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Experiments find a rougher edge than the theory, and nobody knows what the theory leaves out.","posed_since":"","precise":"Model the contact line as an elastic line with long-range elasticity (elastic $\\mathrm{energy}\\sim \\mid k\\mid\\,\\mid h_k\\mid^2$ for a deformation $h_k$ of wavenumber $k$) in a random field of defects. Numerical simulations of this model give the roughness exponent at depinning $\\zeta = 0.388 \\pm 0.002$ (first-order renormalization-group estimate $1/3$), while experiments (liquid helium on cesium, water-glycerol mixtures on disordered surfaces) have reported values near 0.5. Identify what the model omits (nonlinear elasticity at large deformation, thermal activation, crossover or finite-size effects, viscous dissipation, or analysis artefacts) and show that the corrected model reproduces the measured $\\zeta$ and depinning exponents.","problem_ref":null,"references":"","settled_by":"An experiment on a surface with designed, characterized disorder that measures $\\zeta$ over a wide range of scales, matched by simulations of the line model with the same disorder and any added nonlinear elasticity or thermal effects.","status_note":"","title":"Why measured contact-line roughness exceeds the elastic-line model 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