When a film of a liquid suspension of nanoparticles or a polymer solution is deposited on a surface, it may dewet from the surface and as the solvent evaporates the solute particles/polymer can be deposited on the surface in regular line patterns. In this paper we explore a hydrodynamic model for the process that is based on a long-wave approximation that predicts the deposition of irregular and regular line patterns. This is due to a self-organised pinning-depinning cycle that resembles a stick-slip motion of the contact line. We present a detailed analysis of how the line pattern properties depend on quantities such as the evaporation rate, the solute concentration, the Péclet number, the chemical potential of the ambient vapour, the disjoining pressure, and the intrinsic viscosity. The results are related to several experiments and to depinning transitions in other soft matter systems.

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. PACS numbers: 68.15.+e, 81.15.Lm, 81.16.Rf The last decade has seen huge growth in interest in phenomena that accompany evaporative and convective dewetting of suspensions and solutions. Well known are the detailed studies of the coffee stain effect [1,2] that analyse the deposition and resulting structures left behind by a receding three-phase contact line of an evaporating drop of suspension upon a solid substrate. In particular, Ref.[2] describes a large range of different deposition patterns including cellular and lamellar structures, single and multiple rings, and Sierpinski gaskets. Other observed structures include crack [3] and chevron [4] patterns. Recently it has been shown that evaporating polymer solutions [5][6][7] and (nano)particle suspensions [8-10] may be used to fabricate strikingly regular stripe patterns, where the deposited stripes are parallel to the receding contact line and have typical distances ranging from 10-100µm. The goal is to use this effect as a non-lithographic technique for covering large areas with regular arrays of small-scale structures, such as, e.g., concentric gold rings with potential uses as resonators in advanced optical communications systems [11]. The deposited patterns from more complex fluids, such as polymer mixtures [12] and DNA solutions [13], are also investigated. The occurrence of regular stripe patterns is a somewhat generic phenomenon, that is not only observed for different combinations of substances but also in a variety of experimental setups that allow for slow evaporation. Examples include the meniscus technique in a sphere-on-flat geometry [7,9], a controlled continuous supply of liquid between two sliding plates to maintain a meniscus-like surface [5] and dewetting forced by a pressure gradient [10]. Interestingly, besides the stripes parallel to the receding contact line, a variety of other patterns are observed, including regular orthogonal stripes [9], superpositions of orthogonal and parallel stripes [5], regular arrays of drops [5,14] and irregularly branched structures [14,15]. This behaviour is highly sensitive to the particular experimental setup and parameters.Despite the extensive number and variety of experiments, an explanation of the formation of the regular patterns has been rather elusive. Although most studies agree that the patterns result from a stick-slip motion of the contact line caused by pinning/depinning events [2,6,11,16] no dynamical model of the periodic deposition process ex-

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.

We review recent experiments on dewetting thin films of evaporating colloidal nanoparticle suspensions (nanofluids) and discuss several theoretical approaches to describe the ongoing processes including coupled transport and phase changes. These approaches range from microscopic discrete stochastic theories to mesoscopic continuous deterministic descriptions. In particular, we focus on (i) a microscopic kinetic Monte Carlo model, (ii) a dynamical density functional theory and (iii) a hydrodynamic thin film model. Models (i) and (ii) are employed to discuss the formation of polygonal networks, spinodal and branched structures resulting from the dewetting of an ultrathin 'postcursor film' that remains behind a mesoscopic dewetting front. We highlight, in particular, the presence of a transverse instability in the evaporative dewetting front which results in highly branched fingering structures. The subtle interplay of decomposition in the film and contact line motion is discussed.

We study two-dimensional steady concentration and film thickness profiles for isothermal free surface films of a binary liquid mixture on a solid substrate employing model-H that couples the diffusive transport of the components of the mixture (convective Cahn-Hilliard equation) and the transport of momentum (Navier-Stokes-Korteweg equations). The analysis is based on minimising the underlying free energy equivalent to solving the static limit of model-H. Additionally, the linear stability (in time) of relevant layered films is analyzed. This allows for a comparison of the position of certain branching points in the bifurcation diagrams of steady solutions with the value predicted as onset of a linear instability. Results are presented for the cases of (i) a flat film without energetic bias at the free surface, (ii) a flat film with energetic bias, (iii) a height-modulated film without energetic bias, and (iv) a height-modulated film with energetic bias. In all cases we discuss symmetries of the various steady solutions allowing us to order them and to infer properties of solution branches and relations between them.