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Hydric properties evolution during drying differs from one product to another and has been the subject of various studies due to its crucial importance in modeling the drying process. The variation of these parameters in the solid matrix and in time during the drying of
*Spirulina platensis* has not known an advanced understanding. The objective of this study was to evaluate the evolution of the water content profile, the mass flow, the concentration gradient and the diffusion coefficient during the drying of
*Spirulina platensis* taking into account the shrinkage. Modeling and experimental analysis (at 50°C and HR = 6%) by the cutting method a cylinder 20 mm in diameter and 40 mm thick were carried. The water content profiles of two different products grown in semi-industrial farms from Burkina Faso and France with initial water contents respectively of the range from 2.73 kg
_{w}/kg
_{db} and 3.12 kg
_{w}/kg
_{db} were determined. These profiles have been adjusted by a polynomial function. Identical water behavior is observed regardless of the origin of the samples. Water distribution is heterogeneous. Mass flow and concentration gradient are greater at the edge than inside the product. The water transport coefficient, ranging from 1.70 × 10
^{−10} to 94 × 10
^{−10} m
^{2}/s, is determined from a linear approach.

In many countries of sub-Saharan Africa, food imports absorbe for a large proportion of national income. For example, in Burkina Faso, per capita food production is now lower than it was 40 years ago. Post-harvest losses related to the degradation of agro-food products contribute to the decline in agricultural productivity. Spirulina platensis, a nutritional and therapeutic seaweed, is used today for complementary food requirements [

Drying can make a significant contribution to sustainable agricultural development and improved food security by reducing post-harvest losses and improving the shape of dried produce and their nutritional quality. This process, which aims to strengthen the bonds of water molecules by reducing the latter, is one of the most used techniques to protect the product from degrading agents and to extend its conservation. In addition to stresses and cracks, the drying process often induces water density gradients in the solid matrix. The distribution of water in the solid matrix during drying differs from one product to another. Water is often trapped inside the structure by a crusting phenomenon that accelerates the product degradation. The hydrics properties evolution during drying differs from one product to another and has been the subject of various studies because of its crucial importance in the modeling of the drying process [

The diffusion of water in Spirulina platensis had already been approached experimentally by Desmorieux and Dissa [

The present study is divided into three parts. First, we will determine experimentally the water content profiles of the Spirulina platensis. Then we will evaluate the evolution of the mass flow and concentration gradient and establish a relationship between them. Finally, we will estimate the transport coefficient.

The materials used in this study are Spirulina platensis samples from two farm sites located in two different areas:

“Loumbila” farm situated at 15 km in the north of Ouagadougou, Burkina Faso. This material sample will be named sample-B,

“La Fon del Cardaire” farm situated at Gignac in the south of France. This material will be named sample-F.

Their mode of production is not different from one farm to another, from one country to another. These are the methods that change, adapted to the size of the farm, the workforce and the materials available on site. Indeed, the “sample-B” is grown in open ponds and the “sample-F” in glass ponds. However, if these two products were grown in localities with different climates, their seeding is done by strains of the same type “platensis” in basins whose salinity and alkalinity are provided by sodium bicarbonate (NaHCO_{3}). Pretreatments were carried out on each biomass harvested to remove a good part of the culture water until reaching a given water content. The methods pretreatment used is different from one farm to another depending on the available materials. Thus, the water content of the sample-B is reduced to about 2.73 kg_{w}/kg_{db} by manual pressing while that of the sample-F is reduced to about 3.12 kg_{w}/kg_{db} by a spin under the action of vacuum. These water contents obtained after pretreatment are considered as the water contents initial of the samples. The initial characteristic parameters recorded in _{s}.

First, the filtering of biomass through one or two devices superimposed. In general the first consists of a thin mesh of the order of 300 microns which retains any impurities (lumps, insects, leaves). The second is a filter in nylon is of the

Parameters | Symbol and units | sample-B | sample-F |
---|---|---|---|

Solid apparent density | ρ s [kg/m^{3}] | 284 | 255 |

Water apparent density | ρ w [kg/m^{3}] | 776 | 799 |

Solid real density | ρ s * [kg/m^{3}] | 1270 | 1270 |

Ratio of real densities | α […/…] | 0.787 | 0.787 |

Porosity | ϕ […/…] | 0.776 | 0.799 |

Water content | w [kg_{w}/kg_{db}] | 2.730 | 3.120 |

order of 50 μm. After filtering, fresh Spirulina platensis is processed into test-ready samples. A cylindrical shape commonly used in farms for the drying is proposed (_{0} = 0.013 ± 0.0006 kg.

It is assumed that these conditions are met and the samples are uniform in the initial state.

To understand experimentally the distribution of water in the product during drying, we chose to follow the variation of the water content in the product by cutting samples. The water content in a sample slice is determined by considering the mass of this slice at a given instant and that of the solid phase according to the following Equation (1):

w = m ( x , t ) − m s m s (1)

The experimental setup is constituted of a desiccator where the relative humidity is regulated at 6% by a potassium hydroxide KOH solution (

conditions as indicated above. The material being symmetrical, the water contents averages of symmetrical points with respect to the median plane are considered. This approach provides to access to the moisture content profiles w ( x , t ) corresponding to the drying times (

w ( x , t ) = a x 4 + b x 2 + c (2)

This expression ensures to have a symmetrical evolution with a no flux condition at the symmetry plane. The Experiments are carried out and lasted at most 120 hours (5 days). As it for a drying period long the material begins to stiffen and the cutting deviate delicate. For low temperature (less than 25˚C), the drying is too slow for reach values with low water content and the range of water content investigated is too narrow. It appears that for longer time period, the material starts to denature and the development of micro-organisms are observed. This could change the process of water transport and should be avoided.

Simplifying assumptions are considered to develop the descriptive equations of water transport: the material is assumed to remain diphasic along the experiment, the initial water content in the product is homogeneous, both solid and liquid phases are incompressible, water transport is one-dimensional along the cylindrical sample axis x.

The real mass densities are determined over intrinsic volume of water and solid phases:

ρ w * = m w V w ; ρ s * = m s V s (3)

The material being biphasic, the apparent densities are expressed by [

ρ w = ρ w * w α + w (4)

ρ s = ρ s * 1 α + w (5)

α = ρ w * / ρ s * is the ratio of real densities. Considering u w and u s as the water and solid phase velocities along x, mass balance equations are written [

∂ ρ w ∂ t + ∂ ρ w u w ∂ x = 0 (6)

∂ ρ s ∂ t + ∂ ρ s u s ∂ x = 0 (7)

The mass flow of water with respect to the solid phase is written as follows:

F w = ρ w ( u w − u s ) = ρ w u w − w ρ s u s (8)

For reasons of symmetry, u w ( 0 , t ) = u s ( 0 , t ) = 0 and from balance Equations (6)-(7), we obtain by integration the Equations (9) and (10):

ρ w u w ( x , t ) − ρ w u w ( 0 , t ) = ρ w u w ( x , t ) = − ∫ 0 x ∂ ρ w ∂ t d x (9)

ρ s u s ( x , t ) − ρ s u s ( 0 , t ) = ρ s u s ( x , t ) = − ∫ 0 x ∂ ρ s ∂ t d x (10)

By replacing the expressions 9 and 10 in Equation (8) and considering the Equations (8) and (9), the relation of the water flow becomes:

F w = ρ w * ( w ∫ 0 x ∂ ∂ t 1 α + w d x − ∫ 0 x ∂ ∂ t w α + w d x ) (11)

Deriving the Equation (4), the density gradient of the water is written:

G w = ρ w * ∂ ∂ x ( w α + w ) (12)

Fick’s law (Equation (13)) is a relationship that links the water flow to the mass concentration gradient through a phenomenological coefficient [

F w = − D w ∂ ρ w ∂ x (13)

In the case of geometry and boundary conditions used in experiments, radial water transport can be neglected so that water content is considered uniform in a cross-section at abscissa x. From relations 11 and 13, the water transport coefficient is accessed as a function of the water content.

D w = − F w G w (14)

The experimental determination of the water transport coefficient from the exploitation of the water content profiles is carried out as follows. For a particular time step t j and a given water content w k , the fitting of the associated water content profile (Equation (2)) can be inverted to give the corresponding abscissa x i . Knowing this abscissa, the values of the water flow (Equation (11)) and those of the water density gradient (Equation (12)) can be calculated. In fact, in

R 2 = 1 − ∑ z = 1 N ( Y e x p , z − Y p r e , z ) 2 ∑ z = 1 N ( Y ¯ e x p , z − Y p r e , z ) 2 (15)

R M S E = ∑ z = 1 N ( Y e x p , z − Y p r e , z ) 2 ∑ z = 1 N ( Y ¯ e x p , z − Y p r e , z ) 2 (16)

The experimental approach presented above made it possible to obtain a representative evolution of the water distribution inside of the two Spirulina platensis samples types studied (

Time | Parameters | |||
---|---|---|---|---|

t [h] | R^{2} | a | b | c |

0 | 0.989 | 2.733 | −33.826 | 17,144 |

6 | 0.991 | 2.586 | 625.540 | −8,407,669 |

21 | 0.990 | 2.336 | 101.345 | −9,839,223 |

31 | 0.995 | 2.227 | 463.387 | −14,987,570 |

46 | 0.988 | 2.092 | −513.382 | −14,835,938 |

51 | 0.992 | 2.047 | −487.359 | −16,330,653 |

68 | 0.997 | 1.925 | −2655.867 | −10,180,982 |

82 | 0.986 | 1.876 | −3533.390 | −6,610,475 |

102 | 0.987 | 1.672 | −4476.347 | −1,830,454 |

Time | Parameters | |||
---|---|---|---|---|

t [h] | R^{2} | a | b | c |

0 | 0.992 | 3.120 | −9.595 | 0.249 |

6 | 0.996 | 2.850 | 277.445 | −7688264.958 |

21 | 0.996 | 2.830 | −97.477 | −10526006.869 |

31 | 0.992 | 2.308 | −82.477 | −14114767.017 |

43 | 0.994 | 2.191 | −988.399 | −14460053.643 |

51 | 0.991 | 2.122 | −1882.984 | −12724621.226 |

70 | 0.995 | 1.997 | −2908.400 | −103330487.181 |

89 | 0.996 | 1.852 | −3885.733 | −5791090.036 |

120 | 0.997 | 1.586 | −3781.971 | −3583369.902 |

of the spirulina have been theoretically demonstrated for the alumina gel by Chemkhi (2008) [

In

From these profiles above, we have represented on the one hand the evolution of the water transport flow and that of density gradient at different thicknesses in the initial configuration of the sample ( x ≤ 16 mm) as function of time (

Decreasing curves indicate that the flow of water carried by filtration from the interior to the exchange surface is not compensated for in the pores. The main interest of the representation of the gradient as a function of time and as a function of the water content lies in the identification for each slice, a critical period and a critical water content (Figures 8(a)-(d)) to from which the contribution of the solid contraction to the transport of water becomes very negligible. We have just chosen to draw the curves of

In

homogeneous medium, the flow of the liquid phase can be described by a linear relation (Equation (13)).

From the water content profiles, density gradients and fluxes presented above, the range of water content that can be studied is 0.7 < w_{w} < 2.5 kg_{w}/kg_{dm}. That is, from a horizontal line intersecting at least two water content profiles. In this range, the water flow and the apparent density gradient of water are determined by Equations (11) and (12). For each water content value, a relatively linear correlation is observed between the water flow and the gradient. Therefore, the water transport coefficient is determined from the slope of each linear approximation. For both strains (sample-B and sample-F), the dependencies of the water transport coefficients with respect to the water content are presented in

therefore consider that the two results are representative of a single evolution of the water transport coefficient of Spirulina type platensis. Experimental data are accurately described by an exponential equation (Equation (17)).

D w ( w ) = 2.78 × 10 − 10 + 3.33 × 10 − 12 exp ( 3.12 w ) (17)

An optimization algorithm based on a nonlinear regression procedure made it possible to obtain a good correlation between the experimental data and those of the theory with a correlation coefficient R^{2} > 97% and a standard deviation RMSE < 1.16 × 10^{−10} m^{2}∙s^{−1}.

There is a sharp decrease in the transport coefficient for water contents above 2 kg_{w}/kg_{dm} and a low decrease for low water contents. This trend has already been observed with rubber [_{w}/kg_{dm} represents a critical mean value from which the contribution of solid shrinkage to water transport is negligible. In the case of Spiruline platenis, previous work [

This work enabled us to experimentally establish water content profiles during the one-dimensional drying process of Spirulina platensis by cutting samples. These profiles are then used to determine the influence of the water content on the mass flow, the water density gradient and the water transport coefficient that governs the internal phenomena. The distribution of water in the biomass is evaluated with the inclusion of the shrinkage along the cylindrical axis. The determined drying kinetics have similar profiles either in Sample-B or in Sample-F. It is shown that the proposed destructive method satisfactorily evaluates the evolution of the water content of Spirulina platensis over a wide range of water content.

The work carried out therefore provides a prospective tool that may be of interest for the local analysis of the water transport coefficient in other deformable materials. The development of a numerical model is necessary to compare the results and to predict the internal mechanisms during drying.

The authors declare no conflicts of interest regarding the publication of this pap.

Tiendrebeogo, E.S., Tubreoumya, G.C., Dissa, A.O., Compaoré, A., Koulidiati, J., Cherblanc, F., Bénet, J.-C. and Youm, I. (2019) Hydric Properties Evolution of Spirulina platensis during Drying: Experimental Analysis and Modelin. Food and Nutrition Sciences, 10, 516-577. https://doi.org/10.4236/fns.2019.106041

RH: relative humidity (%)

db: dry matter (kg_{w}/kg_{dm})

d: cylinder diameter

w: water content (kg/kg)

a w : water activity (/)

D w : transport coefficient (m2/s)

F w : mass water flux (kg∙m^{−2}∙s^{−1})

G w : gradient of water density (kg/m4)

m e q : equilibrium mass of sample (kg)

m i : sample initial mass (kg)

x: sample thickness (m)

m s : dry mass of sample (kg)

u s : velocity of the solid phase (m/s)

u w : velocity of the liquid phase (m/s)

N: number of observations

R 2 : correlation coefficient (%)

RMSE: root mean square error (kg/kg)

w e q : equilibrium moisture content (kg/kg)

Y: given drying parameter

m ( t ) : sample mass at a instant (kg)

Y p r e , j : the ith predicted value of Y

Y ¯ e x p , j : mean experimental value of Y

Y e x p , j : given drying parameter Y

Greek Letters

α : real densities ratio (/)

ρ s : solid apparent density (kg/m3)

ρ w : water apparent density (kg/m3)

ρ s * : solid real density (kg/m3)

ρ w * : water real density (kg/m3)

ϕ : porosity (/)

0: initial

Z: number counter of parameters

i, j: respectively abscissa and time counters

w, db: water, dry matter

eq: equilibrium

Exp: experimental

Pre: predicted

s: solid

1D: unidimensionnel