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Tuning the Particle Sizes in Spherical Agglomeration Pawel M. Orlewski, Byeongho Ahn, and Marco Mazzotti Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01134 • Publication Date (Web): 05 Sep 2018 Downloaded from http://pubs.acs.org on September 7, 2018
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Crystal Growth & Design
Tuning the Particle Sizes in Spherical Agglomeration Pawel M. Orlewski, Byeongho Ahn, Marco Mazzotti* Institute of Process Engineering, ETH Zurich, 8092 Zurich, Switzerland E-mail:
[email protected] Phone: +41 44 632 24 56. Fax: +41 632 11 41
Abstract
This paper presents an experimental technique for tuning the size of spherical agglomerates together with a simple model that provides qualitative information on the agglomerate size. Spherical agglomerates of benzoic acid of varying sizes using toluene as the bridging liquid were obtained with a very good reproducibility. The bridging liquid was injected into the crystal suspension via a capillary to control the initial size of the bridging liquid droplets. Experimental results obtained at different operating conditions show a clear correlation between the initial droplet size and the agglomerate size. Agglomerate size noticeably decreases with reducing the capillary size. Horizontal injection of the bridging liquid produces smaller agglomerates as compared to those produced with a vertical injection, while the size of agglomerates is insensitive to the different injection positions used in this study. Agglomerate size decreases
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along with the increasing stirring rate. The presented model adequately captures the behavior of the system and gives a qualitative agreement with the experimental results.
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1. INTRODUCTION
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Many chemical and pharmaceutical products are prepared as powders, often consisting of
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particles made of functional materials. The morphology of those particles plays a crucial role, as
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it can have an impact on the efficiency of downstream product handling (e.g., filtration and
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drying) and on the biopharmaceutical properties of particles (e.g., dissolution and
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bioavailability)1. Accordingly, a great deal of attention has been paid to modifying the crystal
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morphology during the crystallization phase by controlling the process parameters, e.g.
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supersaturation, cooling rate, stirring rate or type of additives. However, sometimes undesired
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shapes or size distributions are inevitable, thus often forcing manufacturers to deal with micron-
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sized needle-shaped or platelet-shaped particles that exhibit poor flowability. This leads to a
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considerable decrease in the efficiency of the downstream processes such as filtration, blending
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and compression (tableting).
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Spherical crystallization has recently gained interest in the chemical and pharmaceutical
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industries to address the flowability-related problems by producing crystals in a spherical form
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with better micrometric properties such as flowability, packability, and compressibility compared
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to the needle- or platelet-shaped crystals2. There are two types of spherical crystallization: quasi-
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emulsion solvent diffusion (QESD) and spherical agglomeration. In the case of the former,
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quasi-emulsion droplets of solvent in anti-solvent are formed, within which crystallization occurs
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due to the counter diffusion of solvent out and anti-solvent into the droplets. The latter on the
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other hand is induced by feeding a liquid binder (often called a bridging liquid), i.e. an
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immiscible fluid that preferentially wets the crystals, into the suspension, often after
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crystallization, but also possibly during crystallization3. In such a process, the liquid binder is
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dispersed into a suspension of primary crystals in the form of droplets, which capture primary
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crystals by capillary action4. Due to its higher flexibility and simplicity, preferential
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crystallisation is considered more promising than QESD3.
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Numerous studies have examined the effect of various operating parameters on the spherical
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agglomeration process: stirring rate5,6, stirring time4,6–8, initial size of primary crystals5,9, the
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amount1,4,7,9 and the injection rate5,10 of the liquid binder. Among these parameters, often the
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amount of the liquid binder, together with its injection rate, has been shown to be the most
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critical parameter influencing the size of agglomerates6,8,11. Surprisingly though, the influence of
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the initial binder dispersion, namely the initial size of binder droplets, on the size of spherical
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agglomerates has not been studied so far.
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The goal of this work is to understand the effect of the initial droplet size on the size of
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spherical agglomerates by exploiting the advantages offered by a microfluidic device, which
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enables the generation of a large quantity of binder droplets, whose size can be carefully tuned. It
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also allows decoupling the features of the initial binder dispersion from other critical operating
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parameters, thus enabling a better understanding of the role of the liquid binder in the spherical
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agglomeration process.
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2. TUNING THE SIZE OF DROPLETS: THEORY
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Advances in microfluidics have facilitated droplet generation in a controlled manner, as
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summarized in a recent review paper12. Among the numerous techniques for droplet generation,
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we have employed the simplest method, i.e. injecting the dispersed phase into the continuous
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(immiscible) liquid phase via a cylindrical microcapillary. In this method, under certain flow
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conditions, the droplet forms at the capillary tip and further grows until it reaches a critical size,
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after which the droplet starts to detach thus eventually leaving the capillary (see a high-speed
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camera video of the whole process in the supplementary material available on-line). The size of
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the detached droplet can vary depending on the capillary size, the flow field around the capillary
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tip, and the properties of the fluids involved and of the capillary13. Since the droplet size is at the
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heart of this work, the following section presents a simple model that has been used to estimate
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such droplet size.
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2.1 Droplet Size Estimation
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There are four main forces acting on a droplet forming at the tip of a capillary, namely the
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buoyancy force , the kinetic force , the drag force , and the interfacial tension force .
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The aforementioned forces can be classified into two groups: lifting forces, that act to separate
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the droplet from the tip, and restraining forces, that act to keep it attached to the tip14. If the flow
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directions of the continuous and dispersed phase are assumed to be parallel (Figure 1), then the
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only force keeping the droplet attached to the nozzle is the interfacial tension force, whereas the
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remaining three forces act as lifting forces. As long as the restraining forces are larger than the
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lifting forces, the droplet will stay attached to the tip and continue growing. As soon as the lifting
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forces exceed the restraining forces, the droplet will start clearing the tip of the capillary14. The
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size of droplets at the breaking point corresponds to the size of a droplet, for which the
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restraining forces are balanced by the lifting forces. Below, the definitions of the four forces
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acting on the droplet are provided.
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•
The interfacial tension force , that keeps the droplet at the capillary tip, is given by =
+ # 1 2
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where is the interfacial tension between the two fluids, and and is the inner and
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outer diameter of the capillary respectively. Here, the perimeter of the triple interface has
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been defined as + /2 instead of the usual , because the actual perimeter of
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the triple-phase contact line among the two fluids and the capillary tip is somewhere in
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between and , and well approximated by their arithmetic average15.
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•
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The inertial force , that is generated due to the momentum of the dispersed phase inside the capillary and that pushes the droplet in the streamwise direction, is defined as = # 2
where is the density of the dispersed phase, is its average velocity inside the
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capillary, and is its volumetric flowrate.
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•
The drag force, which also acts to detach the droplet from the capillary, is given by ! " # = # 3 2
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where is the drag coefficient (dimensionless), is the density of the continuous phase,
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is the relative velocity of the continuous phase with respect to the droplet, and " # is
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the reference area. The drag coefficient can be estimated as a function of the Reynolds
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number Re as follows16: 9.06 ! = 0.292 (1 + - # 4 √+,
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Here, the Reynolds number Re is defined as17 +, =
/ 0 − 2 # 5 3
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where 0 is the diameter of the droplet and 3 is the dynamic viscosity of the
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continuous phase. The term 0 − reflects the fact that the capillary shields the
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inner side of the droplet from the continuous phase, as shown in Figure 1. The relative
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velocity of the continuous phase with respect to the droplet is − 0 , where is
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the average velocity of the continuous phase, 0 is the velocity of the droplet in the
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! streamwise direction and it is given by / 0 . The reference area " # is typically
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defined as the area of an object perpendicular to the flow direction. In this work, it is
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defined as17 " # =
! ! − 2 / 0
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# 6
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which accounts for the fact that the droplet is partially shielded from the continuous phase
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flow by the capillary itself, as illustrated in Figure 1.
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The buoyancy force , that is generated due to the density difference between the two phases, is defined as = 5 gΔ# 7
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where 5 is the volume of the droplet, g is the acceleration of gravity, and Δ is the
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difference between the densities of the two phases. Under the investigated conditions, the
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buoyancy force is negligible in comparison with the other three forces, and therefore has
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been neglected; this is often the case in liquid-liquid drop formation13,17–19.
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By balancing the three horizontal forces, the size of droplets at the breaking point can be calculated: = + 0 , # 8
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where only the drag force increases with the droplet size 0 , whereas the interfacial
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tension force and the inertial force are independent of 0 . Here, the average velocity of
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the continuous phase used in the drop size estimation is obtained from computational fluid
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dynamics (CFD) simulations, as explained in Section 2.2.
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There are two main limitations to this model. First, the flow directions of the continuous and
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dispersed phase are assumed to be parallel (referred in this work as the co-flow configuration). In
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the case of cross-flow, the droplet breaks off from the external surface of the capillary rather than
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from the tip, thus providing a larger contact area between the droplet and the capillary, and a
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larger shielding effect from the continuous phase as compared to the co-flow case (Figure 3).
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This increases the effect of the surface tension force and decreases the drag force, thus resulting
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in a larger droplet size at break-off. Unfortunately, the actual break-off point is not known and
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therefore the droplet size cannot be precisely estimated. Since developing a new model for
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droplet formation lays beyond the scope of this paper, we have decided to use the simple model.
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Second, the droplets form in the “dripping regime” where the dispersed phase drips from the
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capillary tip in the form of droplets, thus being not applicable to the “jetting regime” drop
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formation where the dispersed phase forms a liquid jet and brakes up into droplets due to
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Rayleigh instabilities20.
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To check the validity of the second assumption, a theoretical approach to characterize the flow
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regime of droplet formation has been employed by comparing the kinetic energy per unit length
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with the interfacial tension energy per unit length17. When the kinetic energy term is smaller than
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the interfacial energy term, droplets form under the dripping regime. The kinetic energy of pipe
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! flow per unit length is ! /8 , where is the density of the dispersed phase, is the
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average velocity of the dispersed phase inside the capillary, and is the inner diameter of the
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capillary. The interfacial tension energy per unit length is + /2. In this work, the
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interfacial tension energy term is always larger than the kinetic energy term, thus implying that
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the dripping regime governs the drop formation. It is, however, important to note that this
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approach does not consider the energy transferred from the co-flowing continuous phase to the
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droplet, which can influence the drop formation mechanism13.
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Figure 1. Schematic drawing of the droplet formation at the capillary tip in the dripping regime.
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The dispersed phase is injected through a capillary into a co-flowing immiscible outer fluid.
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Three major forces acting on the droplets are displayed with solid arrows: interfacial tension
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force , inertial force , and drag force .
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2.2 CFD Model
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In order to get a better understanding of the flow conditions in the reactor and to obtain the local
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fluid velocities needed for the estimation of the size of the generated droplets, a CFD model of
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the crystallizer has been developed using the commercial CFD software Fluent 17.2. As a
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significant vortex formation due to the intensity of mixing has been observed during the
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experiments, a two-phase model was used to capture this effect. To solve the Navier-Stokes
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equations, a standard Reynolds stress model (RSM) with linear pressure-strain has been used
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together with the volume of fluid (VOF) multiphase model where the liquid phase has been
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modeled as pure water and the gas phase as air. The simulations were run at steady-state using
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the in-built multi reference frame (MRF) model for the description of the motion of the stirrer.
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To reduce the computational burden, periodic boundary conditions have been used with only a
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quarter of the reactor (having a volume of 500 mL, see section 3.2) being sufficient to describe
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the whole system. The grid has been refined until a mesh-independent solution was obtained
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with the final grid consisting of 237,000 cells.
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3. EXPERIMENTAL
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Spherical agglomeration of benzoic acid crystals using toluene as a bridging liquid has been
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investigated in this work, whose main goal is to study the effect of the initial droplet distribution
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of the bridging liquid on the final particle size distribution (PSD) of the spherical agglomerates.
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Therefore, the experiments have been designed (1) to study the effect of the initial droplet size
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distribution on the final size distribution of the spherical agglomerates (series ;< ), (2) to establish
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the effect of feeding position on the final size of agglomerates (series ;! ), and (3) to determine
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which effect dominates in determining the final size of agglomerates – either the agglomeration
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kinetics or the initial dispersion of the bridging liquid (series ;= ). Each experiment consisted of
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two stages: first the unseeded generation of primary crystals (stage I), carried out under the same
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conditions for all the experiments, followed by the agglomeration of the primary crystals into
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spheres (stage II), performed using different operating conditions to explore the effects described
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above.
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3.1 Materials
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In this work, benzoic acid (99.5% purity, Sigma-Aldrich, Switzerland) has been used as solute,
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ethanol (absolute, Fischer Chemicals, Switzerland) as solvent, ultrapure deionized water (18.2
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MΩ cm, Millipore, Switzerland) as antisolvent, and toluene (HPLC grade, Fischer Chemicals,
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Switzerland) as bridging liquid. The physical properties of the liquids at room temperature are
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summarised in Table 1.
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Table 1. Physical properties of liquids used in this work at room temperature. Mixture
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proportions are given in w/w Phase
Composition
[kg/m= ]
3 [mPa s]
Continuous
Water/Ethanol (90/10 w/w)
963a
1.86a
Toluene
865
0.56
Dispersed 3
[mN/m] 20b
a21, b22
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3.2 Experimental Setup
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All experiments have been carried out as a semi-batch process using a 500 mL curved-bottom
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cylindrical vessel with a diameter F=10 cm (GlasKeller, Germany) (see Figure 2). The
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temperature inside the reactor was controlled using a Huber Ministat CC3 thermostat (Huber,
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Germany). The solution was agitated using an overhead, 4-blade glass impeller with a diameter
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of 75 mm and 40° inclined blades. The impeller was powered by a Eurostar Digital stirrer (IKA,
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Germany) and positioned 25 mm above the reactor bottom with the shaft turning counter-
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clockwise, thus resulting, in this case, in an upwards conveying flow direction. The lid of the
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reactor was made of glass and had ports for a thermocouple, a liquid inlet used for antisolvent
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crystallization, and a liquid inlet used for spherical agglomeration.
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Figure 2. Overview of the experimental setup
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Stage I of the process – unseeded antisolvent crystallization – was performed by feeding an
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undersaturated solution of benzoic acid in the solvent (ethanol) to the reactor filled with the
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antisolvent (water). The stock solution was placed on a balance (Mettler Toledo, Switzerland)
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and fed to the reactor using a LabAlliance Series II HPLC pump (Scientific Systems, USA), thus
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enabling a precise dosage of the solution through the process. The feeding tube was located 1 cm
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above the stirrer and 2 cm away from the shaft.
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Stage II of the process – spherical agglomeration – was carried out by feeding the bridging
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liquid (toluene) to the reactor containing crystals suspended in a saturated solution. The bridging
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liquid was introduced using a PHD4400 syringe pump (Harvard Apparatus, USA). Due to the
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high pressure drop in the system, a 20 mL stainless steel syringe (Harvard Apparatus, USA) has
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been used to ensure precise dosage for all the process conditions investigated in this work. As
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feeding tubes, fused silica capillaries (BGB Analytik AG, Switzerland) with four different sizes
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have been selected with different inner and outer diameters, and , respectively (see Table
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2). To protect them from mechanical damage and to allow for a precise positioning of the inlet
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tip in the reactor, the feeding tubes have been guided within the reactor through a metal housing
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(see Figure 3).
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Table 2. Inner and outer diameter of capillaries used for feeding bridging liquid Capillary
H
