Experimental and theoretical investigation of foam-spray drying. 1. Mathematical model for the drying of foams in the constant-rate period

1986 ◽  
Vol 25 (4) ◽  
pp. 723-730 ◽  
Author(s):  
Douglas D. Frey ◽  
C. Judson King
Keyword(s):  
Mathematical Model ◽  
Spray Drying ◽  
Theoretical Investigation ◽  
Constant Rate ◽  
Rate Period

Comments to “Analysis of constant rate period of spray drying of slurry” by Liang et al., 2001

2006 ◽  
Vol 61 (6) ◽  
pp. 2096-2100 ◽  
Author(s):  
Kåre Jørgensen ◽  
Anker D. Jensen ◽  
Jakob Sloth ◽  
Kim Dam-Johansen ◽  
Poul Bach
Keyword(s):  
Spray Drying ◽  
Constant Rate ◽  
Rate Period

Analysis of constant rate period of spray drying of slurry

2001 ◽  
Vol 56 (6) ◽  
pp. 2205-2213 ◽  
Author(s):  
H. Liang ◽  
K. Shinohara ◽  
H. Minoshima ◽  
K. Matsushima
Keyword(s):  
Spray Drying ◽  
Constant Rate ◽  
Rate Period

scholarly journals Mathematical models to describe the drying process of Moringa oleifera leaves in a convective-air dryer

2021 ◽  
Author(s):  
Kivaandra Dayaa Rao Ramarao ◽  
Zuliana Razali ◽  
Chandran Somasundram
Keyword(s):  
Activation Energy ◽  
Mathematical Models ◽  
Moringa Oleifera ◽  
Effective Diffusivity ◽  
Drying Process ◽  
Constant Rate ◽  
Rate Period ◽  
Moringa Oleifera Leaves ◽  
Air Dryer ◽  
Kinetics Of

Drying kinetics of Malaysian Moringa oleifera leaves was investigated using a convective-air dryer. The drying parameters were: temperature (40, 50, 60, 70 °C), air velocity (1.3 m s<sup>–1</sup>, 1.7 m s<sup>–1</sup>). The drying process took place in the falling rate period and there was an absence of a constant rate period in this experiment. Six mathematical models (Lewis, Henderson and Pabis, Wang and Singh, Peleg, Page, and logarithmic) were selected for the description of drying characteristics of the leaves. The Wang and Singh model was determined as the best model based on the highest overall coefficient determinant (R<sup>2</sup>) and the lowest overall root mean square error (RMSE). The effective diffusivity (D<sub>eff</sub><sub> </sub>) was also calculated which was in the range of 3.98 × 10<sup>–11</sup> m<sup>2</sup> s<sup>–1</sup> to 1.74 × 10<sup>–10</sup> m<sup>2</sup> s<sup>–1. </sup>An Arrhenius relation was constructed to determine the activation energy for the samples in the convective air dryer. The activation energy for M. oleifera leaves was 39.82 kJ mol<sup>–1</sup> and 33.13 kJ mol<sup>–1</sup> at drying velocities of 1.3 m s<sup>–1</sup> and 1.7 m s<sup>–1</sup>, respectively.

Influence of Alteration of Variance of Normal Distribution of Microsphere Cavity Radius on the Proccess of Helium Sorption by Microspheres

2011 ◽  
Vol 6 (2) ◽  
pp. 24-27
Author(s):  
Anton S. Vereshchagin
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Normal Distribution ◽  
Theoretical Investigation ◽  
Solid Particles ◽  
Uneven Distribution ◽  
Cavity Radius

Theoretical investigation of the proccess of helium sorption by hollow permeable solid particles (microspheres) is done. Mathematical model of the proccess is derived under the assumption of uneven distribution of radius of microsphere cavity. It's shown that the rate of sorption changes insignificantly for investigated ranges of initial data within normal distribution of microsphere cavity radius

scholarly journals Drying of green bean and okra under solar energy

2011 ◽  
Vol 17 (2) ◽  
pp. 199-205 ◽  
Author(s):  
İbrahim Doymaz
Keyword(s):  
Green Bean ◽  
Chi Square ◽  
Sun Drying ◽  
Constant Rate ◽  
Thin Layer Drying ◽  
Rate Period ◽  
Drying Models ◽  
Drying Curves ◽  
The Times

In this study, sun drying behaviours of green bean and okra were investigated. Drying experiments were conducted in Iskenderun-Hatay, Turkey. The drying study showed that the times taken for drying of green bean and okra from the initial moisture contents of 89.5% and 88.7% (w.b.) to final moisture content of around 15?0.5% (w.b.) were 60 and 100 h in open sun drying, respectively. The constant rate period is absent in drying curves. The drying process took place in the falling rate period. The drying data were fitted to thirteen thin-layer drying models. The performance of these models was investigated by comparing the determination of coefficient (R2), reduced chi-square (c2) and root mean square error (RMSE) between the observed and predicted moisture ratios. Estimations by Approximation of diffusion (for green bean) and Midilli et al. models (for okra) were in good agreement with the experimental data obtained.

Prediction of Field Aging Gradient in Asphalt Pavements

2015 ◽  
Vol 2507 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Xue Luo ◽  
Fan Gu ◽  
Robert L. Lytton
Keyword(s):  
Activation Energy ◽  
Prediction Model ◽  
Prediction Models ◽  
Fast Rate ◽  
Chemical Properties ◽  
Asphalt Pavements ◽  
Model Parameters ◽  
Void Content ◽  
Constant Rate ◽  
Rate Period

The aging of asphalt pavements is a key factor that influences pavement performance. Aging can be characterized by laboratory tests and prediction models. Common aging prediction models use the change of physical or chemical properties of asphalt binders based on regression techniques or aging reaction kinetics. The objective of this study was to develop a kinetics-based aging prediction model for the mixture modulus gradient in asphalt pavements to study long-term in-service aging. The proposed model was composed of three submodels for baseline modulus, surface modulus, and aging exponent to define the change of the mixture modulus with pavement depth. The model used kinetic parameters (aging activation energy and preexponential factor) of asphalt mixtures and combined the two reaction rate periods (fast-rate and constant-rate). Laboratory-measured modulus gradients of 29 field cores at different ages were used to determine the model parameters. The laboratory testing condition was converted to the field condition at a given age and corresponding temperature by introducing the rheological activation energy to quantify the temperature dependence of field cores at each age. The end of the fast-rate period or the beginning of the constant-rate period was accurately identified to model these two periods and to determine the associated parameters separately. The results showed that the predictions matched well with the measurements and the calculated model parameters were verified. The proposed aging prediction model took into account the major factors that affect field aging speed of an asphalt pavement, such as the binder type, aggregate type, air void content, pavement depth, aging temperature, and aging time.

Osmo-Convective Dehydration of Plum (Prunus salicina L)

2008 ◽  
Vol 4 (8) ◽  
Author(s):  
B. B Ibitwar ◽  
Bhupinder Kaur ◽  
Sadhna Arora ◽  
Pankaj B Pathare
Keyword(s):  
Osmotic Dehydration ◽  
High Water ◽  
High Water Content ◽  
Glycerol Solution ◽  
High Concentration ◽  
Solid Gain ◽  
Prunus Salicina ◽  
Constant Rate ◽  
Rate Period ◽  
Osmotic Agents

Plums, which have a high water content level, are highly perishable and it is necessary to find alternatives to minimize product deterioration. Osmotic dehydration is one of these effective alternatives. Besides water removal from the product, the process also promotes solid gain due to high concentration of solute. In this study, the effect of different osmotic agents (sugar and sugar-glycerol) was reported. The Magee model could satisfactorily describe the solid gain and water loss during osmosis. Drying was conducted at 45, 55 and 65°C. Osmotic dehydration followed by air drying reduces the drying period. Osmotic dehydration resulted in a decrease in total convective dehydration time. The osmotic dehydration in sugar and sugar-glycerol solution reduced approximately 240 and 120 minutes as compared to the osmo-convective dehydration time of lye-treated plums at 65°C. The drying rate curves contained no constant rate period and showed a linear falling rate throughout the drying process.

DRYING OF STICKY GRANULAR MATERIALS DWING THE CONSTANT RATE PERIOD IN A VIBRATED FLUIDIZED BED

1991 ◽  
Vol 9 (4) ◽  
pp. 1067-1079 ◽  
Author(s):  
Y.K Pan ◽  
Y.M Gan ◽  
X.D Liu ◽  
Z Wei ◽  
Arun S Mujumdar
Keyword(s):  
Granular Materials ◽  
Fluidized Bed ◽  
Constant Rate ◽  
Rate Period ◽  
Vibrated Fluidized Bed

scholarly journals Perbandingan Model Characteristic Drying Rate Curve dan Reaction Engineering Approach Berdasarkan Hasil Eksperimen Pengeringan Mango Tissues

2019 ◽  
Vol 1 (2) ◽  
pp. 69-76
Author(s):  
Johannes Martua Hutagalung
Keyword(s):  
Mean Square Error ◽  
Reaction Engineering ◽  
Rate Curve ◽  
Drying Rate ◽  
Mean Square ◽  
Engineering Approach ◽  
Constant Rate ◽  
Rate Period ◽  
Model Characteristic

Proses pengeringan dapat dimodelkan secara umum menjadi dua model matematika, model empirikal dan mekanistik. CDRC (Characteristic Drying Rate Curve) and REA (Reaction Engineering Approach) adalah salah satu model mekanistik untuk mencari kondisi fisis di semua bagian, yang tidak bisa dilakukan oleh model empirikal. Hasil yang diperoleh dengan cara simulasi menunjukkan profil temperatur dan kadar air pada jaringan mangga yang telah divalidasi berdasarkan literatur. Mean square error dan nilai variasinya menunjukkan kemiripan antara kadar air dan temperatur. Data eksperimen untuk REA menggunakan temperatur pengeringan 338K dan nilai Y pada 0,0134kg H2O/kg udara kering. CDRC dibagi menjadi dua pendekatan model, Constant Rate Period (CRP) dan Falling Rate Period (FRP) pada temperatur 338K. Penentuan energi aktivasi relatif diperoleh sebagai jumlah kadar air yang hilang, pada temperatur 328K. Hasil yang ditunjukkan model CDRC dan REA relatif sama, dimana CDRC lebih mendekati data eksperimen. Pada kurva pengeringan, kadar air jaringan mangga menurun secara eksponensial sedangkan temperatur jaringan mangga menaik secara eksponensial.

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