Droplet spreading in a wedge: A route to fluid rheology for power-law liquids

TL;DR

This paper introduces a novel method to determine the rheological properties of power-law fluids by analyzing droplet spreading in a wedge, linking spreading dynamics to fluid rheology through a nonlinear diffusion model verified by experiments and simulations.

Contribution

It presents a new approach that infers fluid rheology from capillary spreading dynamics, bypassing traditional shear-based measurements, and establishes a direct relation between spreading exponents and rheological exponents.

Findings

Spreading dynamics follow anomalous diffusion with a power-law growth.

The diffusion exponent directly relates to the fluid's rheological exponent.

Experimental and simulation results confirm the theoretical relationship.

Abstract

Measuring the rheology of liquids typically requires precise control over shear rates and stresses. Here, we describe an alternative route for predicting the characteristic features of a power-law fluid by simply observing the capillary spreading dynamics of viscous droplets in a wedge-shaped geometry. In this confined setting, capillary and viscous forces interact to produce a spreading dynamics described by anomalous diffusion, a process where the front position grows as a power-law in time with an exponent that differs from the value $1/2$ found in classical diffusion. We derive a nonlinear diffusion equation that captures this behavior, and we show that the diffusion exponent is directly related to the rheological exponent of the fluid. We verify this relationship by using both experiments and simulations for different power-law fluids. As the predictions are independent from flow-specific details, this approach provides a robust tool for inferring rheological properties from the spreading dynamics.