlinear differential equation. The analysis indicates that a thin film driven purely by Marangoni stresses is linearly stable to small perturbations of all wavenumbers. The insights gained from this calculation suggest a flow mechanism that can potentially destabilize the spreading process.

scholarly journals Self-similar solutions of kinetic-type equations: The boundary case

2020 ◽  
Vol 130 (2) ◽  
pp. 677-693
Author(s):  
Kamil Bogus ◽  
Dariusz Buraczewski ◽  
Alexander Marynych
Keyword(s):  
Boundary Case ◽  
Self Similar ◽  
Similar Solutions

scholarly journals A laser experiment for studying radiative shocks in astrophysics

2002 ◽  
Vol 20 (2) ◽  
pp. 263-268 ◽  
Author(s):  
X. FLEURY ◽  
S. BOUQUET ◽  
C. STEHLÉ ◽  
M. KOENIG ◽  
D. BATANI ◽  
...  
Keyword(s):  
Laser Pulse ◽  
Pulse Duration ◽  
Experimental Results ◽  
Laboratory Astrophysics ◽  
Laser Pulse Duration ◽  
Radiative Shocks ◽  
Self Similar ◽  
Laser Experiment ◽  
Similar Solutions

In this article, we present a laboratory astrophysics experiment on radiative shocks and its interpretation using simple modelization. The experiment is performed with a 100-J laser (pulse duration of about 0.5 ns) which irradiates a 1-mm3 xenon gas-filled cell. Descriptions of both the experiment and the associated diagnostics are given. The apparition of a radiation precursor in the unshocked material is evidenced from interferometry diagrams. A model including self-similar solutions and numerical ones is derived and fairly good agreements are obtained between the theoretical and the experimental results.

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