Nonreciprocity induces resonances in two-field Cahn-Hilliard model

We consider a non-reciprocically coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour, a suppression of coarsening as well as the existence of localised states. Here, after introducing the model we first briefly review the linear stability of homogeneous states and show that all instability thresholds are identical to the ones for a corresponding Turing system (i.e., a two-species reaction-diffusion system). Next, we discuss possible interactions of linear modes and analyse the specific case of a ``Hopf-Turing'' resonance by discussing corresponding amplitude equations in a weakly nonlinear approach. The thereby obtained states are finally compared with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude by a discussion of the limitations of the weakly nonlinear approach

Thin films of van der Waals fluid: From interface interactions to wetting transitions

We present a theoretical study of wetting phenomena and interactions between liquid-vapor interfaces based on the density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid and between the fluid and substrate. For the latter, we consider two models-hard wall and soft wall approximations-differing by the role of steric effects and leading to a qualitatively different character of phase transitions. We compute numerically the disjoining and conjoining potentials (which are important dynamically for spreading, spinodal dewetting, and coarsening in thin films, as well as resolution of interfacial singularities), and loci of intermediate and complete wetting transitions as functions of the Hamaker constant and temperature. We find that taking into account short-range interactions is essential for the description of wetting transitions in the soft wall limit. We derive an analytical form of the disjoining potential and analyze it in the context of the complete, frustrated and partial wetting.Comment: 13 pages, 12 figure

Droplet motion driven by surface freezing or melting: A mesoscopic hydrodynamic approach

A fluid droplet may exhibit self-propelled motion by modifying the wetting properties of the substrate. We propose a novel model for droplet propagation upon a terraced landscape of ordered layers formed as a result of surface freezing driven by the contact angle dependence on the terrace thickness. Simultaneous melting or freezing of the terrace edge results in a joint droplet-terrace motion. The model is tested numerically and compared to experimental observations on long-chain alkane system in the vicinity of the surface melting point.Comment: 4 pages, 3 figure

Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Asymptotic theory for a moving droplet driven by a wettability gradient

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig

Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics

The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the solvability conditions of the density field equation with appropriate boundary conditions imposed on the solid support. The equation describing the motion of a spreading film are derived in the lubrication approximation. In the case of quasi-equilibrium spreading, is shown that the correct sharp-interface limit is obtained, and sample solutions are obtained by numerical integration. It is further shown that evaporation or condensation may strongly affect the dynamics near the contact line, and accounting for kinetic retardation of the interphase transport is necessary to build up a consistent theory.Comment: 14 pages, 5 figures, to appear in PR

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning