The stretching surface is assumed to be stretched impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar flow on the stretching surface are solved analytically by using the singular perturbation technique and the method of characteristics is used to obtain an analytic expression for film thickness. The results show that the final film thickness is independent of the amount of liquid distributed initially and on the initial film thickness be it uniform or nonuniform. It is also shown that the forceful stretching produces quicker thinning of the film on the stretching surface.

Flow of a thin liquid film on an unsteady stretching sheet

Recent advances in continuous-flow processors, which integrate sustainability metrics including scalability, have established their utility in materials and chemical processing. In this review the spinning disc processor (SDP) and the related rotating tube processor (RTP), are highlighted in the use of highly sheared and micro-mixed dynamic thin films in gaining control over such processing for a wide range of applications. Both SDP and RTP have a number of control parameters beyond traditional batch processing which are effective in (i) manipulating the size, shape, defects, agglomeration, and precipitation of nanoparticles, as well as decorating preformed nano-structures, for a variety of inorganic and organic compounds, (ii) controlling chemical reactivity and selectivity including the formation of polymers, and (iii) disassembling self organised nano-structures, as a tool for probing macromolecular structure under shear conditions.

Controlling nanomaterial synthesis, chemical reactions and self assembly in dynamic thin films

In this paper we have studied a non-planar thin liquid film flow on a planar stretching surface. The stretching surface is assumed to stretch impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar flow on the stretching surface are solved analytically. It is observed that faster stretching causes quicker thinning of the film on the stretching surface. Velocity distribution in the liquid film and the transient film profile as functions of time are obtained.

Transient film profile of thin liquid film flow on a stretching surface

MHD thin film flow of the Oldroyd-B fluid together with bioconvection and activation energy

Unsteady two-layer film flow on a non-uniform rotating disk in presence of uniform transverse magnetic field

We consider an axisymmetric flow of a thin liquid film on a rotating annular disk. The effects of surface tension and gravity terms are included. An asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the film thickness in comparison to the inner disk radius, and then applying the method of matched asymptotic expansion. The asymptotic solution is capable of predicting several features of spin-coating processes. For example, we find that the surface tension enhances film thinning at the central region whereas the gravity does not. The results show that the final film thickness does not depend on the initial distribution of the film thickness (be it uniform or nonuniform) and on the initial amount of liquid deposited. We find that most of the liquid initially deposited on the disk flows out of the disk in a very short time at the initial stages of spinning, regardless of the type of initial distribution of the film thickness. The retention of fluid for nonuniform initial distribution is more than that for uniform distribution at the early stages of the spreading of the thin film.

Asymptotic study of film thinning process on a spinning annular disk

We consider the axisymmetric flow of a Newtonian fluid associated with the spreading of a thin liquid film on a rotating annular disk. The effects of surface tension and gravity terms are included. The asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the thickness of the film and applying the method of matched asymptotic expansion. This solution can be used to calculate the thickness of the film, the velocity field, and the pressure at any point on the disk with good accuracy. Numerical results are presented for a specific initial distribution of the film thickness. Many features of the spin-coating thinning process are captured by our asymptotic solution. We also produce results which are in excellent agreement with the experimental findings of Daughton and Givens (6) and Hwang and Ma (9).

B. S. Dandapat

Papers

Asymptotic study of film thinning process on a spinning annular disk

Thin Liquid Film Flow on a Rotating Annular Disk: Asymptotic Solution