arXiv subjects

R. S. Hutton

Publications and source records attributed to R. S. Hutton.

3 recordsLinked to original sources

arXiv2026

A derivation of viscous thin film flow equations on curved surfaces

General equations are derived for slow viscous thin fluid film flows on curved surfaces through an extension of Leal's pedagogical approach, which leaves the characteristic velocity scale unspecified and employs a direct through-thickness integration of the continuity equation. The derivation neglects inertia, and includes gravitational, capillary, and Marangoni effects, the latter coupling the thickness dynamics to free-surface transport of a dilute, non-diffusing surfactant. The resulting general expression incorporates the leading order terms of each type, as well as additional terms that become leading order for nongeneric cases. A few examples are briefly presented and literature comparisons made. The importance of gradients in curvature is emphasized, and it is suggested that nondimensionalization of geometric features might lead to further useful generalizations. This relatively simple formulation is intended as a starting point for exploring interactions between geometry, gravity, and surface tension.

physics.flu-dyn↗

arXiv2026

A sequence of elastic patterns in a sheared bent sheet

We document a sequence of bifurcations and elastic patterns in sheared bent sheets of intermediate aspect ratio. The sheets undergo inversion of curvature through the passage of localized features, often in S-shaped pairs. Nested force-displacement hysteresis loops provide experimental evidence for snaking. Several mechanisms for coarsening and refinement of the patterns are observed, including splitting, merging, and escape through open boundaries. While most forces, including that required for full snap-through, scale with the length of the sheet, the initial drop in force upon pattern nucleation decreases rapidly with length.

cond-mat.soft↗

arXiv2023

Buckling mediated by mobile localized elastic excitations

Experiments reveal that structural transitions in thin sheets are mediated by the passage of transient and stable mobile localized elastic excitations. These ``crumples'' or ``d-cones'' nucleate, propagate, interact, annihilate, and escape. Much of the dynamics occurs on millisecond time scales. Nucleation sites correspond to regions where generators of the ideal unstretched surface converge. Additional stable intermediate states illustrate two forms of quasistatic inter-crumple interaction through ridges or valleys. These interactions create pairs from which extended patterns may be constructed in larger specimens. The onset of localized transient deformation with increasing sheet size is correlated with a characteristic stable crumple size, whose measured scaling with thickness is consistent with prior theory and experiment for localized elastic features in thin sheets. We offer a new theoretical justification of this scaling.

cond-mat.soft↗