Post-harvest of parsley leaves (<i>Petroselinum crispum</i>): Mathematical modelling of drying and sorption processes

Corrêa Filho, Luiz C.; Martinazzo, Ana P.; Teodoro, Carlos E. de S.; Andrade, Ednilton T. de

doi:10.1590/1807-1929/agriambi.v22n2p131-136

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ARTICLE • Rev. bras. eng. agríc. ambient. 22 (2) • Feb 2018 • https://doi.org/10.1590/1807-1929/agriambi.v22n2p131-136 copy

Post-harvest of parsley leaves (Petroselinum crispum): Mathematical modelling of drying and sorption processes

Pós-colheita de folhas de salsinha (Petroselinum crispum): Modelagem matemática dos processos de secagem e dessorção

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Parsley is a species of wide production and trade in Brazil due to its high consumption as a condiment, fresh or dried. In the development of equipment used for drying, it is important to simulate and obtain theoretical information about the behavior of water loss for each product. Given the increasing use and potential commercialization of condimental plants, the objective of this work was to determine the isosteric heat of parsley leaves and fit mathematical models to the experimental data obtained in drying and desorption processes. The modified GAB and Midilli models were the most appropriate to describe the desorption isotherms and drying curves, respectively, for the studied temperatures. The isosteric heat varied from 3394.6 to 2830.0 kJ kg^-1 for the equilibrium moisture content in the range from 0.0154 to 3.7232 (d.b.).

Key words:
spice plant; processing; isosteric heat

Designation	Model
Chung-Pfost	$X_{e} = a - b \cdot \ln [- (T + c) \cdot \ln (a_{w})]$	(1)
Copace	$X_{e} = e x p [a - (b \cdot T) + (c \cdot a_{w})]$	(2)
Modified GAB	$X e = \frac{a \cdot b \cdot (\frac{c}{T}) \cdot a_{w}}{\{[1 - b \cdot a_{w}] \cdot [1 - b \cdot a_{w} + b \cdot (\frac{c}{T}) \cdot a_{w}]\}}$	(3)
Modified Halsey	$X_{e} = {[\frac{e x p (a - b \cdot T)}{- \ln (a_{w})}]}^{\frac{1}{c}}$	(4)
Henderson	$X_{e} = {[\frac{\ln (1 - a_{w})}{- a \cdot} T_{a b s}]}^{\frac{1}{c}}$	(5)
Modified Henderson	$X_{e} = {\{\frac{\ln (1 - a_{w})}{[- a \cdot (T + b)]}\}}^{\frac{1}{c}}$	(6)
Sabbab	$X_{e} = a \cdot (\frac{a_{w}^{b}}{T^{c}})$	(7)
Sigma-Copace	$X_{e} = e x p [a - b \cdot T + c \cdot e x p (a_{w})]$	(8)
Oswin	$X_{e} = {\frac{(a - b \cdot T)}{[\frac{(1 - a_{w})}{a_{w}}]}}^{\frac{1}{c}}$	(9)
Corrêa	$X_{e} = \frac{1}{(a \cdot T^{b} + a_{w}^{c})}$	(10)

Designation	Model
Approximation of diffusion	$R X = a \cdot e x p (- k \cdot t) + (1 - a) \cdot e x p (- k \cdot b \cdot t)$	(17)
Two terms	$R X = a \cdot e x p (- k_{0} \cdot t) + b \cdot e x p (- k_{1} \cdot t)$	(18)
Two-term exponential	$R X = a \cdot e x p (- k \cdot t) + (1 - a) \cdot e x p (- k \cdot a \cdot t)$	(19)
Henderson-Pabis	$R X = a \cdot e x p (- k \cdot t)$	(20)
Modified Henderson-Pabis	$R X = a \cdot e x p (- k \cdot t) + b \cdot e x p (- k_{0} \cdot t) + c \cdot e x p (- k_{1} \cdot t)$	(21)
Logarithmic	$R X = a \cdot e x p (- k \cdot t) + b$	(22)
Midilli	$R X = a \cdot e x p (- k \cdot t^{n}) + b \cdot t$	(23)
Newton	$R X = e x p (- k \cdot t)$	(24)
Page	$R X = e x p (- k \cdot t^{n})$	(25)
Modified Page	$R X = e x p [- {(k \cdot t)}^{n}]$	(26)
Thompson	$R X = [\frac{- a - {(a^{2} + 4 \cdot b \cdot t)}^{\frac{1}{2}}}{2 \cdot b}]$	(27)
Verna	$R X = a \cdot e x p (- k \cdot t) + (1 - a) \cdot e x p (- k_{1} \cdot t)$	(28)
Wang-Sing	$R X = 1 + a \cdot t + b \cdot t^{2}$	(29)

Groups	Temp. (°C)	Model parameters
Groups	Temp. (°C)	a	b	K	N
1	40	1.0034	-0.0007	0.0908	0.8741
	50	0.9993	-0.0014	0.1350	0.8782
	60	0.9916	-0.0024	0.2377	0.8925
2	40	0.9981	-0.0008	0.1451	0.9058
	50	0.9986	-0.0014	0.1910	0.9495
	60	1.0009	-0.0033	0.2641	0.9501

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[1] lucaalbernaz@gmail.com (Corresponding author)