# Dip-coating of suspensions

## TL;DR

This study investigates the coating behavior of suspensions during plate withdrawal, revealing three regimes based on velocity and particle concentration, and extending the Landau-Levich law to suspensions with effective viscosity.

## Contribution

It provides a comprehensive experimental analysis of suspension coating regimes and extends the Landau-Levich law to account for suspension viscosity effects.

## Key findings

- Identified three distinct coating regimes depending on capillary number.
- Demonstrated that at high velocities, suspension film thickness follows Landau-Levich law with effective viscosity.
- Mapped the parameter space for different coating behaviors based on particle and fluid properties.

## Abstract

Withdrawing a plate from a suspension leads to the entrainment of a coating layer of fluid and particles on the solid surface. In this article, we study the Landau-Levich problem in the case of a suspension of non-Brownian particles at moderate volume fraction $10\% < \phi < 41\%$. We observe different regimes depending on the withdrawal velocity $U$, the volume fraction of the suspension $\phi$, and the diameter of the particles $2\,a$. Our results exhibit three coating regimes. (i) At small enough capillary number $Ca$, no particles are entrained, and only a liquid film coats the plate. (ii) At large capillary number, we observe that the thickness of the entrained film of suspension is captured by the Landau-Levich law using the effective viscosity of the suspension $\eta(\phi)$. (iii) At intermediate capillary numbers, the situation becomes more complicated with a heterogeneous coating on the substrate. We rationalize our experimental findings by providing the domain of existence of these three regimes as a function of the fluid and particles properties.