Fluid Flow During Spin Coating

How the liquid really moves

At the heart of spin coating is fluid flow across a rotating surface. The substrate spins, and the liquid is driven radially outward from the center toward the edge. That outward motion is what spreads the coating and removes much of the excess liquid from the substrate. If that flow stays stable and symmetric, the process has a much better chance of producing a useful film. If it does not, the film usually shows that later.

How the liquid moves

The film is not moving as a rigid sheet. It is deforming continuously while it flows. Different parts of the liquid layer can move at different rates depending on their position in the film thickness, their distance from the center, and the evolving viscosity of the material. The film becomes thinner because liquid is redistributed outward and because some of the material is expelled from the substrate edge.

The math behind flow

For readers who want the physics stated more directly, spin coating flow can be described with a few simplified relationships. These equations are useful because they show the physical trends behind the process, even though they do not capture the full real-world coating behavior by themselves. They are not everyday recipe calculators. They are a way to understand why the liquid responds the way it does and why variables such as spin speed, viscosity, and film thickness matter.

The outward driving acceleration increases with angular speed and radius:

ar2r

Where:

  • ar = radial acceleration
  • ω = angular speed
  • r= radius from center

This helps explain why radial driving becomes stronger as spin speed rises and why the flow field changes from center to edge.

Viscosity resists deformation through shear in the film:

τ = μ du dz

where:

  • τ = shear stress
  • μ = dynamic viscosity
  • du = velocity gradient through the film thickness

 

This matters because the film is not moving as one rigid block. Motion changes through the film thickness, and viscosity resists that internal shear.

Viscosity resists deformation through shear in the film:

dh dt = – 2ρω2 h3

where:

  • h = film thickness
  • t = time
  • = rate of change of film thickness with time
  • ρ = fluid density
  • ω = angular speed
  • μ = dynamic viscosity

 

This is not the full real-world process, but it captures an important truth: higher spin speed drives stronger thinning, higher viscosity resists thinning, and thicker early films change much faster than thinner late films. Real spin coating becomes more complex because evaporation, wetting, material formulation, and system behavior all change the process while the liquid is still moving.

What resists flow

Viscosity and changing mobility

Fluid motion is resisted by viscosity. A lower-viscosity material responds more readily to rotation and redistributes more easily. A higher-viscosity material resists motion more strongly and may retain more thickness under the same nominal spin conditions. Boundary conditions matter too: the liquid near the substrate is constrained, while the top of the film is a free interface, so motion varies through the film thickness.

Lower Viscosity Material
Higher Viscosity Material
Redistributes more easily
Resists redistribution more strongly
Can respond faster to motion
Needs more controlled spreading conditions
Can level more readily early
May preserve unevenness earlier
Usually more sensitive to drying timing
Usually more sensitive to mobility limits

When flow breaks down

Where defects begin

Flow is not automatically stable. Instability can appear when the starting condition is asymmetric, when the liquid dries too quickly relative to how fast it levels, when the dispense introduces off-center loading or entrained air, or when the system itself introduces airflow imbalance or mechanical disturbance. The visible result may be streaks, thickness gradients, radial irregularities, or other non-uniform film behavior. At their core, these are usually disruptions to what should have been a symmetric radial flow field.

This is one of the most useful ways to read coating defects. A streak is often a flow history problem. A radial thickness pattern is often a symmetry problem. A non-uniform film is often a sign that the liquid did not redistribute cleanly while it still had the ability to move. That is why good flow should not be thought of as maximum flow. It should be thought of as controlled flow. The process does not just need strong outward motion. It needs the right motion under the right conditions.



Flow is only the beginning

Then follow the film

Fluid flow explains how the coating spreads and why it thins, but not how it eventually stops being able to move. The next page picks up there: how a mobile liquid film becomes a flow-limited film and eventually locks in.