Fabrication and processing of polymer solar cells: A review of printing and coating techniques

Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.

Long-scale evolution of thin liquid films

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

The suitability of electrowetting-on-dielectric (EWD) microfluidics for true lab-on-a-chip applications is discussed. The wide diversity in biomedical applications can be parsed into manageable components and assembled into architecture that requires the advantages of being programmable, reconfigurable, and reusable. This capability opens the possibility of handling all of the protocols that a given laboratory application or a class of applications would require. And, it provides a path toward realizing the true lab-on-a-chip. However, this capability can only be realized with a complete set of elemental fluidic components that support all of the required fluidic operations. Architectural choices are described along with the realization of various biomedical fluidic functions implemented in on-chip electrowetting operations. The current status of this EWD toolkit is discussed. However, the question remains: which applications can be performed on a digital microfluidic platform? And, are there other advantages offered by electrowetting technology, such as the programming of different fluidic functions on a common platform (reconfigurability)? To understand the opportunities and limitations of EWD microfluidics, this paper looks at the development of lab-on-chip applications in a hierarchical approach. Diverse applications in biotechnology, for example, will serve as the basis for the requirements for electrowetting devices. These applications drive a set of biomedical fluidic functions required to perform an application, such as cell lysing, molecular separation, or analysis. In turn, each fluidic function encompasses a set of elemental operations, such as transport, mixing, or dispensing. These elemental operations are performed on an elemental set of components, such as electrode arrays, separation columns, or reservoirs. Examples of the incorporation of these principles in complex biomedical applications are described.

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Digital microfluidics: is a true lab-on-a-chip possible?

Carbon Nanotube Thin Films: Fabrication, Properties, and Applications

Simulation of Droplet Motion on Low-Energy and Heterogeneous Surfaces

Failure of a liquid coating to remain continuous on a substrate that exhibits a significant equilibrium contact angle is a common occurrence in industrial applications. The term “reticulation” is sometimes used to describe the resulting formation of a pattern of defects. The failure may take the form of coating perforations and dewetting, and it may ultimately lead to a set of isolated drops. We present mathematical and experimental results for reticulation. The theoretical and numerical results use a disjoining–conjoining pressure model to represent the substrate energetics. The theory uses the small-slope or “lubrication” approximation and also includes the effects of evaporation and drying of the coating. The model employs a two-component liquid where the viscosity depends on local values of the nonvolatile mixture fraction. A linear analysis for a slightly perturbed uniform layer predicts a most-unstable wavelength and an associated growth rate. These are in approximate agreement with the modeling results. Computations employing the full nonlinear model show the wide variety of patterns that can arise in the drying liquid. These patterns are both qualitatively and quantitatively similar to actual patterns that we observe experimentally. Small defects that are visible in the experiment are used to initiate reticulation in the numerical simulation.

Dewetting Patterns in a Drying Liquid Film.

Role of surface tension gradients in correcting coating defects in corners

A linear analysis, employing the lubrication approximation, is presented for the leveling history of a thin layer of Newtonian liquid. When the surface tension is taken to be constant, the classic result of Orchard is reproduced. As expected, the presence of surfactant, with resulting surface-tension-gradient forces, slows the rate of leveling of an initial train of periodic ripples. For very weak surfactants, initial leveling rates are unaffected, but ripple amplitude can be lowered only to a plateau level which persists for long times. Surprisingly, critical surfactant concentrations exist, depending on other system parameters such as the coating thickness and ripple wavelength, for which leveling is maximally retarded. To the extent that this retardation is generally undesirable, it is suggested that these critical values be avoided, even by increasing the amount of surfactant present. This anomalous effect is maximized for an assumed nondiffusing, insoluble surfactant and is mitigated by either surface or bulk diffusion of surfactant.

An Analysis of the Effect of Surfactant on the Leveling Behavior of a Thin Liquid Coating Layer

A numerical model is presented for the simulation of cell emptying behaviour when an engraved roller is used to transfer a liquid coating onto a moving substrate. The three-dimensional unsteady liquid motion is calculated where the flow domain is bounded above by a stress-free surface and bounded below by a moving substrate with a complex pattern of indentations. The physical model is simplified through use of the long-wave or lubrication approximation appropriate to flow in thin liquid layers. Specific predictions are made for particular cells and patterns. Cell size is found to be the principal determinant of emptying behaviour with larger cells emptying more completely. Modelling is currently restricted to the flow domain beneath the receding meniscus and drainage due to gravity. There are limitations on the dimensionless measures of coating speed. It is found that both surface tension and cell orientation are also significant in controlling the rate of drainage. Both Newtonian and shear-thinning flows are considered.

Richard R. Eley

Papers

Simulation of Droplet Motion on Low-Energy and Heterogeneous Surfaces

Dewetting Patterns in a Drying Liquid Film.

Role of surface tension gradients in correcting coating defects in corners

An Analysis of the Effect of Surfactant on the Leveling Behavior of a Thin Liquid Coating Layer

Numerical Modelling of Liquid Withdrawal from Gravure Cavities in Coating Operations