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Moisture diffusion during soaking of palm kernel shell (
*Elaeis guineensis*) aggregate concerning DURA variety of Cameroon was studied. Parameters like percentage of water gain at the saturation point and the effective moisture diffusivity were the main purposes. The knowledge of the behavior of those shells in presence of the liquid during the realization of the composite materials is important. Gravimetric method with discontinuous control of the mass of sample after immersion at the ambient temperature was used. Palm kernel shell aggregate of two origins and two considerable sizes respectively in mm: Sizes ≥ 16 and 12.5 ≤ Sizes < 16 were used. The rate of water absorption was found to be [6.18% and 11.74%] respectively for Tombel PKS and Bafang PKS and moisture diffusivity of [5.19 × 10
^{-8} and 7.90 × 10
^{-9} m
^{2}/s] was also determined according to their irregular shapes by fitted soaking data in Becker’s model.

One of the successful methods to valorize green energies and fight against pollution is to transform agricultural biomass into raw materials. Cameroon is the third African country in oil palm production and the industrial and craftsmen transformation co-produce several residues among which we have palm kernel shell (PKS). The PKS has been regarded as waste from oil palm processing [

Palm kernel shells used in this investigation were obtained from the production areas of the west and south-west region of Cameroon. One variety of shell (DURA) is concerned, and it is characterized by the considerable volume of the shell. PKS aggregate,

1) Granulometric analysis

After measuring the mass of PKS aggregate, we pour it into a set of sieves arranged in descending order of fineness. Thereafter it is taken to the automatic sieves shaker D407 for 15 min to achieve complete classification. At the end of sieving operation, according to the pre-selected sieves we have recorded three different sizes respectively in (mm): 12.5 ≤ Sizes < 16; Sizes ≥ 16 and Sizes < 12.5. This last size was not significant for us to carry experimentation.

2) Gravimetric method

Samples were dried in a standard drying oven of mark Memmert model UN 160 at 105˚C for 6 hours, until the mass of the samples doesn’t vary any more [

By using Excel 2007 and Matlab R2014 b software with 95% rate of confidence, the solution of differential diffusion equation for arbitrary shapes provides by Becker was applied. The final mass is obtained when the mass of sample becomes constant. The duration of immersion is estimated about 28 days.

3) Percentage of water absorbed

The rate of absorption of water W compared to the dry matter of the samples is calculated starting from the drying mass M_{0} and the equilibrium mass M_{eq} according to Equation (1).

w ( % ) = M e q − M 0 M 0 ∗ 100 (1)

The instantaneous humidity content M(t) compared to the dry matter is computed by Equation (2).

M ( t ) = M t − M 0 M 0 (2)

where M_{0} and M_{t} are the mass at respectively initial time and the actual time.

In the literature several analytical models are proposed to describe the water diffusion kinetic of seeds and PKS can be ranged. Moisture ratio which is the equivalent without dimension of the instantaneous water content is given by Equation (3).

M R ( t ) = M t − M 0 M e q − M 0 (3)

The volume-surface area ratio (v/s) was calculated by dividing the equivalent volume of sphere by surface area of crushed palm kernel shell as

v s = 4 π r 3 3 s ⇒ v s = r 3 [ 4 π r 2 s ] (4)

where r is equivalent radius. The factor (4πr^{2}/s) is the ratio of equivalent surface area of a sphere of equal volume to the surface area of the crushed palm kernel shell, and can be denoted as sphericity ϕ . Substituting ϕ , Equation (4) gets reduced to

v s = r 3 ϕ ⇒ v s = d 6 ϕ (5)

where d is the equivalent diameter which can be expressed by a relationship as d = ( 6 v / π ) 1 / 3 from Equation (4). Substituting d, in Equation (5) and further simplifying, we get Equation (6) which describes the relationship between volume and surface area explicitly,

v s = [ 6 v π ] 1 / 3 ϕ 6 ⇒ v s = ϕ v 1 / 3 4.836 (6)

Similar expression has also been reported by [

ϕ = ( L B T ) 1 / 3 L (7)

where ϕ is sphericity; L the length, mm; B the breadth, mm; and T thickness, mm [

Spatial dimensions, viz. length, breadth and thickness of 150 units, were measured using digital vernier caliper with 0.05 mm accuracy. These are the dimensions along the longest axis, across the axis perpendicular to the longest in the horizontal direction, and across the third axis perpendicular to both the first and second axis. Sphericity was averaged from 150 crushed palm kernels shells. The mean volume of sample was obtained through Equation (8).

v = ∑ m / ρ n (8)

where m is the mass of sample, ρ the solid density of palm kernel shell and n the number of sample.

Moisture diffusion of a liquid in a solid is primarily caused by concentration gradient. This gradient tends to move the water molecules to equalize concentration. The diffusion coefficient is defined by Fick’s second law as Equation (9).

∂ c ∂ t = D e f f ( ∂ 2 c ∂ x 2 + ∂ 2 c ∂ y 2 + ∂ 2 c ∂ z 2 ) (9)

where, D_{eff} is the diffusivity coefficient; c is the concentration of diffusing substance at a point in solid; x, y and z are Cartesian coordinates of the point under consideration; and t is the diffusion time. It has been demonstrated that Equation (9) can be integrated approximately through Equation (10) for diffusion in solids of arbitrary shape to correlate the moisture gain during soaking in water [

c − c s c 0 − c s = 1 − 2 π X + B X 2 (10)

Subject to the following initial and boundary conditions

c = c 0 at t = 0 ,

c = c s at s = 0 and t > 0 ,

where s is a general coordinate with origin at bounding surface, c the average concentration, c_{s} the concentration at the bounding surface and c_{0} the initial concentration and t the diffusion time. After replacing the concentration term (c) by the moisture content (m) the equation can be rewritten as:

M R = M t − M e q M 0 − M e q = 1 − 2 π X + B X 2 (11)

where MR is moisture ratio. M_{t}, M_{0} and M_{eq} are average moisture contents at any given soaking duration, initial moisture content and moisture content at the equilibrium respectively. Equation (11) can be arranged by Equation (12) and Equation (13) as:

1 − M R = ( 2 / π ) X − B X 2 (12)

where,

X = ( s / v ) D t (13)

in which (s/v) is surface to volume ratio, D moisture diffusivity and t diffusion time. B is a parameter dependent of solid shape. Combining Equations (11)-(13), we get

M t − M 0 = α t − μ t (14)

where,

α = ( 2 / π ) ( M e q − M 0 ) ( s / v ) D (15)

and

μ = B ( M e q − M 0 ) ( s / v ) 2 D (16)

from Equation (15),

D = [ α π / { 2 ( M e q − M 0 ) ( s / v ) } ] 2 (17)

In Equation (17), M_{eq} and M_{0} are constants for a particular PKS sample and the ratio of volume-to-surface area (v/s) may be taken as constant irrespective of moisture content [_{eq} can be estimated by the method provided by [_{eq} and M_{0} do not vary for a particular sample of PKS in Equation (17), Equation (14) can be then rewritten as:

M t − M 0 = ( β − ω ) ( M e q − M 0 ) (18)

where,

β = ( 2 / π ) ( s / v ) D t ; ω = B ( s / v ) 2 ( D t ) (19)

In Equation (18) we can easily see that if the diffusion time t is kept constant, then the quantity ( M t − M 0 ) would be a linear function of M_{0} with a slope of ( β − ω ) with ω > β . On extending the plot to abscissa axis when ( M t − M 0 ) = 0, the intercept can be designated as moisture content M_{eq}.

After evaluating the percentage of water gain by PKS aggregate for the different sizes using Equation (1), the summary of the results for the various samples is illustrated in

We note that the percentage of water absorption of PKS aggregate of the two regions is approximately the same.

Water Absorption (d.b) (%) | |||
---|---|---|---|

Sample of size 12.5 ≤ S < 16 (mm) | |||

Sample N˚ | BAFANG | TOMBEL | |

1 | 20.76 | 18.27 | |

2 | 20.03 | 18.94 | |

3 | 20.57 | 19.27 | |

4 | 20.31 | 19.39 | |

5 | 20.59 | 19.93 | |

Average | 20.45 | 19.16 | |

S D | 0.28 | 0.61 | |

Sample of size S ≥ 16 (mm) | |||

1 | 16.16 | 17.60 | |

2 | 15.39 | 17.97 | |

3 | 16.49 | 17.49 | |

4 | 15.68 | 17.99 | |

5 | 15.97 | 18.97 | |

Average | 15.94 | 18.00 | |

S D | 0.42 | 0.58 | |

PKS final absorption | 18.20 | 18.58 | |

Types of materials | Water absorbed (%) | Soaking duration | T (˚C) | Ref | |
---|---|---|---|---|---|

Coconut nucifera | Speci 1: 17.32 | 35 Days | 23 | [ | |

Speci 2: 20.42 | |||||

Maize varieties | Abotem | 59.16 | 3.5 h to 8 h | (30 - 60) | [ |

Omankwa | 57.67 | ||||

Dorke | 61.11 | ||||

Akposoe | 64.83 | ||||

Abeleehi | 59.38 | ||||

Abrohemaa | 60.04 | ||||

Palm kernel shell | TO Speci: 18.58 | 28 Days | 23 | Case study | |

BA Speci: 18.20 |

Bafang PKS has slow rate for bigger particles compared to others and also has low absorption compared to Tombel PKS. This could be because of the microstructure of Bafang PKS with poor porosity and weak void index according to their geography zone of production.

The surface moisture content (M_{eq}) was evaluated to determine the moisture diffusivity using Equation (16). The experimental data of moisture gain in PKS for a soaking time of 150 min were plotted against diverse initial moisture contents of PKS ranging from 0.045 to 0.07 g/g (db) for Tombel and 0.098 to 0.139 g/g (db) for Bafang at ambient water soaking temperatures as shown in

For Tombel PKS, M_{eq} was 0.092 g/g and 0.082 g/g at ambient temperature and For Bafang PKS, M_{eq} was 0.18 g/g and 0.143 g/g respectively for the two different sizes. Coefficients of soaking curves were determined from

PKS Bafang | PKS Tombel | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Size | N˚ | M_{eq}_{ } (g/g) | (α) (×10^{−2}) | (µ) (×10^{−3}) | R^{2} | RMSE | N˚ | M_{eq} (g/g) | (α) (×10^{−2}) | (µ) (×10^{−3}) | R^{2} | RMSE |

12.5 To <16 | 1 | 0.18 | 1.191 | 0.562 | 0.969 | 0.0024 | 1 | 0.092 | 1.387 | 0.5951 | 0.983 | 0.0022 |

2 | 2 | |||||||||||

3 | 3 | |||||||||||

4 | 4 | |||||||||||

5 | 5 | |||||||||||

S ≥ 16 | 1 | 0.143 | 0.4627 | 0.2068 | 0.930 | 0.0013 | 1 | 0.082 | 1.051 | 0.4584 | 0.984 | 0.0015 |

2 | 2 | |||||||||||

3 | 3 | |||||||||||

4 | 4 | |||||||||||

5 | 5 | |||||||||||

Average | 0.1615 | 0.8268 | 0.3844 | 0.955 | 0.0018 | Average | 0.087 | 1.219 | 0.5267 | 0.9835 | 0.0018 |

Sphericity of PKS aggregate was computed from [

To determine the different moisture diffusivity, we used Becker’s Model [

By looking at the different values presented in

Palm kernel shell aggregate of Cameroon dried in oven to obtain initial moisture content within the interval of [6.18%; 11.74%] was studied with an objective to assess the effective coefficient of diffusion through the phenomenon of water absorption by the shells. Samples were immersed in the distilled water at the ambient temperature of 23˚C and total moisture equilibrium balance of samples is reached after a period of approximately 28 days in water. The rate of water

PKS Bafang | PKS Tombel | |||
---|---|---|---|---|

Size | N˚ | D eff (cm^{2}/s) Average value | N˚ | D eff (cm^{2}/s) Average value |

12.5 To <16 | 1 | 8.76 × 10^{−5} | 1 | 4.94 × 10^{−4 } |

2 | 2 | |||

3 | 3 | |||

4 | 4 | |||

5 | 5 | |||

S ≥ 16 | 1 | 7.04 × 10^{−5} | 1 | 5.45 × 10^{−4} |

2 | 2 | |||

3 | 3 | |||

4 | 4 | |||

5 | 5 | |||

Average | 7.90 × 10^{−5} | Average | 5.19 × 10^{−4} |

Materials | Temp (23˚C) | D_{eff} (m^{2}/s) | Ref | |
---|---|---|---|---|

Initial phase | Final phase | |||

Coconut shell Specie 1 | 1.10 ± 0.23 × 10^{−10}^{ } | 1.90 ± 0.35 × 10^{−12}^{ } | [ | |

Coconut shell Specie 2 | 1.04 ± 0.21 × 10^{−10}^{ } | 2.08 ± 0.31 × 10^{−12}^{ } | ||

Afra wood | 1.38 × 10^{−3} | [ | ||

Ojamlesh wood | 3.71 × 10^{−4} | |||

Roosi wood | 4.88 × 10^{−4} | |||

Date pits | 9.98 × 10^{−12} | [ | ||

Rice grain | 7 × 10^{−10} | [ | ||

Pasta | 5.69 × 10^{−11 } | 4.20 × 10^{−11 } | [ | |

Raphia vinifera fibre | (7.12 × 10^{−11} - 2.36 × 10^{−10}) | (2.87 × 10^{−14} - 6.73 × 10^{−14}) | [ | |

Okra fibre | 5.40 × 10^{−10} | [ | ||

Betel nut fibre | 2.80 × 10^{−10} | [ | ||

Jute fiber | 2.33 × 10^{−12 } | 2.30 × 10^{−13 } | [ | |

flax fiber | 2.11 × 10^{−12 } | 2.11 × 10^{−13 } | ||

fiber of sisal | 4.00 × 10^{−12 } | 4.38 × 10^{−13 } | ||

PKS Tombel | 5.19 × 10^{−8} | Present work | ||

PKS Bafang | 7.90 × 10^{−9} |

absorption percentage is found to be 18.20% and 18.58% respectively for Bafang and Tombel PKS aggregate. Experimental moisture gain following Becker’s equation with the square root of soaking time of 150 min has been plotted. Moisture diffusivity of 5.19 × 10^{−8} and 7.90 × 10^{−9} m^{2}/s was respectively determined for Tombel and Bafang PKS.

The knowledge of moisture diffusion phenomenon through PKS allows mastering the behaviour of composite in their elaboration process, above all total liquid soil that can influence cohesion energies within composite material.

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ndapeu, D., Yagueka, J.B.K., Tamwo, F., Koungang, B.M.G., Fogue, M. and Njeugna, E. (2020) Experimental and Analytical Study of Water Diffusion in Palm Kernel Shell of Cameroon. Materials Sciences and Applications, 11, 733-743. https://doi.org/10.4236/msa.2020.1111049