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 impact of drops impinging one by one on a solid surface is studied experimentally and theoretically. The impact process is observed by means of a charge-coupled-device camera, its pictures processed by computer. Low-velocity impact results in spreading and in propagation of capillary waves, whereas at higher velocities splashing (i.e. the emergence of a cloud of small secondary droplets, absent in the former case) sets in. Capillary waves are studied in some detail in separate experiments. The dynamics of the extension of liquid lamellae produced by an impact in the case of splashing is recorded. The secondary-droplet size distributions and the total volume of these droplets are measured, and the splashing threshold is found as a function of the impact parameters.The pattern of the capillary waves is predicted to be self-similar. The calculated wave profile agrees well with the experimental data. It is shown theoretically that the splashing threshold corresponds to the onset of a velocity discontinuity propagating over the liquid layer on the wall. This discontinuity shows several aspects of a shock. In an incompressible liquid such a discontinuity can only exist in the presence of a sink at its front. The latter results in the emergence of a circular crown-like sheet virtually normal to the wall and propagating with the discontinuity. It is predicted theoretically and recorded in the experiment. The crown is unstable owing to the formation of cusps at the free rim at its top edge, which results in the splashing effect. The onset velocity of splashing and the rate of propagation of the kinematic discontinuity are calculated and the theoretical results agree fairly well with the experimental data. The structure of the discontinuity is shown to match the outer solution.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095002266

Impact of drops on solid surfaces : self-similar capillary waves, and splashing as a new type of kinematic discontinuity

A model is presented for the description of thin films prepared from solution by spinning. Using only the centrifugal force, linear shear forces, and uniform evaporation of the solvent, the thickness of the film and the time of drying can be calculated as functions of the various processing parameters. The model is compared with experimental results obtained on positive photoresists and excellent agreement is obtained. When adequate care are is taken, the liquid forms a level surface during spinning, and the film thickness becomes uniform and independent of the size of the substrate. The film thickness h shows the following dependence on spin speed f, initial viscosity ν0, and evaporation rate e:h∝f−2/3νo1/3e1/3, and e is proportional to f1/2.

Characteristics of resist films produced by spinning

The aim of this article was to elucidate the basic relationships between processing conditions and the mechanical and electrical properties of multiwalled carbon nanotube reinforced polymer composites. In conventional chopped fiber reinforced polymer composites, uniform distributions of fibers throughout the matrix are critical to producing materials with superior physical properties. Previous methods have dispersed carbon nanotubes by aggressive chemical modification of the nanotubes or by the use of a surfactant prior to dispersion. 1, 2 Here, ultrasonic energy was used to uniformly disperse multiwalled nanotubes (MWNTs) in solutions and to incorporate them into composites without chemical pretreatment. Polystyrene (PS) solutions containing MWNTs were cast and spun to yield thin film MWNT composites. The rheology of PS/MWNT suspensions was modeled using the Carreau equation. MWNTs were found to align at the shear rates generated by the spin casting process. The tensile modulus and strain to failure of samples compared well to classical micromechanical models, increasing with MWNT loading. The composite films showed lower strains at the yield stress than neat PS films. The presence of MWNTs at 2.5 vol % fraction approximately doubles the tensile modulus, and transforms the film from insulating to conductive (surface resistivity, ρ, approaching 103 Ω/□). © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2660–2669, 2002

Multiwalled carbon nanotube polymer composites: synthesis and characterization of thin films

The spin coating of thin (> 200 nm thick) and ultrathin (< 200 nm thick) polymer films is examined in several solvents of varying volatility over a broad range of polymer solution concentrations and spin speeds. Experimentally measured film thicknesses are compared with a simple model proposed by Bornside, Macosko, and Scriven, which predicts film thickness based on the initial properties of the polymer solution, solvent, and spin speed. This model is found to predict film thickness values within 10% over the entire range of conditions explored, which gave film thicknesses from 10 nm to 33 μ:m. The model underpredicts film thickness for cases in which a very volatile solvent is used or the initial concentration of polymer is high, while overpredicting film thickness for cases in which a low volatility solvent is used or the initial polymer concentration is very low. These deviations are a consequence of how the model decouples fluid flow and solvent evaporation.

Spin coating of thin and ultrathin polymer films

Equations describing the flow of a Newtonian liquid on a rotating disk have been solved so that characteristic curves and surface contours at successive times for any assumed initial fluid distribution may be constructed. It is shown that centrifugation of a fluid layer that is initially uniform does not disturb the uniformity as the height of the layer is reduced. It is also shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated. Contour surfaces for a number of exemplary initial distributions (Gaussian, slowly falling, Gaussian plus uniform, sinusoidal) have been constructed. Edge effects on rotating planes with rising rims, and fluid flow on rotating nonplanar surfaces, are considered.

Leslie G. Peck

Papers

Flow of a Viscous Liquid on a Rotating Disk