Uppsalator's acceleration

Abstract

Semiquantitative prediction of the Uppsalator (electroosmotical oscillator developed in Uppsala) under constant voltage is confirmed via numerical solution of exact nonlinear integro-differential equations in partial derivatives (PDE). Critical voltage and characteristic features of pressure and liquid flow velocity as functions of time are reproduced with high precision. In particular, the number of inflection points per period of oscillating velocity increases with growing voltage from two to six. A new feature is demonstrated. For sufficiently high voltages the Uppsalator shows normal deceleration, i.e., the oscillation period grows with voltage. However, in some supercritical range of voltages, acceleration is observed, as expressed by decrease of the oscillation period with growing voltage. Thus, the Uppsalator at constant voltage considered earlier as an impossible phenomenon represents a great challenge for experimental verification.