TOWARDS MODELLING THE MORPHOLOGY OF PARTICLES
OBTAINED FROM SPRAY DRIED DROPLETS

Hassan Abdullahi ¹, Christopher
L. Burcham,²  Thomas
Vetter^1* 

¹ School of Chemical Engineering and Analytical
Science, University of Manchester, Manchester, UK

² Eli Lilly & Company, Indianapolis, USA

Spray drying is used to form particles from droplets (clear liquid or a
suspension of particles) in a hot gas stream. There is recent and renewed
interest in this technology within the pharmaceutical industry as it presents a
way to co-formulate active pharmaceutical (APIs) with excipients ^[6].
By manipulating drying conditions (gas temperature, relative humidity, ratio of
gas flow rate to liquid/suspension flow rate) spray drying also allows tuning
the external shape, apparent density, etc. of the particulate product. Figure 1
shows an overview of possible morphologies that can be obtained from such a
process ^[3].

While
there has been progress in describing the formation of such complex structures
during drying in recent years ^[1][5][6],
there is scope to develop a robust mechanistic model coupling the
phenomena of evaporation, mass transfer and particle formation. Such a model is
useful in the prediction of particle morphologies and ultimately product
properties. The aim of this work is to introduce such a mechanistic model based
on population balance equations that allows describing several of the above
morphologies. As a first step, we describe a situation where droplets are
saturated with liquid. The droplet is heated to the wet-bulb temperature where
shrinkage occurs at a near constant rate and particles are formed within the
droplet as illustrated in Figure 1 (first drying stage)^[4]. In the
second stage, shrinkage stops as a locked shell is formed around the droplet.
The evaporation rate falls continuously as the thickness of the shell increases
^[2][3]. In the end, the balance of various forces determines the
type of particle formed ^[3]. An accurate description of such a
process requires detailed formulation of internal and external mass and energy conservation
equations.

By
taking a differential control volume for the homogeneous droplet (Figure 2) and
assuming a radially symmetrical droplet, we can describe the nucleation/growth
of particles as well as the advection/diffusion of liquid and solids within the
droplet during drying.

A material balance for the liquid phase is introduced (Equation 1), where the
change in liquid concentration c of
component i 
(for i = 1Én-1) within the droplet is described
by the rate of advection and diffusion of solute molecules, the rate of
nucleation of particles and the growth rate of particles within the droplet
respectively. The number density distribution of particles N_i and temperature distribution
are described similarly by Equation 2 and 3 respectively ^[4][5].

The equations are complemented by appropriate
boundary conditions. In the second stage, the equations are similar and are
only adapted to describe the presence of a shell region.  Solving the above equations yields data for
the evolution of particle properties such as size, shell lock time and
porosity. Results from simulations are validated using an extensive data set
obtained from the controlled drying of single droplets containing varying
compositions of mannitol and paracetamol
in a solvent using acoustic levitation. In addition, Scanning electron
microscope (SEM) imaging yields external morphology data and X-ray-computed
tomography allows visualisation of the internal structure of individual
particles and hence yields comparable data of shell thickness.  This in fact represents the first time
such a shell thickness analysis is applied to single droplet drying. In the
end, we demonstrate key fundamental understanding of droplet drying and
particle formation through combined mechanistic modelling and detailed
experimental methodologies. The resultant model can be applied to the
simulation of typical spray drying processes when combined with knowledge of
the flow pattern in the processing vessel. 

References

1) Liang, H., Minoshima, H.,Matsushima,
K., Shinohara, K. Basic model of spray drying granulation. Journal of Chemical
Engineering of
Japan 2001, 34 (4), 472–478.

2)
Maurice, U., Mezhericher, M., Levy, A. and Borde, I. (2015). Drying of Droplets Containing Insoluble Nanoscale Particles: Second Drying Stage. Drying Technology, 33(15-16), pp.1837-1848.

3) Mezhericher, M., Levy, A. and Borde,
I. (2011). Modelling the morphological evolution of nanosuspension
droplet in constant-rate drying stage. Chemical Engineering
Science, 66(5), pp.884-896.

4) Mezhericher, M., Naumann, M., Peglow, M., Levy, A., Tsotsas, E.
and Borde, I. (2012). Continuous species transport
and population balance models for first drying stage of nanosuspension
droplets. Chemical Engineering Journal, 210,
pp.120-135.

5) Seydel, P., Blšmer, J. and Bertling, J. (2006). Modeling
Particle Formation at Spray Drying Using Population Balances. Drying Technology, 24(2), pp.137-146.

6) Vehring, R.
(2007). Pharmaceutical Particle Engineering via Spray Drying. Pharmaceutical Research, 25(5), pp.999-1022.