Abstract
The formation of Faraday waves in a liquid inside a cylindrical vessel under the influence of vertical vibration is studied. The stability thresholds and its mode decomposition are obtained using a linear stability analysis. The stability model is validated with a vibration experiment in a vertical vibration table. The Faraday instability threshold is found for accelerations ranging from 0.1 to 1.0 times the gravitational acceleration. The confinement effect by the vessel introduces cut-off the low frequency modes and the allowed frequencies are discretized. The resulting acceleration stability threshold is high at low frequencies and it is the lowest at medium frequencies, , where the discretization of the mode -momenta introduces low stability regions delimited by more stable frequency ranges. The relevance of these characteristics for the agitation of liquids will be discussed.
Highlights
Understanding the sloshing of liquids inside vessels and preventing its negative effects is a problem that has occupied engineers for a long time
The resulting acceleration stability threshold is high at low frequencies and it is the lowest at medium frequencies, 10 – 70 HHHH, where the discretization of the mode kk-momenta introduces low stability regions delimited by more stable frequency ranges
The mode components of the Faraday instability have been calculated with a linear stability theory in a wide frequency range, ranging from 5 HHHH to 150 HHHH
Summary
Understanding the sloshing of liquids inside vessels and preventing its negative effects is a problem that has occupied engineers for a long time. The stabilization of the motion of fuel inside tanks has been a major design problem for jet planes and space rockets [1,2]. Another sort of problems arise from the agitation of biological or pharmaceutical liquid solutions inside vessels. Mechanical stress conditions, such as agitation during shipping, can result in denaturation and aggregation, thereby affecting the stability of the products profoundly [3,4,5]. One important aspect to understand the agitation of aqueous solutions is the stability threshold above which the free surface shows normal modes
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