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Coalescence of Printed Yield Stress Filaments in Direct Ink Writing

In direct ink writing (DIW), neighbouring filaments of yield-stress inks are deposited side-by-side and are expected to merge into smooth, mechanically robust structures. Unlike Newtonian filaments, coalescence can arrest in finite time, leaving a permanent, non-flat ridge set by the competition between capillarity and rheology. Here we study the coalescence of two printed yield-stress filaments, combining scaling theory for the arrested state, direct numerical simulations, and DIW experiments on Carbopol gels imaged by optical coherence tomography. In the viscoplastic limit, we predict and observe an approximately linear decrease of the final bridge height with plastocapillary number and a critical yield stress above which coalescence does not initiate. Simulations further show that elasticity becomes important at high plastocapillary number, enabling larger final bridge heights via a crossover from a rigid Herschel--Bulkley solid to a deformable Kelvin--Voigt response. Our findings provide a framework for predicting deposition profiles and, ultimately, for mitigating residual topography in DIW.