Trajectory across a Washboard Potential Field

Abstract Tilted washboard potentials, realized through acoustic, electric, or optical fields, provide a minimal model for driven transport in periodic energy landscapes. In this work, we develop a unified analytical framework describing particle dynamics in potentials inclined at arbitrary angles to an external flow. The system exhibits a well-defined transition between drift and locked regimes, governed by the ratio of potential to viscous drag forces. In the drift mode, the particle trajectory exhibits an intrinsically nonlinear oscillation with a finite mean slope, while the locked mode yields a straight trajectory along the externally applied potential node. The theory quantitatively reproduces previously reported experiments and establishes universal scaling for the drift-lock transition and particle separation. The universal scaling statement is understood within the stated dilute, overdamped, local-flow model. The exact phase analysis and the added validity criteria below specify where this interpretation applies. This work not only deepens the theoretical understanding of particle transport but also offers a framework for optimizing flow-based microsystem designs under low potential intensities and variable flow conditions.