arXiv subjects

Uwe Thiele

Publications and source records attributed to Uwe Thiele.

107 records · Page 6Linked to original sources

arXiv2011

Modelling fluids and crystals using a two-component modified phase field crystal model

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where modulated and uniform phases are formed and also regions where localised states are formed. We investigate the effectiveness of the phase field crystal model for describing fluids and crystals with defects. We further consider a two component model and elucidate how the structure transforms from hexagonal crystalline ordering to square ordering as the concentration changes. Our conclusion contains a discussion of possible interpretations of the order parameter field.

cond-mat.soft↗

arXiv2011

Ratcheting of driven attracting colloidal particles: Temporal density oscillations and current multiplicity

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a DC or an AC external potential. In addition, the walls of the channel interact with the particles via a ratchet-like periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of DC drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

cond-mat.soft↗

arXiv2010

On the depinning of a drop of partially wetting liquid on a rotating cylinder

We discuss the analogy of the behaviour of films and drops of liquid on a rotating horizontal cylinder on the one hand and substrates with regular one-dimensional wettability patterns on the other hand. Based on the similarity between the respective governing long-wave equations we show that a drop of partially wetting liquid on a rotating cylinder undergoes a depinning transition when the rotation speed is increased. The transition occurs via a sniper bifurcation as in a recently described scenario for drops depinning on heterogeneous substrates.

physics.flu-dyn↗

arXiv2010

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e., time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different system. First, we discuss the linear stability of homogeneous steady states, i.e., flat films; and second the systematics of non-trivial steady states, i.e., drop/hole states for dewetting films and quantum dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing to the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly not related physical systems mathematically, but does as well allow to discuss model extensions in a more unified way.

cond-mat.other↗

arXiv2010

Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.

physics.flu-dyn↗

arXiv2010

Dynamical model for the formation of patterned deposits at receding contact lines

We describe the formation of deposition patterns that are observed in many different experiments where a three-phase contact line of a volatile nanoparticle suspension or polymer solution recedes. A dynamical model based on a long-wave approximation predicts the deposition of irregular and regular line patterns due to self-organised pinning-depinning cycles corresponding to a stick-slip motion of the contact line. We analyze how the line pattern properties depend on the evaporation rate and solute concentration.

physics.flu-dyn↗

arXiv2010

Transport of free surface liquid films and drops by external ratchets and self-ratcheting mechanisms

We discuss the usage of ratchet mechanisms to transport a continuous phase in several micro-fluidic settings. In particular, we study the transport of a dielectric liquid in a heterogeneous ratchet capacitor that is periodically switched on and off. The second system consists of drops on a solid substrate that are transported by different types of harmonic substrate vibrations. We argue that the latter can be seen as a self-ratcheting process and discuss analogies between the employed class of thin film equations and Fokker-Planck equations for transport of discrete objects in a 'particle ratchet'.

cond-mat.soft↗

arXiv2009

Self-ratcheting Stokes drops driven by oblique vibrations

We develop and analyze a minimal hydrodynamic model in the overdamped limit to understand why a drop climbs a smooth homogeneous incline that is harmonically vibrated at an angle different from the substrate normal [Brunet, Eggers and Deegan, Phys. Rev. Lett. 99, 144501 (2007)]. We find that the vibration component orthogonal to the substrate induces a nonlinear (anharmonic) response in the drop shape. This results in an asymmetric response of the drop to the parallel vibration and, in consequence, in the observed net motion. Beside establishing the basic mechanism, we identify scaling laws valid in a broad frequency range and a flow reversal at high frequencies.

cond-mat.soft↗

arXiv2007

Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.

physics.flu-dyn↗

arXiv2006

Liquid transport generated by a flashing field-induced wettability ratchet

We develop and analyze a model for ratchet-driven macroscopic transport of a continuous phase. The transport relies on a field-induced dewetting-spreading cycle of a liquid film with a free surface based on a switchable, spatially asymmetric, periodic interaction of the liquid-gas interface and the substrate. The concept is exemplified using an evolution equation for a dielectric liquid film under an inhomogeneous voltage. We analyse the influence of the various phases of the ratchet cycle on the transport properties. Conditions for maximal transport and the efficiency of transport under load are discussed.

physics.flu-dyn↗

arXiv2006

Drops on an inclined heterogeneous substrate: onset of sliding motion

Pinning and depinning of drops on an inclined heterogeneous substrate is studied as a function of the inclination and heterogeneity amplitude. Two types of heterogeneity are considered: a hydrophobic defect that blocks the droplet in front, and a hydrophilic one that holds it at the back. Two different types of depinning leading to sliding motion are identified, and the resulting stick-slip motion is studied numerically.

physics.flu-dyn↗

arXiv2005

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.

physics.flu-dyn↗

arXiv2005

Morphology changes in the evolution of liquid two-layer films

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions or the Marangoni effect. Using a long wave approximation we derive coupled evolution equations for the interafce profiles for a general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses are performed for isothermal ultrathin layers below 100 nm thickness under the influence of destabilizing long-range and stabilizing short-range interactions. Flat films may be unstable to varicose, zigzag or mixed modes. During the long-time evolution the nonlinear mode type can change via switching between two different branches of stable stationary solutions or via coarsening along a single such branch.

nlin.PS↗

arXiv2004

Alternative pathways of dewetting for a thin two-layer film of soft matter

We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show that depending on the long-range van-der-Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate.

nlin.PS↗

arXiv2004

Dynamical Model for Chemically Driven Running Droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets -- reaction-limited and saturated regime -- are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.

cond-mat.soft↗

arXiv2001

Dewetting of thin films on heterogeneous substrates: Pinning vs. coarsening

We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e. pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than the critical dewetting mode, weak heterogeneities are sufficient for pinning. A large region of coexistence between coarsening dynamics and pinning is found.

cond-mat.soft↗

arXiv1999

Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems

Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal axes. Equations that describe the dependence of front motion on the angle illustrate the mechanism leading to stratified chaos.

patt-sol↗