A study on some thin film coating flow problems

We are living in electronic age and using electronic gadgets frequently in our daily life. Many of these gadgets are having hard disk, screen, electronic circuits etc. In manufacturing these gadgets, coating process is needed in many processing steps. Apart from this, coating on any surface / equipment is necessary to enhance its durability. Basically, in this process, we are covering any surface/ substrate by a thin liquid layer. A film of liquid can be developed over the surface in many ways e.g. spreading of liquid, spin coating, liquid flow on a stretching surface, spray coating, blade coating, thin film flow on an inclined plane etc. We have studied three types of coating flow problems; these are: (i) Spreading of a nonNewtonian liquid drop over any surface (ii) Thin film flow over a non-linear stretching sheet and (iii) Two-layer film flow on a rotating disk. The spreading of a drop of non-Newtonian liquid over horizontal solid and homogeneous rough substrates are analyzed theoretically in the case of complete wetting. Here, the energy based approach is applied to explain the capillary spreading process. In case of smooth solid surface, a relationship is derived between spreading rate and bottom radius of the drop which gives Tanner’s law in case of Newtonian liquid (n = 1). It is shown that spreading rate for shear thickening (n > 1) liquid is more than that of Newtonian liquid while shear thinning (n < 1) liquid is having slower rate than the later one. But, in many practical situations, substrates are rough. A theoretical model is developed for the spreading of a non-Newtonian liquid drop over a homogenous rough substrate ( scale of roughness is too small in comparison to the drop size ) in case of complete wetting. Here, it is shown that surface roughness enhances the spreading rate of a drop. Studies related with the development of thin viscous liquid film flow over a sheet due to non-linear stretching in the presence of uniform transverse magnetic field when the sheet is either in isothermal or in heated condition are presented. To trace the impact of magnetic field, evolution equation for the free surface is derived using the thin film approximation and it is solved numerically for both the cases. In first case, it is observed that the presence of uniform transverse magnetic field resists film thinning process for all types of stretching velocity and initial film profiles. In case of heated non-linear stretching sheet, we found that thermocapillary force enhances or reduces the film thinning rate according to direction of the temperature gradient. Also, we found that the film thinning pattern is not affected by presence of magnetic field, only it slows down the film thinning. We have tried to give physical explanations for the observed flow behaviors. Finally, we have tried to develop a model for two-layer coating on a rotating disk. Development of thin two-layer film over a uniformly rotating disk is studied analytically and numerically under the assumption of planar interface and free surface throughout the film thinning process. A similarity transformation is applied to transform the guiding NavierStokes equations into a set of coupled non-linear unsteady differential equations. The coupled partial differential equations are solved analytically for long time by using the method of asymptotic expansion. It is found that viscous force dominates over centrifugal force as time increases. Also, this flow problem is solved numerically for finite value of Reynolds number by using the finite difference technique. It is observed that the rate of film thickness varies at different time zone depending on the rate of rotational speed of the disk. A physical explanation is provided to justify this anomalous behavior. It is observed that, smaller thickness on the top layer enhance the initial rate of film thinning. But, the overall effect of density, viscosity and the initial film thickness ratio are found to be insensitive to the final film thickness at large time.