Date of Award

2026

Degree Type

Open Access Dissertation

Degree Name

Engineering and Computational Mathematics Joint PhD with California State University Long Beach, PhD

Program

Institute of Mathematical Sciences

Advisor/Supervisor/Committee Chair

Joseph Kalman

Dissertation or Thesis Committee Member

Marina Chugunova

Dissertation or Thesis Committee Member

Ehsan Madadi-Kandjani

Dissertation or Thesis Committee Member

Ali Nadim

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2026 Preston David Silverstein

Keywords

Faraday waves, fluid dynamics, Oscillator flow, particle motion

Subject Categories

Engineering | Mathematics

Abstract

Resonant acoustic mixing (RAM) uses low frequency high acceleration oscillatory forcing to combine fluids, particles, and powders. Although progress has been in adjacent RAM fields, there are still gaps in understanding how Faraday surface instabilities affect momentum transport to the bulk fluid and particles therein. This work investigates the energy pathways that an oscillatory mixer has and connects surface deformation to bulk rotational flow and particle forcing. This study is conducted in three phases. In phase 1, a thermodynamic first- and second-law analysis couples the surface features with the scale of subsurface rotational features. Experimental surface measurements showed that for unstable accelerations (i.e., 15 and 20 g), the mean radius of surface curvature decreased, indicating the transfer of energy from surface energy, to surface kinetic energy, to subsurface rotational motion. The new rotational flow further disturbs the surface continuing the cycle. Phase 2 addresses the effects of Faraday waves on particle motion. The classic Womersley solution to Navier-Stokes was extended to treat the surface as a pressure pump. A theoretical analysis that connects the surface wave dynamics to the subsurface velocity distribution was completed. In the final phase, experimental measurements were made of particle motion under vertical oscillation and compared to the Maxey-Riley model of particle motion in a bulk viscous fluid. Both Womersley-style pressure pump model and rigid body model were examined for fluid velocity in the particle mode. The results of the Womersley solution with an effective wavenumber indicates the inclusion of the additional force from the surface-wave-generated pressure perturbation that more accurately describes the particle amplitude in-cycle, but had little affect on overall particle trajectory over many cycles. Additionally, the work being done by the surface on the particle was amplified for unstable accelerations, and suppressed for stable accelerations. The results of this study will enable a better fluid and particle model and equip industry RAM users with a deeper understanding of energy transfer mechanisms, allowing for more efficient system operation.

ISBN

9798247950905

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