Trapped modes around freely floating bodies in a two-layer fluid channel
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Updated: Apr 22, 2026

A Microfluidic-based Hydrodynamic Trap for Single Particles
Published on: January 21, 2011
Filipe S Cal1, Gonçalo A S Dias1, Juha H Videman1
1CAMGSD/Departamento de Matemática , Instituto Superior Técnico, Universidade de Lisboa , Avenida Rovisco Pais, 1049-001 Lisboa, Portugal.
Abstract:
Unlike the trapping of time-harmonic water waves by fixed obstacles, the oscillation of freely floating structures gives rise to a complex nonlinear spectral problem. Still, through a convenient elimination scheme the system simplifies to a linear spectral problem for a self-adjoint operator in a Hilbert space. Under symmetry assumptions on the geometry of the fluid domain, we present conditions guaranteeing the existence of trapped modes in a two-layer fluid channel. Numerous examples of floating bodies supporting trapped modes are given.
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