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(24)
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The mathematics of diffusion
The mathematics of diffusion,J. Crank
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The mathematics of diffusion
(
Citations: 6641
)
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J. Crank
Published in 1975.
Cumulative
Annual
Citation Context
(1423)
...The aforesaid macroscopic submodel is composed of a set of ordinary differential equations (ODEs) that can be solved by means of any conventional ODE solver; the microscopic submodel is a partial differential equation to which an analytical solution has been presented by Crank:
[
19
]
where
C
eq
is the moisture content of the grain when the time approaches infinity or: In fact,
C
eq
is equal to the first term of the right-hand side of Eq...
Morteza Golmohammadi
,
et al.
Optimization of Drying–Tempering Periods in a Paddy Rice Dryer
...The diffusion coefficient or diffusivity, a measure used to indicate the rate of tocopherol release from the film, was estimated using the following Fickian model derived using the initial and boundary conditions appropriate for this study (Crank
1975
): where
M
t
is amount of tocopherol in food simulant at time
t
;
M
∞
is the equilibrium amount of tocopherol in the food simulant (95% ethanol);
L
p
is film thickness (m);
D
is diffusivity (m
2
s
−1
); and
t
is time (s)...
X. Zhu
,
et al.
Release property and antioxidant effectiveness of tocopherol-incorpora...
...Assuming that the initial moisture distribution is uniform at t = 0 and the shrinkage of material does not significantly alter the product shape, the analytical solution of Fick's diffusion equation
[
22
]
for slab is given as ...
Madeneni Madhava Naidu
,
et al.
Effect of Drying Methods on the Quality Characteristics of Fenugreek (...
...Under these hypotheses, the amount of moisture loss of the chestnut is given (Crank,
1975
), where
D
is the apparent diffusivity and
X
∞
is the moisture loss when the final equilibrium is reached...
Lia-T. Dinis
,
et al.
Influence of the growing degree-days on chemical and technological pro...
...The third portion is attributed to the final equilibrium stage for which the intra-particle diffusion starts to slow down due to the extremely low adsorbate concentration left in the solution
[39]
...
N. Barka
,
et al.
Kinetics and equilibrium of cadmium removal from aqueous solutions by ...
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Citations
(6641)
Optimization of Drying–Tempering Periods in a Paddy Rice Dryer
(
Citations: 1
)
Morteza Golmohammadi
,
Mehdi Rajabi-Hamane
,
Seyed Jalaleddin Hashemi
Journal:
Drying Technology - DRY TECHNOL
, vol. 30, no. 1, pp. 106-113, 2012
Release property and antioxidant effectiveness of tocopherol-incorporated LDPE/PP blend films
(
Citations: 1
)
X. Zhu
,
D. S. Lee
,
K. L. Yam
Journal:
Food Additives & Contaminants: Part A
, vol. ahead-of-p, no. ahead-of-p, pp. 1-8, 2012
Effect of Drying Methods on the Quality Characteristics of Fenugreek (Trigonella foenum-graecum) Greens
Madeneni Madhava Naidu
,
Hafeeza Khanum
,
Guruguntla Sulochanamma
,
Halagur Bogegowda Sowbhagya
,
Umesh Hanglur Hebbar
,
Maya Prakash
,
Pullabhatla Srinivas
Journal:
Drying Technology - DRY TECHNOL
, vol. 30, no. 8, pp. 808-816, 2012
Influence of the growing degree-days on chemical and technological properties of chestnut fruits (var. “Judia”)
Lia-T. Dinis
,
Francisco Peixoto
,
Jorge V. Ferreira-Cardoso
,
José J. L. Morais
,
Amadeu D. S. Borges
,
Fernando M. Nunes
,
João F. Coutinho
,
Rita Costa
,
José Gomes-Laranjo
Journal:
Cyta - Journal of Food
, vol. ahead-of-p, no. ahead-of-p, pp. 1-11, 2012
Kinetics and equilibrium of cadmium removal from aqueous solutions by sorption onto synthesized hydroxyapatite
N. Barka
,
K. Ouzaouit
,
M. Abdennouri
,
M. El Makhfouk
,
S. Qourzal
,
A. Assabbane
,
Y. Ait-Ichou
,
A. Nounah
Journal:
Desalination and Water Treatment - DESALIN WATER TREAT
, vol. 43, no. 1-3, pp. 8-16, 2012