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\begin{minipage}{11.3cm} \vspace{-1cm} \vskip4truept \centerline \textsc{XIII Congreso del Máster en Investigación Matemática y del Doctorado en Matemáticas }
\vskip-4truept \centerline{\textbf{\small{Facultat de Ciències Matemàtiques, Universitat de València}}} 
\vskip-5truept \centerline{\textrm{\small 12 - 14 de Enero de 2026}} \vskip4truept\hrule \vspace{1cm}
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\title{\header \textbf{Modelamiento de una columna de flotación mediante leyes de conservación con flujo discontinuo}}

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\author{
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\textbf{MCarmen Martí Raga}%
\thanks{e-mail: \texttt{maria.c.marti@uv.es}}\\%
Departament de Matemàtiques, Universitat de València,\\ València, Spain
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\noindent Flotation is a unit operation that is extensively used in the recovery of valuable minerals and
coals in mineral processing and related applications. The theory of froth flotation is complex,
involving three phases (solids, water, and froth or gas) with many subprocesses. However, essentisal
insight to the hydrodynamics of a flotation column can be obtained by studying just two
phases: gas and fluid \cite{finchdobby,stev08}. In \cite{bdm2018}, the authors proposed a reformulation of the approach based on the drift-flux theory, as a one-dimensional non-linear conservation law with a multiply discontinuous flux: the unknown is the gas volume fraction as a function of height and time, and the flux function depends discontinuously on spatial position due to feed inlets for gas, feed slurry and wash water. The resulting model adds a new real-world
application to the field of conservation laws with discontinuous flux. Steady-state solutions were studied in detail, including their construction by applying appropriate entropy conditions across each flux discontinuity. This analysis leads to operating charts and tables collecting all possible steady states along with some necessary conditions for their feasibility in each case. Numerical experiments showed that the transient model recovers the steady states, depending on the feed rates of the different inlets.\\
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\noindent Trabajo conjunto con: \\
\textbf{Raimund Bürger}\footnote{e-mail: \texttt{rburger@ing-mat.udec.cl}},
CI$^{\mathrm{2}}$MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile.\\
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\textbf{Stefan  Diehl}\footnote{e-mail: \texttt{stefan.diehl@math.lth.se}},
Centre for Mathematical Sciences, Lund University, Lund, Sweden.\\
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\bibitem{bdm2018} 
\textsc{Bürger, R.; Diehl, S.; Mart\'i, M.C.}, \textit{A conservation law with multiply discontinuous flux modelling a flotation column}, Netw. Heterog. Media {\bf 13(2)}, (2018), pp. 339-371. 

\bibitem{finchdobby} 
\textsc{Finch, J.A.; Dobby, G.S.}, \textit{Column Flotation}, Pergamon Press, London, 1990.  

\bibitem{stev08} 
\textsc{Stevenson, P.; Fennell, P.S.; Galvin, K.P.}, \textit{On the drift-flux analysis of flotation and foam fractionation processes}, Canad.\ J.\ Chem.\ Eng. {\bf 86}, (2008), pp. 635-642. 
  

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