Motivated by recent experimental investigations of the mechanical behavior nanoporous metal we explore an efficient and robust method for generating 3D representative volume elements (RVEs) with strikingly similar behavior. Our approach adopts Cahn's a Gaussian random field taking superposition standing sinusoidal waves fixed wavelength but in direction phase. In its theory part, our study describes closed-form expressions how solid fraction affects binarization level, mean structure size,...

We offer new insights and results on the hydrodynamics of solitary waves inertia-dominated falling liquid films using a combination experimental measurements, direct numerical simulations (DNS) low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with measurements terms main wave characteristics velocity profiles over entire range investigated Reynolds numbers. And, surprisingly, LD model is found predict accurately film height even for high Based detailed analysis...

Abstract Droplet evaporation on solid surfaces is important in many applications including printing, micro-patterning and cooling. While seemingly simple, the configuration of evaporating droplets solids difficult to predict control. This because typically proceeds as a “stick-slip” sequence—a combination pinning de-pinning events dominated by static friction or “pinning”, caused microscopic surface roughness. Here we show how smooth, pinning-free, non-planar topography promote different...

We study effective elastic properties of 3D bicontinuous random composites (such as, e.g., nanoporous gold filled with polymer) considering linear and infinitesimal elasticity using asymptotic homogenization along the finite element method. For generation microstructures, a leveled-wave model based on works Cahn (1965) Soyarslan et al. (2018) is used. The influences volume size, phase contrast, relative fraction phases applied boundary conditions computed apparent moduli are investigated....

We examine the motion of a liquid-air meniscus advancing into microchannel with chemically heterogeneous walls. consider case where constant flow rate is imposed, so that mean velocity interface kept constant, and study effects disorder properties on apparent contact angle for each surface. focus here large diffusivity regime, any possible advection effect not taken account. To this end, we make use phase-field model enables line by diffusive interfacial fluxes takes account wetting show in...

We examine the interaction of two-dimensional solitary pulses on falling liquid films. make use second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. 15, 357 (2000); Fluids 14, 170 (2002)] combining long-wave approximation with a weighted residual technique. The includes (second-order) viscous dispersion effects which originate from streamwise momentum equation tangential stress balance. These play dispersive role that primarily influences shape...

We apply physics-informed neural networks (PINNs) to first-order, two-scale, periodic asymptotic homogenization of the property tensor in a generic elliptic equation. The problem lack differentiability tensors at sharp phase interfaces is circumvented by making use diffuse interface approach. Periodic boundary conditions are incorporated strictly through introduction an input-transfer layer (Fourier feature mapping), which takes sine and cosine inner product position reciprocal lattice...

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While bulk isotropic fluids it is exhaustively studied, this less so anisotropic confined situations. Here, we combine latter two by studying rotation a disk-like inclusion uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms perturbative expansion parameters that quantify anisotropies viscosity additional linear friction with supporting...

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization waves. Direct numerical simulations entire two-phase system are conducted using state-of-the-art finite volume framework interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. present detailed analysis wave shape dispersion...

We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. focus on the front as mean velocity interface $\overline{v}$ is decreased pinning state approached. Scaling arguments allow us to obtain statistics sizes durations, which become power-law distributed due existence a critical point at $\overline{v}=0$. Results are compared with phase-field numerical simulations.

We examine binary interaction of two-dimensional solitary pulses in falling liquid films. make use a two-field system equations for the local flow rate and interface position that includes (second-order) viscous dispersion effects. By applying coherent-structure theory, we obtain dynamical separation length between pulses. The is re-formulated terms potential function which not only allows us to predict bound-state formation but also interpret physically this formation. Numerical results...

Time-series tools are used to analyze how chaotic dynamics interacts with noise in the generalized Kuramoto-Sivashinsky equation, a prototype for falling films. The critical value of intensity chaotic-stochastic transition is quantified terms system control parameter.

We investigate the dynamics of a droplet on planar substrate as volume changes dynamically due to liquid being pumped in or out through pore. adopt diffuse-interface formulation which is appropriately modified account for localized inflow-outflow boundary condition (the pore) at bottom droplet, hence allowing control its volume, moves flat with periodic chemical pattern. find that undergoes stick-slip motion increased (fattening droplet) can be monitored by tracking contact points. If we...

We investigate droplets evaporating on flat pinning-free substrates with smooth wettability patterns. Symmetric patterns lead to a hierarchy of bifurcations in the three-dimensional parameter space represented by droplet cross sectional area $A$, midpoint $\ensuremath{\ell}$, and footprint $R$. In asymmetrical patterns, presence disconnected stable branches forces move towards one direction, hence showing that droplet's motion can be controlled upon evaporation.

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion to interface motion viscous film flows. Our aim develop systematic rigorous low-dimensional representation gKS For this purpose, we approximate it by renormalization group equation which qualitatively characterized error bounds. This formulation allows new stochastic mode reduction...

We study spontaneous imbibition using a phase field model in two-dimensional system with dichotomic quenched noise. By imposing constant pressure mu(a)<0 at the origin, we case when interface advances low velocities, obtaining scaling exponents z=3.0+/-0.1, alpha=1.50+/-0.02, and alpha(loc)=0.95+/-0.03 within intrinsic anomalous scenario. These results are quite good agreement experimental data recently published. Likewise, increase velocity, resulting z=4.0+/-0.1, alpha=1.25+/-0.02,...

The scaling properties of the rough liquid-air interface formed in spontaneous imbibition a viscous liquid by model porous medium are found to be very sensitive magnitude pressure difference applied at inlet. Interface fluctuations change from obeying intrinsic anomalous large negative differences, being super-rough with same dynamic exponent z approximately =3 less finally ordinary Family-Vicsek =2 positive differences. This rich scenario reflects relative importance on different length...

We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. study local activity statistics, kinetics, and temporal correlations global interface velocity, obtaining different relationships among involved critical exponents depending on how far from or close to a point system is. Our arguments are very general connect magnitudes through several relationships. expect our results be applicable wide range systems exhibiting kinetic...

Abstract We examine pulse interaction and bound-state formation in interfacial turbulence using the problem of a falling liquid film as model system. perform direct numerical simulations (DNSs) full Navier–Stokes equations associated wall free-surface boundary conditions we both analytically numerically low-dimensional (LD) for film. For two-pulse system, DNSs reveal existence very rich complex interactions, characterized by either overdamped, underdamped or self-sustained oscillating...

Using a simple configuration, we study stick-slip and hysteresis mostly analytically, compare our results to the classical theories. In particular, highlight changes which occur when varying size of system relative typical heterogeneity.

Abstract We discuss a model for directed percolation in which the flux of material along each bond is dynamical variable. The includes physically significant limiting case where total conserved. show that distribution fluxes asymptotic to power law at small fluxes. give an implicit equation exponent, terms probabilities characterising site occupations. In one dimension occupations are exactly independent, and solvable. two dimensions, independent-occupation assumption gives good...

We show that time-dependent couplings may lead to nontrivial scaling properties of the surface fluctuations asymptotic regime in nonequilibrium kinetic roughening models. Three typical situations are studied. In case a crossover between two different rough regimes, coupling result anomalous for scales above length. setting, from either flat or damping regime, length conspire produce surface, although most relevant term tends flatten surface. addition, our analysis sheds light into an...

Abstract We examine the stability, dynamics and interactions of solitary waves in a two-dimensional vertically falling thin liquid film that exhibits shear-thinning effects. use low-dimensional two-field model describes evolution both local flow rate thickness is consistent up to second-order terms long-wave expansion. The behaviour modelled via power-law formulation with Newtonian plateau limit small strain rates. Our results show emergence hysteresis as control parameter (the Reynolds...

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. show that is mass-conservative and discrete solution satisfies energy law similar one satisfied by exact solution. perform several tests inspired realistic situations verify accuracy performance of method: chemically heterogeneous substrate in three dimensions, wetting-driven nucleation complex two-dimensional domain three-dimensional diffusion through porous medium.

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring may combine to form larger one, also trail split into two. addition, move diffusively. The model is defined parameters quantify the fragmentation rate fragment size. long-time limit, system reaches steady state, our focus limiting distribution weights. find that density...