Spin coating of non-Newtonian fluids with a moving front

We investigate axisymmetric spin coating of power law and Ellis fluids. The flow is driven by centrifugal force, gravity and surface tension. For power law and Ellis models a single equation for the fluid film height is obtained. For a Newtonian fluid the flux only involves linear derivative terms which allows the flux to be easily split for a numerical scheme. For power law and Ellis models the derivatives appear as nonlinear terms. To overcome this we develop an alternative numerical scheme to solve for the film height. Neglecting surface tension and gravity the power law model shows a central spike which is reduced by the introduction of surface tension and gravity. In certain cases the shear thinning power law model predicts slower spreading than the Newtonian model. The Ellis fluid shows no central spike, even for zero surface tension and the film always spreads further than the Newtonian fluid.

Figure 1

Evolution of a Newtonian fluid with $B=0.017$, $C=8.9\times {10}^{-6}$.

Figure 2

Front wave with various rotation velocities at $t=20$.

Figure 3

Evolution of a power law fluid with $n=0.9$, $B=0.017$, $C=8.9\times {10}^{-6}$.

Figure 4

Center with various rotation velocities $n=0.9$, $t=20$.

Figure 5

Front wave with various rotation velocities $n=0.9$, $t=20$.

Figure 6

Profiles for various power law indices.

Figure 7

Evolution of an Ellis fluid with $\alpha =4∕3$, ${\tau }_{1∕2}=5\times {10}^{-4}$.

Figure 8

Profiles for various Ellis indices, ${\tau }_{1∕2}=5\times {10}^{-4}$.

Figure 9

Profiles for various models $n=0.75$, $\alpha =4∕3$.

Figure 10

Profiles for various models $n=0.5$, $\alpha =2$.