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The spreading of newtonian and shear-thinning droplets impacting on a flexible disk
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DOI：10.1016/j.jfluidstructs.2026.104540.png)
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Abstract
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Droplet impact on flexible surfaces is widespread in natural and industrial processes, yet the coupled effects of substrate flexibility and non-Newtonian fluid rheology on droplet spreading remain insufficiently understood. Here, we investigate the spreading dynamics of Newtonian and shear-thinning droplets impacting a flexible disk through numerical simulations based on the phase-field method. We first examine the maximum disk deflection and propose a scaling law that predicts it across both small-deformation and large-deformation regimes. For the maximum spreading factor, we show that substrate flexibility can either suppress or enhance spreading, depending on the competition between viscous dissipation and substrate energy absorption. To capture these competing mechanisms, we introduce effective Weber and Reynolds numbers that incorporate substrate deformation, resulting in a unified scaling law for the maximum spreading factor that accurately describes spreading on flexible disks. Furthermore, we extend this framework to shear-thinning fluids by incorporating an effective shear-rate model, enabling accurate prediction of the maximum spreading factor for shear-thinning droplets impacting flexible disks. The proposed models are validated against numerical simulations and exhibit strong predictive capability. This work provides new insights into the coupled influence of substrate flexibility and fluid rheology on droplet impact dynamics.
Keywords:
Droplet impact
Flow-structure interactions
Rheology
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