Spray Drying of Hypromellose Acetate Succinate | Industrial

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 12291−12300

Spray Drying of Hypromellose Acetate Succinate Derek R. Sturm,† Justin D. Moser,‡ Pavithra Sundararajan,‡ and Ronald P. Danner*,† †

Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States Pharmaceutical Sciences, Merck & Co., Inc., West Point, Pennsylvania 19486, United States

‡

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S Supporting Information *

ABSTRACT: Spray drying has a wide variety of applications from production of dried milk to pharmaceuticals. The detailed characterization of the drying of the resulting drops is an important component of designing any spray drying process. This study focuses on the drying of hypromellose acetate succinate (HPMCAS) primarily because it has found wide application in pharmaceutical production. Numerous models have been published on the rate of drying and the resulting morphology of spray-dried drops. The drying rate is abruptly changed when the crust or skin forms on the drop. The skin formation in many systems is directly related to the onset of the glass transition state. This paper treats in detail the modeling of the drying of an HPMCAS drop taking into account the radical change in the mutual diffusion coefficient as the concentration changes. The onset of the glass transition corresponds to the formation of the polymer-rich crust at the surface. Experimental data from pendent drop and acoustical levitation methods are compared with the model predictions of the timing of the formation of the crusts. The experiments examine cases with different solvents, multiple airflow rates, multiple gas phase temperatures, and multiple solvent starting concentrations. In all cases the model predictions are in good agreement with the experimental data indicating the importance of considering the diffusion behavior inherent in the drying of polymeric drops.

1. INTRODUCTION Spray drying is a process that rapidly dries a liquid or slurry into a solid using hot gas. This process is commonly employed in the pharmaceutical and food processing industries. A primary reason is often the thermal sensitivity of the products, but spray drying is also more economical in terms of production costs and energy requirements than alternative methods.1,2 In the case of pharmaceuticals, active pharmaceutical ingredients (APIs) are frequently incorporated into a spray dried dispersion along with hypromellose acetate succinate (HPMCAS). This polymer is commonly used because it stabilizes the API in an amorphous form thereby increasing its kinetic solubility and bioavailability, preventing it from crystallizing, and enhancing its delivery in the high pH regions of the gastrointestinal system such as the small intestine.3−5 The mixture of HPMCAS and API is dissolved in a solvent such as acetone or methanol and spray dried to form a solid powder that is pressed into the desired dosage form.6−8 There have been many studies of spray drying. Comprehensive reviews of spray drying and its application to pharmaceuticals and foods have been presented by Schutyser et al.,1 Miller and Gil,9 Fu et al.,2 and Vehring and coworkers.10,11 These reviews cover the basics of drop dryer operation, methods of characterizing the drying of individual drops, systems containing dissolved or insoluble solids, the presence of volatile components which lead to the formation of bubbles in the drops, the morphological development in the drops, etc. Many researchers have developed mathematical models which capture the behavior observed. These studies typically divide the drying into several stages. Of particular importance is establishing the time when a crust forms on the surface of the drop.1 Once the solvent concentration at the surface is reduced to a critical concentration, the rate of © 2019 American Chemical Society

evaporation of the solvent decreases significantly, and the volume of the drop tends to stabilize. Before the crust occurs at the surface the particles are spheres, but after the crust forms various particle morphologies can occur. Depending upon the temperature and concentration the particle might balloon or shrink, or the shell might burst or form a hollow sphere.2,12 Schutyser et al.1 have defined three morphological stages as a drop dries: (1) the constant drying period, (2) the appearance of the skin formation, and (3) formation of the final drop shape. The transition from a liquid solution to a solidlike phase occurs when the glass transition is reached. As the volatile components evaporate from the drop the highest concentration of the nonvolatiles will occur at the surface, and thus that is where the glass transition will initially occur and where the skin will form. The rate and concentration gradients within the drop depend upon a number of things including the diffusion coefficient. The current paper is focused on predicting the critical time when the crust forms. In most of the mathematical models developed to describe the drying of a drop, when a diffusion coefficient was invoked, it was deemed to be a constant. This was not true for every model, however. Nesic and Vodnik13 treated the evaporation of drops containing a gel of colloidal silica where the diffusion coefficient changed radically with concentration. They used an exponential equation from the work of Wijlhuizen et al.14 involving three constants which were determined from the experimental data. While treating the drying of liquid foods, Meerdink and van’t Riet15 used the Maxwell−Stefan Received: Revised: Accepted: Published: 12291

December 13, 2018 June 18, 2019 June 18, 2019 June 18, 2019 DOI: 10.1021/acs.iecr.8b06183 Ind. Eng. Chem. Res. 2019, 58, 12291−12300

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Industrial & Engineering Chemistry Research

Here, η represents the nondimensional radius, which is 0 at the center of the sphere and 1 at the surface of the drop for all time. R* is the nondimensional radius, which uses the radius at time zero, R0, to account for the change in radius as a function of time, R(t). t* is the dimensionless time which uses the radius at time zero and the reference diffusion coefficient in the polymer phase, Dp0. ρ1* is the dimensionless concentration of solvent in the polymer phase which is calculated using the concentration of solvent in the polymer phase at time zero, ρ1,0. ρ*2 is the dimensionless concentration of the polymer in the polymer phase, and D* is the dimensionless diffusion coefficient. The dimensionless equation that describes drop drying with a changing radius is

equations16 to correlate the required three mutual diffusion coefficients based on their experimental data. They found that different sets of coefficients would give equally good correlations. Hecht and King17 modeled the drying of a drop containing a volatile component in a water−sucrose solution. The model required four mutual diffusion coefficients which were estimated from independent experimental data. None of these approaches are directly applicable to systems containing polymers. In systems using polymers, there can be a 3 or 4 orders of magnitude change in the diffusion coefficient as the concentration or temperature changes. Sturm et al.18 have examined the diffusion coefficient behavior in a number of HPMCAS−solvent systems. The primary objective of the current work was to use their results to examine how the diffusion coefficient variation affected the drying of drops, in particular, to see if one could predict when the surface of the drop reached the glass transition state, thus establishing when the skin or crust begins to form.

Here the term

≠

+ ∇·(ρi v ) = ∇·ji

∂t

∂ρ1 ∂r

∂ρ1

=

∂t

1 r2

(

∂

ρ1,0

; D* =

Dp D0p

accounts for the rate at which the

(5)

=0 (6)

η= 0

By using a jump balance of the solvent species at the surface of the drop, it becomes apparent that the rate of change in solvent concentration at the surface is controlled by three aspects: • The mass flux at the surface: m̂ . • The rate at which the solvent is moving toward the

(1)

∂ρ

surface through diffusion:−D p ∂r1

r = R(t )

• The rate at which the radius of the drop is decreasing: ∂R −ρ1|r = R(t ) ∂t

) (2)

Thus −D p

∂ρ1 ∂r

−ρ1|r = R(t ) r = R(t )

∂R = m̂ ∂t

(7)

In dimensionless form this equation becomes −D*

∂ρ1* ∂η

−ρ1*|η = 1 R * η=1

∂R * = m̂ * ∂t *

(8)

Here the dimensionless mass flux is given by

m̂ * =

mR ̂ 0R * D0pρ1,0

(9)

Similarly, the mass jump balance for the polymer phase is ÅÄÅ ÑÉ ÅÅ D* ∂ρ2 * ÑÑÑ ∂R * Å ÑÑ R* = −ÅÅ ÅÅ ρ * ∂η ÑÑÑ ∂t * 2 ÅÇ ÑÖη= 1 (10)

ρ D pt R (t ) r ; R* = ; t * = 0 2 ; ρ1* = 1 ; ρ2 * = R0 R (t ) ρ R0 1,0

ρ2

(4)

=0

∂η

Here ρ1 is the concentration of solvent, r represents the radial distance, and Dp is the mutual diffusion coefficient in the polymer phase. The determination of the mutual diffusion coefficient in HPMCAS dissolved in acetone and methanol has been treated in detail by Sturm et al.20 The relevant equations are provided in the Supporting Information. Unfortunately eq 2 does not account for the change in radius of the drop as the solvent leaves the polymer phase and partitions into the gas phase. In spray drying the majority of the drop’s initial volume is solvent. Thus, modeling the removal of the solvent from the drop requires a more complex version of the solvent continuity equationone which accounts for the moving boundary at the surface. The first step is to transform the equation into a nondimensional form using the following: η=

)

r=0

∂ρ1*

≠

∂r

∂η

In dimensionless form this boundary condition becomes

Here ρi is the concentration of component i, t is time, v≠ is the volume average velocity, and j≠i is the mass diffusion flux for component i. The simplest form of the continuity equation occurs if the radius of the sphere does not change with time in which case it is a one-dimensional process: ∂ρ D pr 2 ∂r1

η ∂R * ∂ρ1 * R * ∂t * ∂η

∂ρ1 *

polymer phase and gas phase interface changes with time. At the center of the sphere there is no flux, and the boundary condition is

2. MODEL FOR BINARY DROP DRYING 2.1. Continuity Equation. The purpose of this work was to create a model that can be used to approximate the process of drop drying. While diffusion may not be the only mechanism of mass transfer of the components, it is expected to be the dominant one. Internal fluid circulation is assumed to be negligible due to the drop’s small size.11,17,19 The drop in this process is approximated by a sphere that can be described by a single radius. The species continuity equation is ∂ρi

(

∂ D*η2 η ∂R * ∂ρ1* 1 − = ∂η ∂t * R * ∂t * ∂η (R *)2 η2

∂ρ1*

Unlike the solvent, the polymer does not leave the drop. The polymer jump balance does not require the mass flux term. By integrating eqs 8 and 10 with respect to dimensionless time,

(3) 12292

DOI: 10.1021/acs.iecr.8b06183 Ind. Eng. Chem. Res. 2019, 58, 12291−12300

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Industrial & Engineering Chemistry Research the boundary conditions yield an expression that can be used to determine the sphere’s radius as a function of time: ÄÅ ÉÑ ÄÅ ÉÑ t2* Å t2* Å ÅÅ D* ∂ρ1* ÑÑÑ ÅÅ m̂ * ÑÑÑ 1 2 2 t * ÅÅ Ñ ÅÅ Ñ − (R *|t *1 ) = − Å ρ * ∂η ÑÑÑ Å ρ * ÑÑÑ 2 t1* Å t1* Å ÅÅÇ 1 ÑÑÖη = 1 ÅÅÇ 1 ÑÑÖη = 1

Here ktherm is the thermal conductivity. Equation 14 can be rearranged to use the Nusselt number:

(11)

2.3. Determining the Mass and Energy Flux at the Surface. Over the last few decades, drop drying has been studied for single component and multicomponent systems. For a drop where the gas phase surrounding the drop is stagnant, the evaporation rate can be determined using the Spalding mass transfer coefficient, BM (eq 20), in combination with the average gas density to capture the concentration gradient.22

∫

∂Tdrop

∫

and 2 2 (R *|tt * *1 )

ÄÅ É ÅÅ D* ∂ρ2 * ÑÑÑ Å ÑÑ = −2 ÅÅ Ñ ÅÅÇ ρ*2 ∂η ÑÑÑÖ t *1 Å η= 1

∫

∂t

t *2

(12)

p

D* is a function of D which is a function of the glass transition temperature of the polymer−solvent mixture, Tgm, which in turn is a strong function of the solvent concentration. Using the Gordon−Taylor equation21 Sturm et al.20 have developed an equation for the glass transition temperature as a function of the solvent concentration Tgm =

(13)

ρg̅ = ρg,s +

BM =

(14)

(19)

g w1,s − w1,g ∞ g 1 − w1,s

(20)

ji 1 zyzz 2 ln a1 = ln(1 − ϕ2) + jjjj1 − zϕ + χϕ2 j rseg zz 2 (21) k { Here a1 is the activity of the solvent, ϕ2 is the polymer volume fraction, rseg is the number of segments in the polymer chain, and χ is the Flory−Huggins interaction parameter. Interaction parameters were obtained by regressing the solubility data with eq 21. Sturm et al.26,27 have shown that the interaction parameters for acetone and methanol in HPMCAS are not strong functions of temperature. They found that χacetone = 0.78 and χmethanol = 0.99 did well in correlating the solubility data. • Using the ideal gas law and assuming the other component in the gas phase is only nitrogen, the weight fraction of the solvent in the gas phase is

Here ΔHv is the heat of vaporization, hg is the gas phase heat transfer coefficient, R(t) is the radius of the drop, Cp,l is the average specific heat of the liquid phase inside the drop, ρ̅l,drop is the average density of the drop, Tsurface is the temperature at the surface at the previous time step, T∞ is the temperature of the gas flow far from the surface, and m″ is the evaporation rate at the surface. The relation between the evaporation rate at the surface and the mass flux at the surface is (15)

The dimensionless Nusselt number that describes the ratio of convective energy transfer to conductive transfer is 2R(t )hg k therm

1 (ρ − ρg,s ) 3 g, ∞

• The pressure of the solvent at the surface of the drop was determined by multiplying the vapor pressure of the solvent at the temperature of the drop by the activity determined by regression of the Flory−Huggins correlation.25 For a binary solvent polymer mixture the activity of the solvent is

dT 4 ρ̅ πR(t )3 Cp,l dt l,drop 3

Nu =

(18)

Here wg1,s is the weight fraction of solvent at the surface of the drop and wg1,∞ is the weight fraction of solvent in the bulk gas phase. wg1,s was calculated as follows:

Thus,

m″ 4πR(t )2

(17)

Here ρg,s denotes the gas phase density at the surface and ρg,∞ is the gas phase density far from the drop. The average diffusion coefficient in the gas phase in this work was treated as a constant. Patankar and Spalding22 showed that the driving force for evaporation can be found using the following approximation:

• The rate of energy lost due to evaporation. • The rate of energy gained from heat transfer from the gas phase. • The amount of energy required to change the entire drop temperature.

m̂ =

4

ρl,drop πR(t )3 Cp,l ̅ 3

Here ρ̅g is the average density of the gas, D̅ g is the average diffusion coefficient in the gas phase, ShAS is the modified Sherwood number for a stagnant gas phase as proposed by Abramzon and Sirignano,23 and BM is the Spalding mass transfer coefficient. The average density ρ̅g was calculated using the approximation of Yuen and Chen24 known as the rule of thirds:

They provide all the constants needed for relevant systems. This equation designates the concentration when the glass transition occurs. From the model, the location and time of this critical concentration can be determined. Further details are given in the Supporting Information. 2.2. Energy Balance. The drop temperature is assumed uniform until the crust begins to form. This assumption is reasonable since the thermal diffusivity in the system is 3 orders of magnitude faster than the mass diffusivity, creating a negligible gradient throughout the drop.13,19 The temperature of the drop as a function of time is controlled by three mechanisms:

= m″ΔH v + 4πR(t )2 hg (T∞ − Tsurface)

m″ΔH v + 2πR(t )Nu·k therm(Tgas − Tdrop)

m″ = 2πρg̅ Dg̅ R(t )ShAS ln(1 + BM )

ω1Tg1k GT + (1 − ω1)k GT ω1k GT + (1 − ω1)

=

(16) 12293


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Industrial & Engineering Chemistry Research w1g

=

P1 MW1 P1 MW1

+

P2 MW2

Thus, the governing equation is a nonlinear partial differential equation. The well-established finite volume method (FVM) which approximates the governing equations with a series of algebraic equations was used to solve the equations. The method requires that the governing equations be broken down into a series of nonlinear algebraic equations and then the governing equations be discretized. That is, the nonlinear partial differential equations are approximated by evaluating them at various discrete points in time and space also known as nodes. A Taylor series expansion is employed to approximate the PDE at each node. For all simulations shown below the governing equations were solved using the backward Eulars model. Vrentas and Vrentas29 provided the following function for grid spacing in spherical coordinates:

(22)

Here Pi and MWi are the partial pressures and molecular weights of nitrogen (2) and the solvent (1). The Sherwood number represents the ratio of the convective and diffusive mass transport rates. If the gas phase is stagnant, the Sherwood number for a sphere is 2. When the gas phase is not stagnant, Clift et al.28 provide an approximation for the average Sherwood number around a sphere as Sh = 1 + (1 + ReSc)1/3 f (Re) l 1 Re ≤ 1 | o o o f (Re) = o m } o o 0.077 o Re 1 < Re ≤ 400 o n ~

(23)

Here

ηi =

(24)

(Sh − 2) FM

(25)

where FM is a correction factor FM = (1 + BM )0.7

log(1 + BM ) BM

(26)

The Reynold’s number, Re, can be calculated by Re =

2R(t )ρg̅ vg μg

(27)

Here vg is the velocity of the gas and μg is the viscosity of the gas phase. The Schmidt number can be calculated as μg Sc = ρg̅ Dg (28) For determining the heat flux of a system, the Nusselt number, Nu, is analogous to the Sherwood number. The Nusselt number is the ratio of convective to conductive heat transfer across a boundary. Similar to the approximation for the Sherwood number, the Nusselt number can also be approximated by Nu = 1 + (1 + RePr )1/3 f (Re)

(29)

3. EXPERIMENTAL METHOD There are a number of single drop methods reported in the literature: pendant, sessile, acoustic, and free falling.1 In the current study both the pendant drop and acoustic suspended drop methods were used. In the latter method the drop is suspended in an acoustic field. This approach has the advantage that the drop is suspended freely in the air and the mass and morphology can be monitored. The acoustic waves, however, affect the heat transfer and the shape of the drop. A pendant drop is easy to stabilize and also allows the monitoring of the mass and morphology of the drop. However, it also has some disadvantages: the drops do not rotate freely, and the thermocouple or other suspension device may provide

Here f(Re) is given by eq 24. The Prandtl number, Pr, can be calculated as Pr =

Cp,gμgas k therm

(31)

Here N is the number of discretization points, ηi is the dimensionless radius for point i, and Ω is a parameter which adjusts the degree to which the points are distributed. The details of the solution method are presented in the Supporting Information and in ref 27. 2.5. Limitations of the Model. There are limitations to this model. The first is that the diffusion is assumed to be Fickian. Thus, the mass transport in the model does not take into account any relaxation of the polymer chains, nor does it account for the buildup of stresses in the polymer drop due to the glass transition. The model assumes that the specific volumes of the components are constant, but in reality the specific volumes of the solvent and polymer are functions of temperature. Other factors such as dispersion effects due to the porous nature of the crust are not considered. After the surface of the drop undergoes the glass transition, the drop begins to warm due to a reduction in evaporative cooling as the mass flux at the surface is reduced. This could produce a stress at the surface of the drop as the solvent-rich region at the center of the drop begins to expand. Assuming that the drop remains spherical in nature is a fatal flaw if one were to use the model for the entire drop drying process. To truly capture the entire drying process, a model is required which does not rely on symmetry and can characterize any shriveling exhibited by the drops. This work chose to use Abramzon and Sirignano approximation to the Sherwood number, which has previously been applied to spray drying models. A more accurate model for drops dried using acoustic levitation may result from using Sherwood numbers which take into account the acoustic waves amplitude and frequency as described by Yarin et al.30

In reality the velocity field around the drop is not uniform, and the approximation of Clift et al.’s lumps the differences in convective and diffusive rates at the surface of the drop into one average Sherwood number. Abramzon and Sirignano23 provide a further modification to the effective Sherwood number for nonstagnant gas phase. ShAS = 2 +

1 − e−[(i − 1)/(N − 1)Ω] 1 − e−1/ Ω

(30)

Here Cp,g is the specific heat of the gas. Abramzon and Sirignano provide a modification for the Nusslet number similar to that of the Sherwood. 2.4. Solution of the Equations. As mentioned previously and detailed in the Supporting Information, the mutual diffusion coefficients for systems below their glass transition temperature are strong functions of solvent concentration.20 12294


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the equations to describe the mass flux at the surface from the polymer phase to the gas phase. The surface concentration is controlled by the mass flux and the mutual diffusion coefficient. Determining the surface concentration at the time when the change of the radius abruptly stops indicates the formation of a polymer-rich crust. Figure 2 compares the experimental drop diameters (points) and those predicted by the model (solid line) for a set of

a heat source. Nonetheless a pendant drop provides valuable data for the evaluation of drying models.31 With either method the diameters are an order of magnitude larger than in a typical spray dryer, The pendant experiments were performed by using a 50 μL syringe to drop cast a polymer−solvent solution onto a thermocouple with a 0.62 mm diameter. The initial percent weight of polymer in the solution ranged from 6% to 13% polymer. The flow rate of air past the polymer−solvent drop was determined by a flow meter and ranged from 0.4 to 3.0 m/ s. In all cases the air was solvent free. The air temperature was determined individually for each experiment and did not deviate out of the range of 18−20 °C. The diameter of the drop was determined using a cathetometer connected to a web camera. The dynamic behavior was recorded using the open source computer vision library, OpenCV.32 After the drop was formed, recording was initiated, and the background image previously recorded was subtracted from each frame. The diameter of the drop was determined from the contour of the drop with a resolution of 0.01 mm (Figure 1). The program records the time of each

Figure 1. Example of drop image with bounding box used to determine diameter.

frame along with its height and width. At early times all the drops were near spherical in shape. The rate of change in radius was constant until a distinct plateau occurred. The radius then remained constant until large scale deformations began to occur. The acoustic levitation data were determined using a Niro’s Drop Kinetic Analyzer. This method was used only to study drops containing 0.94 weight fraction acetone and 0.06 weight fraction HPMCAS at 30 and 45 °C. As in the case of the suspended drops, the diameter and morphology were monitored by a camera and image analysis software.

Figure 2. HPMCAS−acetone drops at 20 °C with 0.94 weight fraction acetone and a dry air velocity of 0.4 m/s at varying temperatures. Experimental datapoints; model predictionsolid line. The end of the line indicates the glass transition point.

4. RESULTS 4.1. Prediction of When the Glass Transition Occurs: Experiment versus the Model. The goal for the simulations was to accurately predict when and where the glass transition occurred. This is also when the geometry of the drops deviates from being spherical. The model determines this condition when eq 13 is satisfied. The drop drying behavior was studied at various starting weight fractions of HPMCAS (0.06−0.13), airflow rates (0.4−3.0 m/s), and temperatures (20−45 °C). A comparison of the rate of change in diameter of the sides of the drop with the FVM solution was used to evaluate the ability of

acetone−HPMCAS experiments that have the same starting weight fraction of acetone and air velocity while the temperature of the gas was varied. The experiment conducted at 20 °C was conducted with the pendant drop method, while the experiments at 30 and 45 °C were performed by the levitation method using the Niro’s Drop Kinetics Analyzer. The starting drop size was the same order of magnitude for all the experiments, although not exactly the same. The points 12295


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Industrial & Engineering Chemistry Research where the solid lines stop represent the times at which the surfaces of the drops undergo the glass transition as determined by eq 13. There is good agreement between the time at which the glass transition occurs at the surface of the drop as determined by the model and the experimental time when the rate of change in diameter of the drop changes. This confirms the onset of the glass transition at the surface of the drop is an excellent criterion for when a polymer-rich crust develops. The experimental data shows that the time at which the polymer-rich crust formed decreased with increasing temperature. Figure 3 shows results for three acetone−HPMCAS drop drying experiments at constant temperature and air velocity. The starting concentrations of HPMCAS in the drops were 0.06, 0.10, and 0.13 weight fraction. The initial drop size was similar between experiments. In these experiments, the initial

drying rate of the drops was constant, but as the initial weight fraction of the polymer increased, the time at which the polymer crust formed decreased. The model did an excellent job of predicting both the rate of change of the diameter and when the polymer crust is formed. Figure 4 provides a comparison of the drying of three acetone−HPMCAS drops. These drops were dried at a

Figure 4. HPMCAS−acetone drops with 0.94 weight fraction acetone at 20 °C and varying velocities of solvent-free air. Experimental datapoints; model predictionsolid line. The end of the line indicates the glass transition point.

constant temperature and constant starting weight fraction of acetone, but the air velocity was varied. As the air velocity increases so does the Reynolds number, and, thus, the mass flux at the surface increases. This is shown in both the experimental data and the model solutions by the slope of diameter versus time increasing with increasing air velocity up to the onset of the glass transition. Similar to the previous comparisons, the polymer-rich crust forms in the experimental

Figure 3. HPMCAS−acetone drops at 20 °C and a solvent free air velocity of 0.4 m/s at varying starting weight fractions of HPMCAS. Experimental datapoints, model predictionsolid line. The end of the line indicates the glass transition point. 12296


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• Increasing the air velocity increases the drying rate and decreases the amount of time required for a polymerrich crust to form at the surface. A comparison of Figures 3 and 5 clearly shows that the drying rate of the drops of methanol was much slower than that for the acetone containing drops. This is expected since methanol is less volatile than acetone As shown by the experimental data and the terminal point of the solid lines in Figures 2−5 the time at which the polymer-rich crust formed at the surface is captured well by the model. The modeling in this work is an initial step to characterize accurately the spray drying behavior of HPMCAS. It shows that the deviation from spherical geometry is dictated by the onset of the glass transition temperature at the surface of the polymer corresponding to the sharp decrease in the rate of change of the drop diameter. Figure 6a shows an example of

data, and the glass transition temperature occurs in the model solutions at the same time. At higher air velocity the experimental data have more noise due to increased vibration of the drops at high air flow rates. Figure 5 shows the drop drying experiments conducted for methanol−HPMCAS: three experiments with constant air

Figure 6. Comparison of drying behavior of a drop drying at 45 °C with 0.94 weight fraction acetone and a solvent-free air velocity of 0.4 m/s after the polymer-rich crust forms at the surface. (a) Diameter of the drop as a function of time. (b) Concentration profiles at various times.

Figure 5. HPMCAS−methanol drops at 20 °C and a solvent-free air velocity of 0.4 m/s and varying starting weight fractions of HPMCAS. Experimental datapoints; model predictionsolid line. The end of the line indicates the glass transition point.

how the radius is predicted to change as a function of time. The model predicts that after the onset of the glass transition temperature at the surface of the drop, the mass flux does not instantaneously plateau but continues to reduce at a much slower rate. Figure 6b highlights the difficult task of modeling the concentration profile at the surface of the drop at later times where it falls off very rapidly. 4.2. Predictions of the Model for Different Initial Conditions. The model simulations can be used to characterize some generic conditions as the drops dry. Figure 7 shows the weight fraction, the temperature, and the diffusion coefficient at the surface of the drop as a function of time for an acetone−HPMCAS drop starting with 0.94 weight

velocity and air temperature, with the starting concentrations of HPMCAS varying from 0.06 to 0.10 to 0.13 weight fraction. A comparison of the experimental data and the model provides the same observations as seen in the acetone−HPMCAS system: • Increasing initial weight fraction of HPMCAS has no effect on mass flux at the surface but does decrease the amount of drying time required to form the polymer skin at the surface. 12297


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Figure 8. Simulation of the time required for various size drops of HPMCAS−acetone to undergo the glass transition at the surface for an 80 μm drop starting at 0.94 weight fraction acetone and drying at 20 °C.

glass transition at the surface on a log−log plot. At constant Sherwood number, temperature, and concentration of the solvent in the gas phase, the time at which the drop’s skin forms shows a scaling relationship with starting radius, with a power of approximately 2 (ΔR2 ∝ Δt). The time at which the surface goes through the glass transition for an HPMCAS− acetone drop starting with 0.94 weight fraction acetone and a diameter of 80 μm drying at 20 °C is only 0.084 s. This is much quicker than the 44 s required for a drop that has a starting diameter of 1920 μm. For the Sherwood number to be constant between the two different drop sizes the air velocity must be 20 times larger for the smaller drop. The early time evaporation rate is significantly reduced by having a residual concentration of solvent in the gas phase. Due to the slower mass flux at the surface, the time at which the surface undergoes the glass transition increases with increasing solvent concentration, but the size of the drop is smaller when the surface undergoes the glass transition. Figure 9 provides a comparison of diameter as a function of time up Figure 7. (a) Surface weight fraction of acetone, (b) drop temperature, and (c) surface diffusion coefficient for a 1920 μm drop starting at 0.94 weight fraction acetone and drying at 20 °C with a solvent-free air velocity of 0.4 m/s.

fraction acetone and a diameter of 1920 μm at 20 °C with an air velocity of 0.4 m/s. Initially there is a rapid change in the surface concentration as the drop temperature is still decreasing due to evaporative cooling. Once the temperature achieves the wet bulb temperature of acetone, the change in concentration at the surface is fairly linear with time until the surface concentration reaches a weight fraction of 0.45 solvent. The slight deviation from being linear is due to the diffusion coefficient being a weak function of weight fraction in this range. When the solvent concentration at the surface reduces below 0.45 weight fraction, the diffusion coefficient becomes a much stronger function of the solvent concentration. In this range both the diffusion coefficient and the surface solvent weight fraction decrease rapidly. In an actual spray drying process the starting drop size is much smaller, typically around 50−100 μm. Figure 8 shows the predicted time at which various size drops undergo the

Figure 9. Simulations of drops with an 80 μm starting diameter containing an initial concentration of 0.94 weight fraction acetone at a temperature of 20 °C and a dry gas phase velocity of 8.0 m/s. The curves are truncated when the glass transition occurs at the surface. 12298


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until the onset of the glass transition at the surface for an 80 μm drop, with a starting polymer concentration of 0.94 weight fraction of acetone at various gas phase activities. As the concentration of the acetone in the gas phase increases the drop dries more slowly, increasing the time before the onset of the glass transition temperature.

5. CONCLUSIONS A finite volume model for the drying of single drops has been developed that predicts the time at which the crust begins to form on surface of the drops. The model incorporates the effects of the strong concentration dependence of the diffusion coefficient which is critical in polymer−solvent systems. The model has been applied to HPMCAS systems because of their importance in the production of pharmaceuticals. Comparison with experimental data from both pendant drop and acoustical levitated drop methods shows that the model accurately predicts the time of the crust formation for systems containing acetone or methanol at varying airflow rates, gas temperatures, and solvent concentrations. Simulation results provide insight into the rate of change of the surface weight fraction, drop temperature, and diffusion coefficient; how the diameter of the drop affects the onset of the glass transition; and how the bulk gas solvent activity affects drop drying.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b06183.

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Additional information on the calculation of the diffusivity and the FVM method used to compute the results (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ronald P. Danner: 0000-0001-8921-7801 Notes

The authors declare no competing financial interest.

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REFERENCES

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