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Accessible Unlicensed Requires Authentication Published by De Gruyter August 26, 2015

Pectin Extraction from Mango Peels in Batch Reactor: Dynamic One-Dimensional Modeling and Lattice Boltzmann Simulation

Ricardo Durán, Aída L. Villa, Rogers Ribeiro and José A. Rabi

Abstract

A dynamic one-dimensional model accounting for pectin generation from protopectin in the solid matrix of mango peels and its degradation in both interstitial and extra-particle (i.e. reactor-filling) acid solution is proposed. The model assumes that pectin diffusive transport occurs in the interstitial fluid while eventual diffusive, thermal and pH influences in the solid phase were lumped into the kinetic coefficient of protopectin-pectin conversion. First-order kinetic was assumed to pectin degradation. Differential equations were numerically solved by adapting an in-house simulator of bioprocesses via the lattice Boltzmann method (LBM). As part of the LBM method, particle distribution functions were assigned to the pectin concentration in interstitial and reactor-filling fluid as well as assigned to the protopectin concentration in the solid phase. Equilibrium distribution functions were adopted by considering stationary solid phase, diffusive transport in interstitial fluid, and no spatial dependence in the reactor-filling fluid. Model parameters were assessed by comparing numerically simulated extraction yield curves with existing experimental data of pectin extraction using a batch reactor under either conventional or microwave heating. While the expected behavior of extraction yield curves was fairly reproduced in LBM simulations, discrepancies with respect to the experimental data can be assigned to assumptions in this preliminary model (e.g. first-order degradation kinetic and/or lumping effects into the protopectin-to-pectin kinetic). Prospective influence of slab thickness on extraction yields was also examined in LBM simulations.

Funding statement: Funding: Authors acknowledge the financial support from Colciencias, SENA and Universidad de Antioquia (UdeA) through project 1115-479-22043 and from UdeA through “Estrategia de Sostenibilidad 2013-2014”. R.D. acknowledges to Universidad Popular del Cesar, Colciencias and Gobernación del Cesar, his doctoral fellowship.

Nomenclature

Aslab

surface area of peel slab for pectin transfer to reactor-filling fluid (m2)

c

particle velocities for lattice Boltzmann method (m s−1)

cpf

pectin concentration in interstitial fluid (kg m−3)

cpp

protopectin concentration in solid phase (kg m−3)

cpr

pectin concentration in reactor-filling fluid (kg m−3)

Dpf

pectin diffusivity in interstitial fluid (m2 · s−1)

f

particle distribution function (units depend on the model framework)

j0

mass (pectin) flux from peel bottom surface to reactor-filling fluid (kg m−2 s−1)

jL

mass (pectin) flux from peel top surface to reactor-filling fluid (kg m−2 s−1)

kd

kinetic coefficient of pectin degradation (s−1)

km

mass (pectin) transfer coefficient from interstitial to reactor-filling fluid (m · s−1)

kp

kinetic coefficient of protopectin-to-pectin conversion (s−1)

L

mango peel thickness (m)

Nslabs

number of peel slabs uniformly filling up the reactor volume (dimensionless)

r˙pd

instantaneous rate of pectin degradation (kg m–3 s–1)

r˙pp

instantaneous rate of protopectin-to-pectin conversion (kg m–3 s–1)

r˙pr

instantaneous rate of pectin (net) accumulation in reactor-filling fluid (kg m–3 s–1)

t

time (s)

Vrf

reactor volume occupied by the fluid phase (m3)

w

weighting factors for lattice Boltzmann method (dimensionless)

z

axial position within the peel slab (m)

Greek symbols
ε

mango peel porosity (dimensionless)

τ

relaxation time (s)

ω

relaxation parameter (dimensionless)

Subscripts and superscripts
0

referring to initial condition

1

referring to forward streaming

2

referring to backward streaming

eq

referring to particle distribution function at equilibrium

k

referring to streaming directions

pf

referring to pectin in interstitial fluid phase

pp

referring to protopectin in solid phase

pr

referring to pectin in reactor-filling fluid phase

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Published Online: 2015-8-26
Published in Print: 2015-9-1

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