# Critical Marangoni Number for Disappearance of Striations during Spin-Coating

## TL;DR

This study identifies a critical Marangoni number range (90–160) that determines when striations disappear during spin-coating processes.

## Contribution

The paper introduces a novel method to determine the critical Marangoni number for striation disappearance using numerical simulation and experimental observation.

## Key findings

- Striations decreased by 3 orders of magnitude when using an epoxy resin and diglyme solvent mixture.
- The critical Marangoni number range for striation disappearance was determined as Ma_c = 90–160.
- The decay of striations correlates with the Marangoni number falling below a subcritical threshold.

## Abstract

This study investigated the striations, which arise as
spoke-like
thickness undulations during the spin-coating process. It was found
that the striations, which once appeared, then disappeared when a
mixture of epoxy resin and diglyme solvent was used as the coating
fluid. The time-dependent wavelength spectrum was obtained by applying
short-time Fourier analysis to the optically measured spatiotemporal
thickness variation. The wavelength components corresponding to the
striations decreased by 3 orders of magnitude before and after the
decay. Under the hypothesis that striations are generated by the type
of solutal Marangoni-Bénard instability, the disappearance
of the striations can be regarded as the result of the Marangoni number
falling below the subcritical value for the occurrence of striations.
To determine the critical Marangoni number for the disappearance of
the instability, the transient Marangoni number Ma was predicted by a numerical simulation taking the thickness-thinning
due to centrifugal force and solvent evaporation into account, together
with the time evolution of the concentration distribution. The critical
Marangoni numbers were determined as values of numerically predicted Ma corresponding to the time when the experimentally observed
striations started to decay, and they were in the range of Ma
c = 90–160.