Capillary confinement selects the monolayer-to-multilayer transition in bacterial swarms: a theoretical model

Abstract Swarming bacterial populations commonly occupy partially hydrated surfaces fed from beneath agar, and many systems exhibit a spatial architecture in which the advancing edge remains approximately one cell thick while regions farther behind the front become multilayered. Existing explanations for escape from a bacterial monolayer emphasize growth-generated compression, local jamming, motility-induced clustering, and cell-substrate mechanics. Here we develop a complementary theoretical mechanism in which the liquid-air interface supplies a spatially varying vertical confinement. A cell that sits on agar and is partially wetted by water from below creates a meniscus and experiences a normal capillary force. We combine the capillary scaling F cap ~ γd with a minimal spatial model for interfacial exposure and cell packing to define an extrusion number E, the ratio of active compressive stress to the sum of substrate and capillary restoring stresses. The monolayer is predicted to lose stability where E first reaches unity. For an illustrative Bacillus-scale parameter set, the model predicts a transition approximately 70 µm behind the leading edge. Parameter sweeps show that increasing surface tension widens the monolayer region, reducing edge interfacial exposure shifts the transition toward the edge, and increasing active stress likewise promotes earlier multilayering. These trends persist over alternative capillary exposure laws and under broad parameter uncertainty. The model does not claim experimental validation; rather, it identifies a quantitative, falsifiable mechanism that connects thin-film capillarity to a dimensional transition in active bacterial matter. Direct measurements of film thickness, surface tension, cell density, and the multilayer boundary provide clear tests of the theory.