The effects of inertia and interfacial shear on film flow on a rotating disk

Abstract

In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self-similar form are solved numerically by a finite-difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start-up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.

Dynamics of polymer film formation during spin coating

“…5(a) shows the axial velocities V RBD and V SE , which continuously decrease until a minimum is reached, and then they increase to zero in around two thirds of the time needed for the film to dry. This is in agreement with previous work, 6 where the modeling of the vertical velocity showed a rapid acceleration followed by a gradual deceleration. (The velocities in Fig.…”

“…The discrepancy between the Meyerhofer model and the experimental data is due to the Meyerhofer model not accounting for the initial acceleration of the fluid and therefore overestimating the radial outflow, as has been reported elsewhere. 6 In accordance with the improvement of the fits observed for thickness profiles with the RBD model in the presence of vapor, V SE and V RBD are indistinguishable at the highest partial pressure measured (Fig. 5(a)).…”

“…Other experiments were performed which showed that when the overlaying layer is filled with a gas, interfacial shear increases the thinning rate. 6 Because spin coating is a rapid process, much of the work performed to date on its dynamics is purely theoretical. This is due to the paucity of suitable in situ techniques to measure the film thickness.…”

Thermocapillary flow of thin Cu-water nanoliquid film during spin coating process

“…The value of Prandtl number Pr % 6:8 for the base liquid water is obtained using the definition of Prandtl number and thermophysical properties of water (see , Table 1) along with l f ¼ 1 Â 10 À3 Pa s at 20 C. The results presented in Figs. 4,5,6,7,8,9,10,11,12 are based on the thermal conductivity model predicted by the Maxwell [46] and in rest of the figures we have considered the effective thermal conductivity model given by Yu and Choi [47]. Figure 4 shows variation of the film thickness H with time t for different values of the nanoparticle volume fraction /.…”

“…The full Navier-Stoke equations for unsteady film development was first considered by Higgins [9] to study the flow problem from the initial stage of film development through the match asymptotic analysis. Later, Rehg and Higgins [10] obtained the numerical solution of transient film flow on a rotating disk for large value of Reynolds number and different spin-up protocols. Dandapat and Ray [11,12] investigated the effects of heating/cooling on thin liquid film development over a rotating disk in presence of the thermocapillarity at the free surface and found that the film thins faster due to thermocapillary effect for the cooling of the disk.…”