Static behavior and classification of shear-thinning droplets on inclined hydrophobic substrates

This study presents a comprehensive investigation into the static behavior and shape evolution of shear-thinning liquid droplets compared to Newtonian droplets when gently deposited on a rigid substrate. The manner of droplet placement significantly influences the resulting equilibrium shape, with these effects becoming more pronounced when the droplet is placed on an inclined surface due to the action of gravitational tangential forces. A mathematical analysis highlights that the shear stress within a hemispherical droplet varies along its height when placed on an inclined substrate, leading to asymmetrical deformation and resulting in macroscopic contact angle hysteresis (CAH). Experimental observations reveal that this deformation is notably different for shear-thinning liquids compared to Newtonian ones. Shear-thinning droplets demonstrate a more compact and deformable shape, exhibiting up to 20.12% shorter base length (L) and 12.5% greater height (H) than Newtonian droplets. These geometric differences contribute to a significantly higher CAH, up to 115.68% greater, which enhances the droplet's ability to resist motion and increases its retention on the surface. Retained volumes of shear-thinning droplets were found to be 50%–350% greater than those of their Newtonian counterparts on the inclined polydimethylsiloxane-coated glass substrate. To quantify these differences, a novel dimensionless number, the droplet rheology classifier (DRC) number [DRC=H/L (cos θR−cos θF)], is introduced, capturing the combined effects of droplet geometry and macroscopic contact angle hysteresis. The DRC number is found to successfully classify sessile droplets placed on inclined substrates into shear-thinning and Newtonian populations. Building upon these distinct geometrical and wetting characteristics, this study demonstrates a novel classification approach using support vector machine (SVM) modeling. By training the SVM on geometric features extracted from side-view images of droplets placed on an inclined surface, the model effectively differentiates between Newtonian and shear-thinning fluids with 95% classification accuracy. This image-based, non-invasive technique offers promising potential for fluid classification in biomedical diagnostics, particularly for detecting diseases where changes in the rheology of biological fluids (e.g., blood, saliva, sputum) serve as key indicators of pathological conditions.