Mathematical Modeling of Spray Impingement and Film Formation on Pharmaceutical Tablets during Coating
Introduction
Coating of tablet cores is one of the oldest manufacturing processes utilized by the pharmaceutical industry Porter (2012), Felton (2013). Tablets are coated for several reasons, including enhancement of appearance, taste masking, protection of sensitive ingredients and control of the Active Pharmaceutical Ingredient (API) release Cole (1995). Due to the complexity of the spray coating process, problems are often encountered with the final product Amidon et al. (1999), Muliadi and Sojka (2010). Some of the most common tablet defects are bridging, cracking, colour variations, roughness/orange-peel roughness, picking and sticking Cole (1995). One main cause of such defects is failing to adopt the right values for the process parameters in the coating drum, such as spray mass flow rate or coater temperature and rotational speed Muliadi and Sojka (2010).
To address the above issues, researchers have investigated the coating spray atomization process Aliseda et al. (2008), as well as the deceleration and the evaporation of the generated droplets during their flight from the nozzle to the tablet bed Cole (1995), Wang et al. (2012). By combining these spray models with a thermodynamic model that calculates air temperature and humidity inside the coating drum am Ende and Berchielli (2005), one can estimate the droplet size and velocity before impact Niblett et al. (2017). Recent work on coating behavior after impact on a tablet core has been mainly focused on single droplet cases Niblett et al. (2017), Bolleddula et al. (2010), and therefore the information concerning spray impact and film formation under coating process conditions is limited Felton (2013). Moreover, general spray impingement models found in the literature are either empirical or based on computationally expensive Computation Fluid Dynamics (CFD) simulations.
Previous work aiming to numerically simulate spray impingement on impermeable solid substrates mainly relied on models derived from single droplet impact studies Cossali et al. (2005). Models following this approach describe the spray impingement as a superposition of single droplet impacts. Roisman et al. (2006) questioned this modeling strategy, because it neglects interactions between neighbouring spreading droplets, a limitation that makes these models insensitive to spray density. Nevertheless, information about single droplet impacts offers useful insight into the complex spray impingement process Moreira et al. (2010). Additionally, using Volume-Of-Fluid (VOF) CFD simulations, in the appendix of this article we show that in the conditions investigated in this work droplet-droplet interactions on the tablet are negligible.
The models for single droplet impingement fall into two categories: those considering impact on dry substrates and those considering impact on wetted surfaces or liquid films. The impingement of a single droplet on a dry substrate can have several outcomes: the droplet may deposit into a cylindrical or spherical-cap film, disintegrate (splash) into secondary droplets, or recede and potentially rebound Roisman et al. (2006), Moreira et al. (2010). In the literature, one can find a few predictive theoretical models that simulate the spreading, receding, splashing and rebounding after droplet impingement on dry walls Bechtel et al. (1981), Kim and Chun (2001), Roisman et al. (2002), Attané et al. (2007). For pharmaceutical coating, Shaari (2007) and Bolleddula et al. (2010) experimentally investigated single droplet spreading on tablets, while we developed a model predicting the behavior of Opadry coating droplets after impact on dry porous substrates Christodoulou et al. (2018).
As mentioned, in the literature there are also a few models describing the impingement of a single droplet on a wetted surface. Roisman et al. (2006) and Yarin and Weiss (1995) experimentally and theoretically investigated droplet impingement on liquid films covering rigid substrates. They found that droplets with low impact velocity and small size can deposit on the film surface or coalesce, whereas droplets with moderate and high impact velocities tend to form a crater at the impingement region that leads to splashing and even to film disintegration. Few researchers have proposed empirical splashing and disintegration criteria or developed models for predicting the outcome of droplet impact on liquid films of different thickness Kalantari and Tropea (2007).
About spray impingement, obtaining accurate and detailed information through experiments or mathematical modeling is challenging Cossali et al. (2005). In the literature, one can find experimental work concerning the interaction of spray droplets impinging on a wall, and about splashing and breakup Yarin and Weiss (1995), Barnes et al. (1999). Moreira et al. (2010) reviewed the aforementioned studies that were mainly focused on simultaneous and subsequent impacts of two droplets. Mundo et al. (1998) modeled spray impingement as a superposition of single droplet collisions without considering liquid film formation and the film-droplet interactions. Roisman et al. (2002) developed a model to estimate the velocity and shape of the uprising liquid film, accounting for droplet collisions on the substrate and the influence of droplet spacing, but not including predictions for possible break-up of the uprising film. One drawback of these models is that they do not calculate the final film thickness after spray impingement.
Concerning the prediction of film thickness after spray impact, Lee and Ryou (2001) developed an empirical model aiming to predict the outcome of diesel spray impingement on a rigid wall. Recently, Kalantari and Tropea (2007) conducted experiments and derived a semi-empirical relation for the film thickness. We used their detailed experimental data and semi-empirical relation to validate the model developed in this work. In general, research for pharmaceutical sprays is focused on droplet atomization and evaporation Muliadi and Sojka (2010), and therefore we were unable to find previous work that deals in detail with coating spray impact on tablets. To conclude, spray impact models available in the literature are either based on empirical equations or on computationally expensive CFD simulations Moreira et al. (2010).
In this paper, we present a novel model (Section 2) that describes spray impact on tablets during film-coating, without requiring prior knowledge of the process via empirical relations. The model predicts the time required for the wetting of the entire tablet surface facing the spray, as well as the liquid film thickness, while taking into account coating (viscosity, density, surface tension) and spray (droplet size, velocity, mass flow rate) properties.
Compared with CFD simulations – which take hours or days to output results – our model yields solutions considerably faster (simulation time < 5s) without sacrificing accuracy significantly. This allowed us to perform variance-based sensitivity analysis to study the influence of process parameters on the coating spreading behavior. We validated the numerical results with experimental data from the literature (Section 3). With this work, we aim to provide insight into the process of coating application on pharmaceutical tablets and to assist in the selection of the appropriate values for the process parameters required to minimize the number of defective tablets.
Section snippets
Mathematical model
Film coatings are generally applied on tablets by spraying a polymer solution or dispersion on their surface Felton (2013). After impingement onto the tablet, the droplets spread on its dry surface. Based on the experimental work of Bolleddula et al. (2010) for pharmaceutical coating droplets, we assumed that the droplets spread without disintegrating or rebounding after impact. The spreading of a droplet that impacts on a dry rigid substrate can be divided into two consecutive regimes
Numerical results and validation
We validated the numerical results from the model described above with experimental data from the literature. In Section 3.1, we used experimental data from the work of Bolleddula et al. (2010) to compare the numerical results concerning single droplet impingement on pharmaceutical tablets. In Section 3.2, we compared the model predictions for the film final thickness with the corresponding experimental results of Kalantari and Tropea (2007), who investigated water spray impingement on rigid
Conclusions
Our work considers the film-coating process, which is widely employed by the pharmaceutical industry. Film coating is a complex process that is difficult to simulate accurately with reasonable computational cost. In this work, we developed a novel mathematical model that can quickly calculate the film thickness and spreading rate on the surface of a tablet passing through the spray zone. The detailed derivations of the main equations are presented in the main article and in the appendix. The
Declaration of interests
None.
References (39)
Mechanisms of polymeric film formation
International journal of pharmaceutics
(2013)- et al.
Atomization of viscous and non-Newtonian liquids by a coaxial, high-speed gas jet, Experiments and droplet size modeling
International Journal of Multiphase Flow
(2008) - et al.
An evaluation of process parameters to improve coating efficiency of an active tablet film-coating process
International journal of pharmaceutics
(2012) - et al.
Development and evaluation of a dimensionless mechanistic pan coating model for the prediction of coated tablet appearance
International journal of pharmaceutics
(2017) - et al.
Impact of a heterogeneous liquid droplet on a dry surface: Application to the pharmaceutical industry
Advances in colloid and interface science
(2010) - et al.
Advances and challenges in explaining fuel spray impingement: How much of single droplet impact research is useful?
Progress in energy and combustion science
(2010) - et al.
Multiple drop impact onto a dry solid substrate
Journal of colloid and interface science
(2002) - et al.
Mathematical modelling of water absorption and evaporation in a pharmaceutical tablet during film coating
Chemical Engineering Science
(2018) - et al.
Spray impact onto flat and rigid walls: Empirical characterization and modelling
International Journal of Multiphase Flow
(2007) Solidification of droplets on a cold surface
International Journal of Heat and Mass Transfer
(1976)