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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 91-98 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The capillary instability of a thin liquid layer on a cylinder is studied. Using an integral approach and lubrication approximation, transport equations governing the spatiotemporal evolution of a film thickness and the temperature along the film are obtained. Evolution of the system under both isothermal and nonisothermal conditions is studied numerically. It is shown that nonlinear interaction of the linearly unstable modes begets an additional mode with a wavelength equal to that of the fastest growing wave. This, in turn, causes the formation of satellite drops along with the main ones. Application of these results in a possible continuous technology of high-temperature superconductor wire fabrication is discussed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1155-1165 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear evolution of interfacial waves separating liquids of different viscosity and density (Rayleigh–Taylor instability) in a 2-D channel is studied. Using a new approach, which accounts for large gradients, the nonlinear evolution of the interface, y=εA(τ,ξ),ε(very-much-less-than)1, is shown to be governed by the regularized Kuramoto–Sivashinsky equation Aτ +βAAξ+{αA+γAξξ/ (1+ε4A2ξ)3/2}ξξ=0, where the constants α,β, and γ are determined at equilibrium, ξ is the slow coordinate along the channel, ξ=ε(x−c0t), and τ=ε2t. It is shown numerically that for ε2≥0.1β linearly unstable waves (while always of finite amplitude) are propelled by convection toward breaking in a finite time.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 1107-1117 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dynamics of a condensing apolar ultrathin liquid film is studied in the framework of long-wave theory in the cases of both horizontal and slightly tilted solid coated surfaces. When condensation is slow, the film on a horizontal substrate passes through the stages of hole opening driven by the "reverse reservoir effect," hole closing, eventual thickness equilibration and further spatially uniform growth of the condensate. When condensation is faster and the resistance to phase change is lower, secondary droplet(s) may emerge within the hole. During the film evolution the thickness of the microlayer covering the hole remains practically constant due to the "reverse reservoir effect." The total heat flux across the condensate film is found to decrease with the absolute value of the condensation constant. When the solid substrate is tilted, the film dynamics exhibits the formation of multidrop structures and their coarsening along with the stages typical for the horizontal case. The increase of the tilt angle leads to faster transition from dropwise to filmwise condensation and to the increase of the total heat flux through the condensate. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 506-508 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The role of interfacial viscosities in a two-dimensional vertically falling liquid film is examined. A nonlinear evolution equation for the free interface displacement from planar shape is found to possess classical form (i.e., combining the Korteweg–de Vries and Kuramoto–Sivashinsky equations), with interfacial viscosities supporting the existence of a dispersive term whose physical role has formerly been shown in the literature to effect an ordering of interfacial disturbances in the form of solitonlike patterns.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1763-1766 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An amplitude equation is derived, which describes the evolution of a disturbed film interface H(τ,Z,Y) flowing down an infinite vertical cylindrical column. Using a new approach, which accounts for fast spatial changes, the nonlinear evolution of the interface is shown to be governed by Hτ+βHHZ+αHZZ +γ∇2{N[(1/ω2)H+∇2H]}=0, where ω is the normalized cylinder radius and α, β, and γ are constants, ∇≡(∂Z, ∂Y), and N=[1+ε4(∇H)2]−3/2. It is shown numerically that for some linearly unstable equilibria the evolving waves break in a finite time.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 2622-2636 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The two-dimensional spatiotemporal dynamics of falling thin liquid films on a solid vertical wall periodically oscillating in its own plane is studied within the framework of long-wave theory. A pertinent nonlinear evolution equation referred to as the temporally modulated Benney equation (TMBE) is derived and its solutions are investigated numerically. The bifurcation diagram of the Benney equation (BE) describing the film dynamics in the unforced regime is computed depicting the domains of linearly stable, linearly unstable bounded, and unbounded behaviors. The solutions obtained for film dynamics via the BE are compared to those documented for direct numerical simulations of the Navier–Stokes equations (NSE). The comparison demonstrates that the BE constitutes an accurate asymptotic reduction of the NSE in the domain preceding the transition to the regime of its unbounded solutions. It is found that periodic planar boundary excitation does not alter the fundamental unforced bifurcation structure and the spatial topological structure of the interfacial waves. The film evolution as described by TMBE is found to be primarily of quasiperiodic tori complemented by several types of strange attractors. In the case of relatively thick films increase of either the amplitude or the frequency of wall oscillation results in significant decrease of the peak-to-peak size of interfacial waves. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 29-41 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dynamics of irradiated volatile thin liquid films is studied in the framework of long-wave theory. Strongly nonlinear evolution equations describing the spatio-temporal dynamics of the film in both the optically thin and thick cases are derived. Various kinds of time-dependent base states are found and their linear stability is considered using the quasi-steady method. The results of the numerical study of the governing evolution equations support the results of the linear analysis. It is found that irradiation can partially suppress the growth of the interfacial disturbance. The nonlinear effects accelerate the film rupture with respect to the disappearance time of the corresponding base state. The film rupture time is found to decrease with the intensity of irradiation. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 537-539 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Stability properties of a thin liquid film subject to internal heat generation are studied within the framework of the long-wave theory. A strongly nonlinear evolution equation for the film interface is derived, studied, and solved numerically. Linear stability analysis is performed by a further reduction of the evolution equation. Internal heat generation is found to stabilize the film interface. The film is linearly stable if the intensity of internal heat generation is sufficiently strong. Within the range of linear instability the nonlinear evolution of the film results in the film rupture. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 3433-3435 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Long-wave approximation for the spatiotemporal evolution of thermal and evaporative instabilities of a thin liquid film lying on a "thick'' solid substrate is considered. It is shown that accounting for a nonzero thermal resistance of the solid eliminates the emergence of temperature, heat and mass flux singularities at the rupture point. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 1633-1645 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The three-dimensional evolution of the long-wave Marangoni instability of thin liquid films is studied. According to earlier theoretical predictions no continuous steady states exist and the film ruptures. As in two dimensions, the mechanism of fingering is found to be a main route to rupture. A four-fold rotational symmetry of the film interface is retained, when a square periodic domain and the harmonic initial disturbance are used. A use of initial random disturbances in general eliminates the square symmetry of the solution. An increase of the domain size results in a growing complexity of the emerging patterns. In contrast with the dynamics in two dimensions the evolution of the interface in three dimensions and in particular the pattern emerging at rupture may strongly depend on the choice of the initial condition. The two-dimensional evolution of the film is found to be unstable to small three-dimensional random disturbances. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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