Continuous and discontinuous dynamic unbinding transitions in drawn film flow.

When a plate is withdrawn from a liquid bath a coating layer is deposited whose thickness and homogeneity depend on the velocity and the wetting properties of the plate. Using a long-wave mesoscopic hydrodynamic description that incorporates wettability via a Derjaguin (disjoining) pressure we identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of known equilibrium unbinding transitions. Namely, these are continuous and discontinuous dynamic wetting and emptying transitions. Several of their features have no equivalent at equilibrium.

Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems.

A liquid film is studied that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of an additional temperature gradient along the plate that induces a Marangoni shear stress significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we numerically obtain steady solutions and analyse their behaviour as the plate velocity is changed. We observe that the bifurcation curve exhibits collapsed (or exponential) heteroclinic snaking when the plate inclination angle is above a certain critical value. Otherwise, the bifurcation curve is monotonic. The steady profiles along these curves are characterised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we prove with a Shilnikov-type method that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.

Noise induced state transitions, intermittency, and universality in the noisy Kuramoto-Sivashinksy equation.

Consider the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation close to the instability onset. When the noise acts only on the first stable mode (highly degenerate), the KS solution undergoes several state transitions, including critical on-off intermittency and stabilized states, as the noise strength increases. Similar results are obtained with the Burgers equation. Such noise-induced transitions are completely characterized through critical exponents, obtaining the same universality class for both equations, and rigorously explained using multiscale techniques.

Liquid film coating a fiber as a model system for the formation of bound states in active dispersive-dissipative nonlinear media.

We analyze the coherent-structure interaction and the formation of bound states in active dispersive-dissipative nonlinear media using a viscous film coating a vertical fiber as a prototype. The coherent structures in this case are droplike pulses that dominate the evolution of the film. We study experimentally the interaction dynamics and show evidence for formation of bound states. A theoretical explanation is provided through a coherent-structures theory of a simple model for the flow.

[Endoscopic methods in the diagnosis and treatment of mechanical jaundice of non-neoplastic etiology]. / Endoskopicheskie metody v diagnostike i lechenii mekhanicheskoi zheltukhi neopukholevogo geneza.

The authors analyse the results of treatment of 255 patients with obstructive jaundice of nonneoplastic origin. Various endoscopic methods were used. Endoscopic interventions were carried out in the first two days in 79.8% of cases. Laparoscopic cholecystostomy was conducted in 138 patients; jaundice was relieved in 3 to 20 days in 95% of cases. It is shown that the best results of operative treatment of patients with acute cholecystitis complicated by choledocholithiasis are produced in concurrent use of laparoscopic cholecystostomy and endoscopic papillosphincterotomy.

Dynamics of an electrostatically modified Kuramoto-Sivashinsky-Korteweg-de Vries equation arising in falling film flows.

The gravity-driven flow of a liquid film down a vertical flat plate in the presence of an electric field acting in a direction perpendicular to the wall is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. A strongly nonlinear long-wave evolution equation is developed for flow parameters near the critical instability conditions. The equation retains terms up to second order in the slenderness parameter in order to incorporate the effects of shear-induced growth, short-wave damping due to surface tension, electric stress effects, and dispersive effects. In the additional asymptotic limit of small but finite interfacial perturbations the dynamics are shown to be governed by a Kuramoto-Sivashinsky (KS) equation with Korteweg-de Vries dispersion, also known as the Kawahara or the generalized Kuramoto-Sivashinsky (gKS) equation, which also includes a nonlocal energy growth term that arises from the electrostatics. Extensive numerical experiments are carried out to characterize solutions to this equation. Using perturbation theory and numerical solutions, it is shown that the electric field alters the far-field decay characteristics of bound states of the gKS equation from exponential to algebraic behavior. In addition, it is demonstrated numerically that chaotic solutions of the KS equation that are regularized into traveling-wave pulses when sufficient dispersion is added can in turn become chaotic by applying a sufficiently strong electric field. It is suggested, therefore, that electric fields can be utilized to enhance interfacial turbulence and in turn increase heat or mass transfer in applications. A physical example involving electrified falling film flows of ethelene glycol fluids is furnished and shows that the theory is within reach of experiments.