Matematično modeliranje sočasne ekstrakcije in reakcije v mikrofluidnem sistemu

Rajšter, Sebastijan (author), Plazl, Igor (mentor)

Namen diplomskega dela je bil razviti matematični model, ki opisuje obnašanje dveh topljencev, ki med sabo reagirata, v svojih topilih. V obzir je bil vzet tudi produkt in obnašanje tega na podlagi difuzivnosti in porazdelitvenega koeficienta. Opisani so bili osnovni pojmi mikroreaktorjev, reakcije, ekstrakcije in matematičnega modeliranja. Delo zaobjame tudi računsko določitev difuzivnosti in porazdelitvenega koeficienta, prikaže pa tudi preprost primer modeliranja, kjer je obravnavan primer biotransformacije progesterona. Zapisan je tudi sistem Navier – Stokesovih enačb, s katerim lahko numerično pridemo do hitrostnega profila, ki je odvisen od dveh spremenljivk. Poglavitno sta bila v delu razvita dva matematična modela, vsak iz štirih diferencialnih enačb, s pripadajočimi robnimi pogoji, ki sistem opisujeta pod različnimi predpostavkami. Najprej je bil razvit model, ki predpostavlja netopnost enega reaktanta in produkta v topilu, kjer je topen drugi reaktant, drug model pa opisuje hitro reakcijo na medfazni površini, hkrati pa je hitrost fluida konstantna. Za slednjega je bil razvit tudi računalniški model v programu Wolfram Mathematica 12.1. Za numerični postopek je bila uporabljena metoda končnih razlik. Pri robnih pogojih dobimo dve možni rešitvi, prikazana pa je ena. Prvi model ni bil zapisan v računalniškem programu. Ker je diplomsko delo teoretične narave, modela oziroma rezultatov, ki so bili pridobljeni s pomočjo simulacije, ni moč ovrednotiti do te mere, da bi lahko z gotovostjo govorili o njegovi zanesljivosti. To lahko pomeni, da model ni pravilen ali pa je bila izbrana napačna rešitev pri robnih pogojih. Obstaja možnost, da je pravilen tudi prvi model. Brez eksperimentalnih podatkov, lahko le ugibamo o zanesljivosti modelov, najverjetneje pa sta pravilna oba, vendar vsak za svojo skupino reakcij, ki vsaj približno ustrezajo privzetim predpostavkam.

• Language: Slovenian
• Keywords: modeliranje, mikroreaktor, prenos snovi, ekstrakcija, reakcija
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Year: 2020
• PID: 20.500.12556/RUL-119511
• COBISS.SI-ID: 27991555
• Publication date in RUL: 09.09.2020

Secondary language

• Language: English
• Title: Mathematical Modelling of Simultaneous Extraction and Reaction in a Microfluidic System

Abstract

The aim of this bachelor’s thesis was to develop a mathematical model that describes the behaviour of two solutes, each in its own solvent. The two solutes react between each other and form a product, which was also taken into consideration regarding its diffusivity and its partition coefficient. Basic concepts of microreactors, reaction, extraction and mathematical modelling were described. The thesis also includes computational determination of the diffusivity and the partition coefficient and a simple example of modelling, where a biotransformation of progesterone was examined. A system of Navier – Stokes equations was written to help numerically determine the velocity profile in the future. The profile is determined by two variables. The main objective of this bachelor’s thesis was to develop two mathematical models with their boundary conditions. Each model consists of four partial differential equations. For each model some assumptions were made. The first model assumes that one solute and the product are not soluble in the solvent, which contains the other reactant. The second one describes a quick reaction on the phase border, where the product is formed, and velocity of the fluid is constant. A computer program in Wolfram Mathematica 12.1 was developed for the latter model. The numerical procedure was based on the finite-difference method. When dealing with the first pair of boundary conditions we can see that there are two possible solutions, but later only one is represented. The first model was not written in a computer program. The thesis is of theoretical nature, so there is no definitive way to determine the reliability of said model. This may mean that the model is far from correct or that we simply chose the wrong solution when dealing with boundary conditions. It is also possible that the first model is far more accurate, but there is no right answer without the experimental data. Most likely scenario is that both models are correct, but each is best suited for their own purposes and assumptions.

• Keywords: modelling, microreactor, mass transfer, extraction, reaction