The paper proposes a general framework allowing the analysis of wetting problems in thesituation when interfacial tensions depend on external fields. An equation predictingapparent contact angles of sessile droplets deposited on rough surfaces in the presence ofexternal fields is derived. The problem of wetting is discussed in the framework of thevariational approach. Derivation of a general equation generalizing the Cassie and Wenzelapproaches is presented. The effects related to the line tension which are important fornano-structured surfaces are considered.

Motivated by recent experiments on the electro-hydrodynamic instability of spin-castpolymer films, we study the undulation instability of a thin viscoelastic polymer filmunder in-plane stress and in the presence of either a close by contactor or an electricfield, both inducing a normal stress on the film surface. We find that the in-plane stressaffects both the typical timescale of the instability and the unstable wavelengths. Thefilm stability is also sensitive to the boundary conditions used at the film-substrateinterface. We have considered two conditions, either rigidly attaching the film to thesubstrate or allowing for slip.

The impacts of the two-beam interference heating on the number of core-shell and embeddednanoparticles and on nanostructure coarsening are studied numerically based on thenon-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20nm) metallic bilayers. The model incorporates thermocapillary forces and disjoiningpressures, and assumes dewetting from the optically transparent substrate atop of thereflective support layer, which results in the complicated dependence of lightreflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillaryeffect is due to the local thickness-dependent, steady-state temperature profile in theliquid, which is derived based on the mean substrate temperature estimated from theelaborate thermal model of transient heating and melting/freezing. Linear stabilityanalysis of the model equations set for Ag/Co bilayer predicts the dewetting length scalesin the qualitative agreement with experiment.

We introduce a model, similar to diffusion limited aggregation (DLA), which serves as adiscrete analog of the continuous dynamics of evaporation of thin liquid films. Withinmean field approximation the dynamics of this model, averaged over many realizations ofthe growing cluster, reduces to that of the idealized evaporation model in which surfacetension is neglected. However fluctuations beyond the mean field level play an importantrole, and we study their effect on the conserved quantities of the idealized evaporationmodel. Assuming the cluster to be a fractal, a heuristic approach is developed in order toexplain the distinctive increase of the fractal dimension with the cluster size.

A small vicinity of a contact line, with well-defined (micro)scales (henceforth the“microstructure”), is studied theoretically for a system of a perfectly wetting liquid,its pure vapor and a superheated flat substrate. At one end, the microstructure terminatesin a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. Atthe other end, for motionless contact lines, it terminates in a constant film slope(apparent contact angle as seen on a larger scale), the angle being non-vanishing despitethe perfect wetting due to an overall dynamic situation engendered by evaporation. Here wego one step beyond the standard one-sided model by incorporating the effect of vaporpressure non-uniformity as caused by a locally intense evaporation flow, treated in theStokes approximation. Thereby, the film dynamics is primarily affected throughthermodynamics (shift of the local saturation temperature and evaporation rate), thedirect mechanical impact being rather negligible. The resulting integro-differentiallubrication film equation is solved by handling the newly introduced effect (giving riseto the “integro” part) as a perturbation. In the ammonia (at 300   K) example dealt withhere, it proves to be rather weak indeed: the contact angle decreases while the integralevaporation flux increases just by a few percent for a superheat of  ~1   K.However, the numbers grow (roughly linearly) with the superheat.

We analyze the problem of shear-induced electrokinetic lift on a particle freely suspended near a solid wall, subject to a homogeneous (simple) shear. To this end, we apply the large-Péclet-number generic scheme recently developed by Yariv et al. (J. Fluid Mech., Vol. 685, 2011, p. 306). For a force- and torque-free particle, the driving flow comprises three components, respectively describing (i) a particle translating parallel to the wall; (ii) a particle rotating with an angular velocity vector normal to the plane of shear; and (iiii) a stationary particle in a shear flow. Symmetry arguments reveal that the electro-viscous lift, normal to the wall, is contributed by Maxwell stresses accompanying the induced electric field, while electro-viscous drag and torque corrections, parallel to the wall, are contributed by the Newtonian stresses accompanying the induced flow. We focus upon the near-contact limit, where all electro-viscous contributions are dominated by the intense electric field in the narrow gap between the particle and the wall. This field is determined by the gap-region pressure distributions associated with the translational and rotational components of the driving Stokes flow, with the shear-component contribution directly affecting only higher-order terms. Owing to the similarity of the corresponding pressure distributions, the induced electric field for equal particle–wall zeta potentials is proportional to the sum of translation and rotation speeds. The electro-viscous loads result in induced particle velocities, normal and tangential to the wall, inversely proportional to the second power of particle–wall separation.

In this paper we present a theory describing the diffusion limited evaporation of sessilewater droplets in presence of contact angle hysteresis. Theory describes two stages ofevaporation process: (I) evaporation with a constant radius of the droplet base; and (II)evaporation with constant contact angle. During stage (I) the contact angle decreases fromstatic advancing contact angle to static receding contact angle, during stage (II) thecontact angle remains equal to the static receding contact angle. Universal dependencesare deduced for both evaporation stages. Obtained universal curves are validated againstavailable in the literature experimental data.

Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler numbers. We analyze the steady state, its linear stability and nonlinear regime. In the latter case, long-wave models are compared with integral-boundary-layer ones and bifurcation diagrams for permanent solitary wave solutions of the different models are constructed. Time-dependent computations with the integral-boundary-layer models show that the system approaches a train of coherent structures that resemble the solitary pulses obtained in the bifurcation diagrams.