arXiv subjects

Serafim Kalliadasis

Publications and source records attributed to Serafim Kalliadasis.

42 records · Page 3Linked to original sources

arXiv2012

The overdamped limit of dynamic density functional theory: Rigorous results

Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously derived for the one-particle distribution function. This new equation includes a novel definition of the diffusion tensor. A comparison with existing formulations of dynamic density functional theory is also made.

math-ph↗

arXiv2012

Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system

We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas. Flow 19, 589 (1993)], to the more commonly used continuum fluid dynamical equations augmented with the Navier-slip condition. Considering quasistatic droplet evolution and using the method of matched asymptotics, we find that the evolution of the droplet radius using the interface formation model reduces to an equivalent expression for a slip model, where the prescribed microscopic dynamic contact angle has a velocity dependent correction to its static value. This result is found for both the original interface formation model formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features of the model, such as the pressure behaviour and rolling motion at the contact line, and their relevance, are also considered in the prototype system we adopt.

physics.flu-dyn↗

arXiv2012

Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly het- erogeneous domains. To the best knowledge of the authors, this seems to be the first attempt of upscaling the Cahn-Hilliard equation in such domains. The new homog- enized equation should have a broad range of applicability due to the well-known versatility of phase-field models. The additionally introduced feature of systemati- cally and reliably accounting for confined geometries by homogenization allows for new modeling and numerical perspectives in both, science and engineering. Our results are applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls.

math-ph↗

arXiv2011

Wavy regimes of film flow down a fibre

We consider axisymmetric traveling waves propagating on the gravity-driven flow of a liquid down a vertical fibre. Our starting point is the two-equation model for the flow derived in the study by Ruyer-Quil \emph{et al.} [\emph{J. Fluid Mech.} {\bf 603}, 431 (2008)]. The speed, amplitude and shape of the traveling waves are obtained for a wide range of parameters by using asymptotic analysis and elements from dynamical systems theory. Four different regimes are identified corresponding to the predominance of four different physical effects: Advection by the flow, azimuthal curvature, inertia and viscous dispersion. Construction of the traveling-wave branches of solutions reveals complex transitions from one regime to another. A phase diagram of the different regimes in the parameter space is oferred.

physics.flu-dyn↗

arXiv2010

Equilibrium gas-liquid-solid contact angle from density-functional theory

We investigate the equilibrium of a fluid in contact with a solid boundary through a density-functional theory. Depending on the conditions, the fluid can be in one phase, gas or liquid, or two phases, while the wall induces an external field acting on the fluid particles. We first examine the case of a liquid film in contact with the wall. We construct bifurcation diagrams for the film thickness as a function of the chemical potential. At a specific value of the chemical potential, two equally stable films, a thin one and a thick one, can coexist. As saturation is approached, the thickness of the thick film tends to infinity. This allows the construction of a liquid-gas interface that forms a well defined contact angle with the wall.

physics.flu-dyn↗

arXiv2009

Two-dimensional droplet spreading over random topographical substrates

We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions. The variance of the droplet shift at both early times and in the long-time limit is deduced and the droplet footprint is found to be a normal random variable at all times. It is shown that substrate roughness decreases droplet wetting, illustrating also the tendency of the droplet to slide without spreading as equilibrium is approached. Our theoretical predictions are verified by numerical experiments.

physics.flu-dyn↗