•A mathematical model based on non-equilibrium formulation was established.•The simulation results show better accordance with the experimental results compared with the model based on equilibrium ...formulation.•The heat and mass transfer during the drying stage were analyzed.•The effects of different operating parameters on the drying time were investigated.
Spray freeze drying has been expanding its influence in many fields. However, the long duration dramatically hinders its further development. A model established based on non-equilibrium formulation was established in this paper. The accuracy of the model proposed with that established based on equilibrium formulation was compared. And the history of temperature, vapor concentration and ice saturation were then investigated. Lastly, the effects of product thickness, particle diameter on the drying time were investigated. The simulation results reproduce well with the experimental data, and show a better agreement with the increase rate of experimentally measured temperature curve than that based on equilibrium formulation. In addition, the temperature increases from the bottom to the top region while the vapor concentration distribution presents the opposite trend. The ice saturation first obtains a slight increase and then decreases. Lastly, the drying time decreases as: (i) the product thickness decreases, (ii) the packing porosity increases and (iii) the chamber temperature increases. The mathematical model proposed in this paper could offer better understanding of the process and guide the design and optimization for the process.
A model including simultaneous droplet heating and water evaporation is proposed to simulate temperature, shrinking and mass profiles of a spherical droplet subjected to convective drying, being ...valid for the first drying stage. Experimental data on drying skim milk and colloidal silica obtained in the literature were used for validation, but there is no restriction in the model that prevents it from being suitable for other materials. There were not significant differences observed concerning to the droplet components (dissolved or insoluble materials). The initial heating time of the particle upon reaching the constant temperature is relatively short ($\Delta t\approx7s$) for both simulated materials and water evaporation during the first drying stage occurs mostly at the wet bulb temperature of the air. Discrepancy between simulated and experimental values did not exceed $9\%$ for skim milk and $7\%$ for colloidal silica in this first stage, indicating good applicability of the model. Considering the applicability of the model in a more generic way, Whitaker correlation evaluated at the film temperature showed better results. Finally, the small discrepancy found is discussed and some improvements are proposed.
Modeling spray drying is based on the behavior of individual droplets involved in the process. The drying history of single droplets is generalized to the entire spray by incorporating drying ...kinetics equations into Euler-Lagrange models of spray drying process. The morphological evolution of single droplet is determined by parameters of the drying agent and properties of solid material in the droplet. In this study, the possible causes for bubble inception are discussed and different morphological evolutions and deformations are examined. A novel mathematical model of single droplet containing insoluble nanoscale particles and internal bubble has been developed and parametrically studied.
A theoretical model describing the second drying stage of a droplet containing a liquid with insoluble nanoscale primary particles is presented. The model enables two possible pathways for the ...evolution of the particle morphology, leading to the formation of either a full solid particle or a hollow particle containing internal aggregates. It was found that the final morphology of the dry particle depends on the size of the suspended primary particles, the strength of the particle crust, the initial moisture content, and the parameters of the drying agent. The formation of a hollow particle morphology is more likely for smaller primary particles and stronger inter-particle forces.
Microwave freeze drying (MFD) normally contains three stages, i.e., pre-freeze stage, primary drying stage and secondary drying stage, just as in conventional freeze drying. This research examines ...the variations of structure, starch content, reducing sugar content, color change as well as expansion ratio during these stages of microwave freeze drying banana chips. Results show that biggest changes are found at the primary drying stage in the banana slices’ starch content, reduced sugar content, their structure and their changed colors while the biggest change of expansion ratio occurs at the secondary drying stage. Similar results can also be obtained for FD samples. Thus it is concluded that the primary stage can do most damage to the banana chips.
A new porous media mathematical model for freeze-drying was developed based on the adsorption–desorption relationship proposed in this paper. A finite difference solution was obtained from a moving ...boundary problem for the dielectric-material-assisted microwave freeze-drying process. Silicon carbide (SiC) was selected as the dielectric material; and frozen skim milk was used as the aqueous solution to be dried. Simulation results showed that the dielectric material can significantly enhance the microwave freeze-drying process. The drying time was 33.1% shorter than that of ordinary microwave freeze-drying under typical operating conditions. When the solid content of the solution to be freeze-dried was very low, or the solid product had a very small loss factor, microwave heating was less effective without the assistance of dielectric material. The mechanisms of heat and mass transfer during drying were analyzed based on profiles of ice saturation, temperature and vapor concentration. Drying rate-controlling factors were discussed. A comparison was made between the model predictions and the reported experimental data.
Die Gefriertrocknung bietet gegenüber anderen Trocknungsmethoden den Vorteil einer schonenden Behandlung. Ein Nachteil ist jedoch die längere Trocknungszeit. Abhilfe kann diesbezüglich die dynamische ...Gefriertrocknung schaffen. Hierbei wird der Wärmeübergang auf das Produkt verbessert und die sich bildende Trockenstoffschicht wird permanent entfernt. Somit wird der Wärme‐ und Stofftransportwiderstand der Trockenschicht reduziert und es wird in der Nähe der Eiskristalle getrocknet. Dies bringt eine Steigerung der Trocknungsgeschwindigkeit mit sich, da im ersten Trocknungsabschnitt getrocknet werden kann.
Freeze‐drying offers the advantage of mild drying. However, a drawback is the long drying time. One way to reduce the drying time is to use dynamic freeze‐drying. Here, the heat transfer to the product is improved and the forming dry layer is permanently removed. Thus, the heat and mass transfer resistance is reduced and it is dried in the vicinity of the ice crystals. This results in an increase of the drying rate, since it can be dried in the first drying section.
Die Gefriertrocknung ist eine der produktschonendsten Trocknungsmethoden, aber auch eine der langsamsten. Um wirtschaftlicher Produkte zu erzeugen, muss die Trocknungszeit reduziert werden. Ein Ansatz ist die dynamische Gefriertrocknung, die eine höhere Trocknungsgeschwindigkeit aufweist, weil die sich bildende Trockenschicht während der Trocknung entfernt wird.
Dry-cured sausages were treated with two types of dehydrated lemon albedo (raw and cooked) at five concentrations (0-100 g kg-1 in 25 g kg-1 increments). Several physical and chemical analyses were ...made during the drying stage, and compositional, textural and sensory analyses were conducted on the finished products. The addition of albedo improved the nutritional properties as a result of fibre addition and may have beneficial effects due to the presence of active biocompounds as evidenced by a decrease in residual nitrite levels and delayed oxidation (based on TBARS values). The sensory properties of samples that resembled the control sausages were those that contained up to 50 g kg-1 dehydrated raw albedo and 75 g kg-1 dehydrated cooked albedo.
The existence of the first drying period is usually demonstrated by the observation of a constant drying rate stage. However, with highly deformable materials, the overall drying rate is misleading ...due to the substantial decrease of the exchange surface. The drying flux is a more useful quantity to consider, but it requires both the exchange surface area and the overall drying rate to be determined during the entire drying process.
Another proof of evidence of a first drying stage lies in the sample temperature, which should stay equal to the wet bulb temperature during the first drying period.
In this paper, we proposed a new experimental set-up that allows the existence of a first drying stage to be proved by two independent experimental data. Using a climatic chamber, a microbalance and two contactless methods (two laser beam micrometers and an infrared thermometer) the sample dimensions, the drying rate and the surface temperature can be collected simultaneously versus time.
The results obtained from both methods were consistent and confirmed the existence of a constant drying flux period for potato. The effect of relative humidity and sample dimension was also analyzed.
