# Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Nonthermal Pulsed Filamentary Microplasma Treatment Assisted by TE

#### 2.3. Drying

_{t}, m

_{0}, and m

_{e}are moisture content at any time t (kg water/kg dry matter), initial moisture content (kg water/kg dry matter), and equilibrium moisture content (kg water/kg dry matter), respectively. Thermodynamic methods for moisture analysis transfer are based on the concept of potential. Transfer potential is a function of the state of the system and is equal at all points of the system at equilibrium. The potential gradient determines the direction and transfer rate of the corresponding substance [18]. By analogy with heat transfer, in which thermodynamical methods of analysis are successfully applied, the concept of mass content is similar to heat content. Briefly, moisture potential determination was based on finding the mass content of the sample in contact with a reference sample, for which the maximum specific sorption mass content is equal to 100 units. Obtained moisture content of potato samples was transformed in to moisture potential using Luikov expression [18]:

_{m}is a material property termed “the specific moisture capacity” (kg of moisture/kg of dry matter °M) by Luikov [18]. The value of c

_{m}, is usually determined experimentally based on using a reference scale built on the hygroscopic properties of filter paper upon Equation (2) or can be taken from literature.

#### 2.4. Statistical Analysis

## 3. Theory

#### 3.1. Problem Definition

${\mathrm{K}}_{11}=\left({\mathrm{k}}_{\mathrm{q}}+\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{m}}\right)\mathsf{\delta}/{c}_{m}$ | ${\mathrm{K}}_{12}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{m}}\mathsf{\delta}/{c}_{m}$ | ${\mathrm{K}}_{13}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{p}}\mathsf{\delta}/{c}_{m}$ |

${\mathrm{K}}_{21}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{m}}\mathsf{\delta}/{c}_{m}$ | ${\mathrm{K}}_{22}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{m}}$ | ${\mathrm{K}}_{23}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{p}}$ |

${\mathrm{K}}_{31}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{p}}\mathsf{\delta}/{c}_{m}$ | ${\mathrm{K}}_{32}=\in {\mathsf{\lambda}\mathrm{k}}_{\mathrm{p}}$ | ${\mathrm{K}}_{33}=-\mathsf{\lambda}\left(1-\in \right){\mathrm{k}}_{\mathrm{p}}^{2}/{\mathrm{k}}_{\mathrm{m}}$ |

_{21}= K

_{12}; K

_{31}= K

_{13}and K

_{32}= K

_{23}.

#### 3.2. Boundary Conditions

_{m}is a convective coefficient of a mass transfer, kg/m

^{2}s; α

_{q}—convective coefficient of a heat transfer, W/m

^{2}K). Subscript “a” designates surrounding. The first term ${\mathrm{k}}_{\mathrm{q}}\frac{\partial \mathrm{T}}{\partial \mathrm{n}}$ in the Equation (12) is amount of heat passing into the body, the second j

_{q}and the third term [α

_{q}(T–T

_{a})] are heat, brought to a surface, and the last term α

_{m}λ (l − ϵ) (M − M

_{a})) is amount of heat spent in the course of phase transition of liquid.

#### 3.3. Finite Element Formulation

_{T}, C

_{M}, C

_{P}, K

_{11}, K

_{12}, K

_{13}, K

_{21}, K

_{22}, K

_{23}, K

_{31}, K

_{32}, K

_{33}, F

_{T}, F

_{M}and F

_{P,}are appropriate matrices corresponding to the temperature, moisture and pressure terms in Equations (6)–(8).

## 4. Results and Discussion

#### 4.1. Solution Method of a Coupled System of the Differential Equations

_{1}, x

_{2}, …, x

_{MaxX−1}(nodes of a space grid), for the temporary variable we also select a finite number of values τ

_{0}, τ

_{1}, …, τ

_{MaxT}(nodes of a temporary grid): i = 1, … MaxT; j = 1, … MaxX−1.

_{i,j}, m

_{i,j}, p

_{i,j}-nodes of a grid of a temperature, moist field and a field of pressure. Let us express t

_{i,j+1}of Equation (19) and the explicit scheme of a solution for three equations is as follows:

- Heat conductivity coefficient ${\mathrm{k}}_{\mathrm{q}}$ = 0.6 j/m·K·s, which can be defined from the literature [22];
- Heat capacity ${\mathrm{c}}_{\mathrm{q}}=1600\text{}$J/kg·K [24];
- Thermogradient coefficient δ for food products can be defined in the range of δ = 0.01–0.02 °M /K [15];
- Latent heat λ is a thermodynamic constant and has a value of λ = 2258 kJ/kg for water evaporation during drying [26];
- The m-basic moisture content is depending on relative humidity according to tables [25].

#### 4.2. Experimental Results

#### 4.3. Results of Numerical Modelling

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Traffano-Schiffo, M.V.; Tylewicz, U.; Castro-Giraldez, M.; Fito, P.J.; Ragni, L.; Dalla Rosa, M. Effect of pulsed electric fields pre-treatment on mass transport during the osmotic dehydration of organic kiwifruit. Innov. Food Sci. Emerg. Technol.
**2016**, 38, 243–251. [Google Scholar] [CrossRef] - Smith, K.C.; Weaver, J.C. Electrodiffusion of molecules in aqueous media: A robust, discretized description for electroporation and other transport phenomena. IEEE Trans. Biomed. Eng.
**2012**, 59, 1514–1522. [Google Scholar] [CrossRef] [PubMed] - Granot, Y.; Rubinsky, B. Mass transfer model for drug delivery in tissue cells with reversible electroporation. Int. J. Heat Mass Transf.
**2008**, 51, 5610–5616. [Google Scholar] [CrossRef] [PubMed] - Shorstkii, I.A. Evaluation of the effect of a pulsed electric discharge on the process of substance transfer in plant material at the initial moment of time. Universities proceedings. Food Technol.
**2019**, 2, 73–77. [Google Scholar] - Shorstkii, I.A.; Khudykov, D.A. Pulsed electric field pre-treatment efficiency analysis in processes of biomaterials drying. Vestnik VGUIT [Proc. VSUET]
**2018**, 80, 49–54. [Google Scholar] [CrossRef] - Wiktor, A.; Śledź, M.; Małgorzata, N.; Chudoba, T.; Witrowa-Rajchert, D. Pulsed Electric Field Pretreatment for Osmotic Dehydration of Apple Tissue: Experimental and Mathematical Modeling Studies. Dry. Technol. Int. J.
**2014**, 32, 408–417. [Google Scholar] [CrossRef] - Mahnič-Kalamiza, S.; Vorobiev, E. Dual-porosity model of liquid extraction by pressing from biological tissue modified by electroporation. J. Food Eng.
**2014**, 137, 76–87. [Google Scholar] [CrossRef] - Parniakov, O.; Bals, O.; Lebovka, N.; Vorobiev, E. Pulsed electric field assisted vacuum freeze-drying of apple tissue. Innov. Food Sci. Emerg. Technol.
**2016**, 35, 52–57. [Google Scholar] [CrossRef] - Won, Y.C.; Min, S.C.; Lee, D.U. Accelerated Drying and Improved Color Properties of Red Pepper by Pretreatment of Pulsed Electric Fields. Dry. Technol. Int. J.
**2015**, 33, 926–932. [Google Scholar] [CrossRef] - Pavlin, M.; Miklavcic, D. Theoretical and experimental analysis of conductivity, ion 1285 diffusion and molecular transport during cell electroporation—Relation between short-lived and long-lived pores. Bioelectrochemistry
**2008**, 74, 38–46. [Google Scholar] [CrossRef] [PubMed] - Bouzrara, H.; Vorobiev, E. Solid-liquid expression of cellular materials enhanced by pulsed electric field. Chem. Eng. Process.
**2003**, 42, 249–257. [Google Scholar] [CrossRef] - Lebovka, N.I.; Shynkaryk, N.V.; Vorobiev, E. Pulsed electric field enhanced drying of potato tissue. J. Food Eng.
**2007**, 78, 606–613. [Google Scholar] [CrossRef] - Liu, C.; Grimi, N.; Lebovka, N.; Vorobiev, E. Convective air, microwave, and combined drying of potato pre-treated by pulsed electric fields. Dry. Technol.
**2018**, 1–10. [Google Scholar] [CrossRef] - Zhang, X.L.; Zhong, C.S.; Mujumdar, A.S.; Yang, X.H.; Deng, L.Z.; Wang, J.; Xiao, H.W. Cold plasma pretreatment enhances drying kinetics and quality attributes of chili pepper (Capsicum annuum L.). J. Food Eng.
**2019**, 241, 51–57. [Google Scholar] [CrossRef] - Li, S.; Chen, S.; Han, F.; Xv, Y.; Sun, H.; Ma, Z.; Chen, J.; Wu, W. Development and Optimization of Cold Plasma Pretreatment for Drying on Corn Kernels. J. Food Sci.
**2019**, 84, 2181–2189. [Google Scholar] [CrossRef] [PubMed] - Khan, M.I.H.; Wellard, R.M.; Nagy, S.A.; Joardder, M.U.H.; Karim, M.A. Experimental investigation of bound and free water transport process during drying of hygroscopic food material. Int. J. Therm. Sci.
**2017**, 117, 266–273. [Google Scholar] [CrossRef] - Kudra, T.; Martynenko, A. Electrohydrodynamic drying: Theory and experimental validation. Dry. Technol.
**2019**. [Google Scholar] [CrossRef] - Lykov, A.V. Drying Theory; Energiya: Moscow, Russia, 1968. [Google Scholar]
- Kamangar, T.; Farsam, H. Composition of pistachio kernels of various Iranian origins. J. Food Sci.
**1997**, 42, 135–136. [Google Scholar] [CrossRef] - Shorstkii, I.; Mirshekarloo, M.S.; Koshevoi, E. Application of Pulsed Electric Field for Oil Extraction from Sunflower Seeds: Electrical Parameter Effects on Oil Yield. J. Food Process Eng.
**2017**, 40, e12281. [Google Scholar] [CrossRef] - Lykov, A.V.; Mihailov, Y.A. Heat and Mass Transfer Theory; Energiya: Moscow, Russia, 1963. [Google Scholar]
- Ginzburg, A.S. Thermophysical Characteristics of Foodstuffs and Food Materials; Food Industry: Moscow, Russia, 1975. [Google Scholar]
- Wu, Y. Effect of Pressure on Heat and Mass Transfer in Starch-based Food Systems. Ph.D. Thesis, University of Saskatchewan, Saskatoon, SK, Canada, 1997. [Google Scholar]
- Tsukada, T.; Sakai, N.; Hayakawa, K. Computerised model for strain-stress analysis of food undergoing simultaneous heat and mass transfer. J. Food Sci.
**1991**, 56, 1438–1445. [Google Scholar] [CrossRef] - Nikitina, L.M. Thermodynamic Parameters and Mass Transfer Coefficients in Moist Materials; Energiya: Moscow, Russia, 1968. [Google Scholar]
- Barron, R.F.; Nellis, G.F. Cryogenic Heat Transfer, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar] [CrossRef]

**Figure 1.**Experimental set-up used to provide nonthermal pulsed filamentary microplasma (NTPFM) treatment assisted by thermionic emission (TE) (

**a**); schematic visualization of treatment trajectory in a treatment cell (not to scale) (

**b**); and visualization of a NTPFM treatment process (

**c**).

**Figure 2.**Potato intact sample surface (

**a**); and potato sample after NTPFM treatment with drops of liquid on the surface after PEF treatment (

**b**) (not the same samples).

**Figure 4.**The schedule of an average on thickness of value of moisture content over time, according to the model (the continuous line) and an experiment (marker) for control samples (

**a**), and PEF-treated samples (

**b**).

**Figure 5.**Predicted temperature potential T (

**a**) and pressure potential P (

**b**) profile curves based on the specified kinetic coefficients for control and NTPFM-treated samples.

${\mathrm{k}}_{\mathrm{q}}$ = 0.6 J/m·K·s | δ = 0.02 °M/K |

${\mathrm{k}}_{\mathrm{m}}$ = 0.03 kg/ m·K·s | $\in $ = 0.1 |

${\mathrm{k}}_{\mathrm{p}}$ = 9 × 10^{−4} kg·m·K/s | ${\mathsf{\rho}}_{0}$ = 210 kg/m^{3} |

${\mathrm{c}}_{\mathrm{q}}=1600\text{}$J/kg·K | $\mathsf{\lambda}$ = 2.25 × 10^{6} J/kg |

c_{m} = 0.02 kg/kg·°M | ${\mathrm{c}}_{\mathrm{p}}$ = 0.8 × 10^{−3} kg/kg·K |

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**MDPI and ACS Style**

Shorstkii, I.; Koshevoi, E. Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice. *ChemEngineering* **2019**, *3*, 91.
https://doi.org/10.3390/chemengineering3040091

**AMA Style**

Shorstkii I, Koshevoi E. Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice. *ChemEngineering*. 2019; 3(4):91.
https://doi.org/10.3390/chemengineering3040091

**Chicago/Turabian Style**

Shorstkii, Ivan, and Evgeny Koshevoi. 2019. "Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice" *ChemEngineering* 3, no. 4: 91.
https://doi.org/10.3390/chemengineering3040091