Mathematical Modeling of Heat Transfer to Determine Cooling Drum Temperatures and Gelatin Material Properties for Softgel Manufacturing. by Colleen Spiegel, Ph.D.

The purpose of this study was to create a transient heat transfer model to predict the temperature requirements for the formation of triple helices during the gelatin sol to gel transition on the encapsulation cooling drum. The new heat transfer model determines the ideal temperatures on each side of the ribbon to predict residence time, cooling conditions, and extent of triple helix formation in order to understand the potential impact of heat transfer on the cooling drum on softgel sealing.

Model Diagram and properties used for the mathematical model

The total ribbon volume is divided into nodes in order to accurately calculate the cooling of the ribbon.

For the uniform distribution of nodes, the location of each node (xi) is:

The distance between adjacent nodes (x) is:

Numerical Calculation of Helix conversion and concentration [1, 4, 5]:

Minimum stable lengths of triple helices:

Total helix conversion:            

Helix concentration and total cross linking density:

Temperature distribution of the gelatin and SS 304 layers on the cooling drum:

METHODS:

A Matlab-based program was developed to analyze the temperature distribution in a gelatin ribbon with different cooling temperatures, residences times, and coolant flow rates with a ribbon thickness ranging from 20 to 40 thousandths of an inch. The total ribbon volume is divided into nodes in order to accurately calculate the cooling of the gelatin ribbon. The energy balances and thermal resistance equations for each node are integrated simultaneously using MATLAB’s ode45 function. Arrays were created for the node temperatures, heat transfer coefficients, heat flows, specific heats, and thermal conductivities of each node. The cross linking density was determined by calculating the concentration of single loop and triple-looped triple helices based upon the temperature distribution in the gelatin ribbon.

Mechanism of coil-helix transition being dependent on concentration and temperature

Temperature distribution of the gelatine ribbon on the cooling drum after 15 seconds

Temperature distribution of the gelatine ribbon on the cooling drum after 60 seconds

RESULTS

The results of the study showed that a similar gelatin temperature distribution can be obtained with different cooling conditions. The residence time on time on the drum was an important process parameter for predicting the gelatin material properties. The simulation showed that increasing the cooling flow rates had a minimal effect in comparison with the setpoint temperatures of the cooling conditions. In addition, when one of the cooling parameters were changed, all of the other parameters on the cooling drum had to be changed in order to produce an equivalent result in terms of triple helix formation.

Temperature distribution of the gelatine and SS 304 layers on the cooling drum from 0 -95 seconds

CONCLUSIONS

Simulation of gelatin processes can provide insight into the sol-gel phenomena that cannot be visually observed. It can be used to determine optimal states of temperature in the gelatin ribbon in order to predict the ideal heat and mass transfer, which determines the gelatin material properties which are directly correlated with soft gel seal quality.

REFERENCES

[1] Chen, Xiliang, Yuxi Jia, Ligang Feng, Sheng Sun, and Lijia An. Numerical Simulation of Coil-Helix Transition Processes of Gelatin. Polymer, 50 (2009) 2181 – 2189.

[2] Guo, L, Colby RH, Lusignan CP, Whitesides TH. Kinetics of triple helix formation in semidilute gelatin solutions. Macromolecules 2003, 36, 9999 – 10008.

[3] Flory PJ, Weaver ES. Helix-Coil Transitions in Dilute Aqueous Collagen Solutions. Journal of the American Chemical Society, 1960; 82:4518-25.

[4] Chen, Xiliang. Numerical Simulation of Gelatin Physical Gelatin Processes under Non-uniform Temperature Field Preformulation Data Summary Report, Catalent, NJ. September 02, 2010. Dissertation, Shandong University, 2010.

[5] Guo, L. Gelation and Micelle Structure Changes of Aqueous Polymer Solutions. Dissertation, Pennsylvania State University, 2003.

[6] Bigi, A., S. Panzavolta, and K. Rubini. Relationship between triple-helix content and mechanical properties of gelatin film. Biomaterials, 25 (2004) 5675 – 5680.

[7] Yapel, Robert A., J. L. Duda, X. Lin, and E. Meerwall. Mutual and self-diffusion of water in gelatin: experimental measurement and predictive test of free-volume theory. Polymer (35) No. 11, 1994.

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Related Topics and Keywords

bioavailability, drug delivery, gelatin, Heat Transfer, Lipid based drug delivery, manufacturing, Softgel, softgel manufacturing, solubility