\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{A new perspective on vegetable oil epoxidation modeling: reaction and
mass transfer in a liquid-liquid-solid system}



\author[1]{Tapio Salmi}%
\author[2]{Vincenzo Russo}%
\author[1]{Adriana Aguilera}%
\author[1]{Pasi Tolvanen}%
\author[1]{Johan Wärnå}%
\author[2]{Martino Di Serio}%
\author[2]{Riccardo Tesser}%
\author[2]{Tommaso Cogliano}%
\author[3]{Sebastien Leveneur}%
\author[1]{Kari Eränen}%
\affil[1]{Abo Akademi}%
\affil[2]{University of Naples Federico II}%
\affil[3]{INSA de Rouen-LSPC}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
A rigorous mathematical model was developed for a complex
liquid-liquid-solid system in a batch reactor. The approach is general
but particularly well applicable for the indirect epoxidation of
vegetable oils according to the concept of N. Prileschajew. The model
considers intra- and interfacial mass transfer effects coupled to the
reaction kinetics. The liquid phases were described with chemical
approach (aqueous phase) and a reaction-diffusion approach (oil phase).
The oil droplets were treated as rigid spheres, in which the overall
reaction rate is influenced by chemical reactions and molecular
diffusion phenomena. The model was tested with a generic example, where
two reactions proceeded simultaneously in the aqueous and oil phases.
The example (i.e. fatty acid epoxidation \selectlanguage{ngerman}à la Prileschajew) illustrated
the power of the real multiphase model in epoxidation processes. The
proposed modelling concept can be used for optimization purposes for
many applications, which comprise a complex water-oil-solid catalyst
system.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{Hosted file}

\verb`Manuscript.docx`  available at \url{https://authorea.com/users/425054/articles/529973-a-new-perspective-on-vegetable-oil-epoxidation-modeling-reaction-and-mass-transfer-in-a-liquid-liquid-solid-system}

\selectlanguage{english}
\FloatBarrier
\end{document}

