# Directional Motion of Coalesced Viscous Droplets on Fibers with Wettability Gradients

## TL;DR

This study explores how oil droplets move directionally on fibers with wettability gradients, focusing on the effects of viscosity and droplet behavior.

## Contribution

A novel dynamic contact angle model combined with VOF simulations reveals how wettability gradients influence droplet migration and viscous dissipation.

## Key findings

- Droplets migrate directionally along wettability gradients, with higher gradients increasing migration velocity.
- Low viscosity droplets show oscillations during acceleration, while high viscosity droplets move smoothly due to energy dissipation.
- Normal strain dissipation accounts for about 63% of total viscous dissipation during droplet deformation.

## Abstract

The coalescence and directional migration dynamics of
oil droplets
on wettability gradient fibers were investigated based on the volume
of fluid (VOF) method combined with an improved dynamic contact angle
model. We clarified the effects of initial configuration, wettability
gradient, and liquid viscosity on droplet morphology, migration velocity
and viscous dissipation. The results indicate that after coalescence,
droplets migrate directionally along the wettability gradient, and
a larger gradient leads to a higher migration velocity. Low viscosity
droplets exhibit noticeable oscillations during acceleration, while
high viscosity droplets move more smoothly due to increased energy
dissipation. As viscosity increases from 0.024 Pa·s to 0.093
Pa·s, normal strain dissipation dominates the total viscous dissipation,
accounting for about 63% at the peak stage, corresponding to liquid
bridge formation and strong droplet deformation. The average sensitivity
of maximum velocity to viscosity is approximately 7.5%, with stronger
competition between driving and resistive forces in the low viscosity
regime and a transition to viscosity dominated behavior at higher
viscosities. A stronger wettability-driven force slightly weakens
the suppressive effect of viscous resistance and increases kinetic
energy conversion efficiency. These findings provide insight into
the migration dynamics of microdroplets driven by wettability gradients.