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# Graduate Thesis of Yolanda Vásquez

ProgramPhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción
Enrollment Year2017
Senior Year2022
Thesis TitleConservation laws with discontinuous flux modeling flotation columns

#### Thesis Summary:

In this thesis, a newly developed dynamic one-dimensional model formulated in terms of PDEs is used to predict the process of simultaneous flotation of bubbles and sedimentation of particles that are not attached to bubbles. The governing model is a triangular system of conservation laws for the primary phase (aggregates, bubbles with particles attached) and secondary phase (solids) volume fractions as functions of height and time. The thesis has the following objectives. The first objective of this thesis is to demonstrate that the model and numerical scheme provide a tool for the simulation of the operation of a flotation column in the case of a common feed inlet of the three phases and when no aggregation occurs in the column. In particular, responses of the unit to changes in operating conditions such as changes in the rates and composition of feed flows as well as transitions between operating conditions are illustrated. The second objective of this thesis is to show applications of the model and numerical scheme to the wastewater treatment industry and identify desired steady states for the dissolved air flotation application analyzing the non-linear ingredients of the governing equations. The third objective of this thesis is to generalize the triangular system of conservation laws and show that the numerical scheme is monotone and satisfies an invariant-region property, i.e., the volume fractions of the three phases stay between zero and one. The fourth objective of this thesis is to demonstrate that the numerical scheme for the primary and secondary phases converge to a solution under certain simplifying assumptions. The fifth goal of this thesis is to extend the one-dimensional hyperbolic model of the hydrody- namics of a flotation column into one that include capillarity, which means that the governing PDE is of parabolic type in the froth region, whereas it is hyperbolic in regions without froth.

Thesis Director(s) Raimund Bürger, Stefan Diehl, María del Carmen Martí
Thesis Project Approval Date2019, May 03
Thesis Defense Date2022, June 30
Professional Monitoring

#### ISI Publications from the Thesis

Raimund BüRGER, Stefan DIEHL, María Carmen MARTí, Yolanda VáSQUEZ: A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows. Networks and Heterogeneous Media, vol. 18, no. 1, pp. 140-190, (2023).

Raimund BüRGER, Stefan DIEHL, María Carmen MARTí, Yolanda VáSQUEZ: A degenerating convection-diffusion system modelling froth flotation with drainage. IMA Journal of Applied Mathematics, vol. 87, pp. 1151-1190, (2022).

Raimund BüRGER, Stefan DIEHL, María Carmen MARTí, Yolanda VáSQUEZ: Flotation with sedimentation: Steady states and numerical simulation of transient operation. Minerals Engineering, vol. 157, Art. Num. 106419 (18pp), (2020).

Raimund BüRGER, Stefan DIEHL, María Carmen MARTí, Yolanda VáSQUEZ: Simulation and control of dissolved air flotation and column froth flotation with simultaneous sedimentation. Water Science and Technology, vol. 81, 8, pp. 1723-1732, (2020).

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