AAPS PharmSciTech

, 20:209 | Cite as

A Thermodynamic Balance Model for Liquid Film Drying Kinetics of a Tablet Film Coating and Drying Process

  • Bumjoon Cha
  • Shaun C. Galbraith
  • Huolong Liu
  • Seo-Young Park
  • Zhuangrong Huang
  • Thomas O’Connor
  • Sau Lee
  • Seongkyu YoonEmail author
Research Article


A tablet film coating and drying process was assessed by an experimentally validated thermodynamic balance model. Mass conservation equations were derived for the process air and the aqueous coating solution. Thermodynamic behavior of the solution was described by evaporation at the tablet surface and penetration into the tablet. Energy balance equations including heat loss to the atmosphere were coupled to the mass conservation equation. Experimental data using the ConsiGma™ coater (GEA, Belgium) were used for both parameter estimation and model validation. The results showed the proposed model can investigate primitive outlet variables and further internal variables representing evaporation and penetration. A sensitivity analysis revealed that evaporation depended more on the input parameters while penetration hinges on the tablet properties, particularly on the tablet volume affecting the tablet porosity.


tablet film coating and drying thermodynamic balance model evaporation and penetration parameter estimation sensitivity analysis 



surface area (m2)


heat capacity (J/kg·K)


diffusion coefficient (m2/s)


diameter (m)


energy (J)


elasticity index (−)

\( \hat{H} \)

specific enthalpy (J/kg).

\( \Delta {H}_{\mathrm{eva}}^0 \)

latent heat of vaporization at T = 0°C (J/kg)


thickness (m)


heat loss factor (W/K)


heat transfer coefficient (W/m2·K)


molecular weight (g/mol)


mass (kg)

\( \dot{m} \)

mass flowrate (kg/s)


number of tablet (−)


number of coating runs (−)


pressure (Pa)


pressure (mbar)


saturation vapor pressure (mbar)

\( \dot{Q} \)

heat flowrate (J/s)


gas constant (m3·Pa/K·mol)


particle Reynolds number (−)


relative humidity (%)


Schmidt number (−)


sensitivity index (−)


specific humidity (kg/kg)


Sherwood number (−)


temperature (°C)


speed (m/s)

\( \overline{u} \)

relative speed (m3/s).

\( \dot{V} \)

volumetric flowrate (m3/s).

Greek Letter


evaporation coefficient (m/s)


penetration coefficient (1/m)


density (kg/m3)


perimeter (m)


viscosity (kg/m·s)


surface tension (N/m)


evaporative ratio (%)


drying efficiency (%)


rotating speed (rpm)


input parameter.


response output variable



humid air


calculated variable


coating spray




estimated variable


dry air


liquid film


in, out, kand k2




air knife 1


air knife 2


measured variable


heat loss






ambient surroundings




water vapor


liquid water


coating wheel



The authors wish to thank Dr. HaeWoo Lee for insightful conversations. A license for the gSOLIDS process modeling software (4.1.0) has also been provided by Process Systems Enterprise Ltd. (London, UK) for the modeling and simulation. The project is also partially supported by Merck & Co., Inc., Kenilworth, NJ, USA, who shared the dataset used in this work. The dataset was originally collected by GEA, GmBH, Dusseldorf, Germany. The authors extend their thanks to Merck & Co and GEA for the data making this work possible.

Funding Information

This study was financially supported by the U.S. FDA (grant number 5U01FD005294).

Compliance with Ethical Standards


Views expressed in written materials or publications and by speakers and moderators do not necessarily reflect the official policies of the Department of Health and Human Services; nor does any mention of trade names, commercial practices, or organization imply endorsement by the United States Government.


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Copyright information

© American Association of Pharmaceutical Scientists 2019

Authors and Affiliations

  • Bumjoon Cha
    • 1
  • Shaun C. Galbraith
    • 1
  • Huolong Liu
    • 1
  • Seo-Young Park
    • 1
  • Zhuangrong Huang
    • 1
  • Thomas O’Connor
    • 2
  • Sau Lee
    • 2
  • Seongkyu Yoon
    • 1
    Email author
  1. 1.Department of Chemical EngineeringUniversity of MassachusettsLowellUSA
  2. 2.Office of Pharmaceutical Quality, Center for Drug Evaluation and ResearchFood and Drug AdministrationSilver SpringUSA

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