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

Spin-coating is widely employed for the highly reproducible fabrication of thin film coatings over large areas with high structural uniformity. Research in recent years has extended the scope of spin-coating by chemically engineering the interface of support and solution to obtain specific structural order in the resulting supported thin films. This review will discuss both the fundamental physical and chemical processes governing the conventional spin-coating process and describe methodologies for the preparation of spin-coated polymer thin films. Furthermore, a range of advanced applications and recent developments within this field will be reviewed with focus on engineering chemical and topological structure during the coating process.

6 Studies of spin-coated polymer films

The process of spin coating is described, with particular attention to applications in microelectronics. The physical mechanisms involved in the process are discussed and those mechanisms that affect the final state are identified, viz., centrifugal and viscous forces, solute diffusion, and solvent evaporation: A model is proposed that incorporates only the latter mechanisms, with viscosity and diffusivity depending on solute concentration. The evaporation of solvent during spinning causes the solution viscosity to increase and the flow is reduced. The thickness of the final solid film is related to the thickness of a diffusion boundary layer near the free surface. The model predicts the final dry film thickness in terms of the primary process variables, spin speed, and initial polymer concentration. A similarity boundary‐layer analysis leads to a simple approximate result for the final film thickness that is consistent with limited experimental data, hf ∼KC0(ν0D0)1/4/Ω1/2, where K is a number of order un...

The mechanics of spin coating of polymer films

The equations describing the flow of a power‐law non‐Newtonian fluid on a rotating disk have been solved in general form. This makes it possible to calculate how the shape of an initial surface contour will vary with time and to investigate the possibility of producing uniform films by applying the materials to a rapidly spinning disk. It is shown that the latter process, which has potential industrial applications, has a much better chance of succeeding if the fluid is Newtonian than if it is not, in the sense that whereas for a Newtonian substance centrifugation will smooth out irregularities in the surface contour, for a non‐Newtonian fluid even an initially uniform film thickness will be deformed by rotating the plate.

E. E. Petersen

Papers

On the Flow of a Non‐Newtonian Liquid on a Rotating Disk