THE EFFECT OF SYSTEM TEMPERATURE AND PRESSURE ON THE FLUID-DYNAMIC BEHAVIOR OF THE SUPERCRITICAL ANTISOLVENT MICRONIZATION PROCESS: A NUMERICAL APPROACH

The Supercritical Antisolvent (SAS) technique allows for the precipitation of drugs and biopolymers in nanometer size in a wide range of industrial applications, while guaranteeing the physical and chemical integrity of such materials. However, a suitable combination of operating parameters is needed for each type of solute. The knowledge of fluid dynamics behavior plays a key role in the search for such parameter combinations. This work presents a numerical study concerning the impact of operating temperature and pressure upon the physical properties and mixture dynamics within the SAS process, because in supercritical conditions the radius of the droplets formed exhibits great sensitivity to these variables. For the conditions analyzed, to account for the heat of mixture in the energy balance, subtle variations in the temperature fields were observed, with almost negligible pressure drop. From analyses of the intensity of segregation, there is an enhancement of the mixture on the molecular scale when the system is operated at higher pressure. This corroborates experimental observations from the literature, related to smaller diameters of particles under higher pressures. Hence, the model resulted in a versatile tool for selecting conditions that may promote a better control over the performance of the SAS process.


INTRODUCTION
The supercritical state of a mixture is obtained when its temperature and pressure are above their critical values.Techniques for the production of micro-and nanoparticles using supercritical fluids (SCF) have been modified and explored towards diverse applications, including the pharmaceutical, Brazilian Journal of Chemical Engineering cosmetics, and food industries as alternatives to traditional fine powder production.
In the RESS techniques, the solute must be soluble in the supercritical fluid (SCF).They are characterized by a pre-expansion chamber where the mixture of solute and the SCF are pressurized and then expanded through a convergent-divergent nozzle causing a sudden pressure drop and the precipitation of the solute.
The SAS technique, which is the object of this study, is used as an alternative when the solute of interest is not soluble in the SCF and such technique requires that the organic solvent possess a greater affinity for the antisolvent than for the solute.This technique generally makes use of CO 2 and allows the processing of a large variety of high quality industrial products (Martín et al., 2007;Sanguansri and Augustin, 2006).An organic solution of solvent/solute and the CO 2 enter continuously through a coaxial capillary into a pressurized precipitation chamber pre-charged with antisolvent (CO 2 ).The solution interacts with the antisolvent, increasing the diffusion in the organic antisolvent mixture and causing the precipitation of the solute.
Among its applications, we highlight the development of biomedical materials based on prolonged liberation mechanisms, such as nanoencapsulation applied to vaccine production, allergy and even cancer treatment, e.g.(Balcão et al., 2013;Cushen et al., 2012).
In a supercritical mixture, physical properties such as density, and thermodynamic parameters such as solubility may be adjusted within a wide range of processing conditions through varying pressures, flow rate, and temperatures.The rapid transfer of mass that occurs upon injecting a solution into a fluid such as CO 2 under supercritical conditions is characterized by an elevated diffusivity and low viscosity.Such characteristics are considered beneficial to precipitating tiny spherical particles from the solute (on a nanometric scale) and necessary for their industrial application.
There are several key operational SAS parameters such as: solution and antisolvent flow rates; injection capillary length and diameter; chamber geometry; operational pressure and temperature (T 0 and P 0 ); these last two have been reported in the literature as being of special importance.More specifically, near the critical point of the mixture, the droplets formed exhibit high sensitivity to the thermodynamic coordinates T 0 and P 0 , which have great influence on the morphological changes of the precipitated substances (Reverchon et al., 2008;Werling and Debenedetti, 2000).
With respect to the variation of particle size, contradictory behavior can be found in the relevant literature.For example, increased operational pressure of the system may result in gains (Franceschi, 2009), losses (Miguel et al., 2006), or in practically no noticeable impact upon the precipitated particles (Chang et al., 2008).As to increases in operational temperature, some solutes diminish in size while others expand.These discrepancies among results depend on the physical nature of the solute and require further and more profound study (Erriguible et al., 2013b).
Modulation of the operating pressure and temperature directly influences the variation of density.In turn, this influences the dimensions or the sizes of the precipitated particles, which thus depend upon the differences in density between regions rich in organic solvent and CO 2 -rich regions.
Concerning density differences, Werling and Debenedetti (2000) utilized toluene as an organic solvent and CO 2 as an antisolvent and reported an increase in size of the particles when the solvent is denser than the antisolvent; otherwise, the particles decrease in size.This indicates a faster mass transfer from the solution to the surrounding CO 2 .
Some published studies have intended to evaluate the impact of thermodynamic coordinates on precipitated particle size (Franceschi, 2009;Franceschi et al., 2008;Imsanguan et al., 2010;Lengsfeld et al., 2000;Martín and Cocero, 2008;Miguel et al., 2006;Reverchon and De Marco, 2011).In their majority, they are experimental and designed for solute systems with specific physical-chemical properties.They are also designed for experimental adequacy to obtain good T 0 and P 0 limits for a determined system (for particular combinations of solutes and organic solvents), given the time expended to carry out several experimental runs and high material costs (Erriguible et al., 2013b).Beyond this, under high pressure, optical measurements to observe the flow patterns (as shadowgraphs or schlieren techniques) of the precipitation process may be obscured by temperature gradients, species concentration, and large numbers of very small particles that accompany flow in the precipitation chamber (Jerzy et al., 2004).This changes the way in which light passes through the flow, since the density variation may interfere with refractive indices and cause delay associated with non-homogeneity in the mid-section (Raffel et al., 1998).
Experimentally, with respect to the influence of T 0 and P 0 upon the size and formation of particles, one knows that: increased temperature keeping all other variables constant (solvent and CO 2 flows, pressure, and chamber geometry) increases the tendency to agglomerate; irregular particles (Boschetto, 2013), expanded microparticles and fibers, as well as increased particle size prevail (Reverchon and De Marco, 2011).It has also been shown that pressure increases favor obtaining smaller sized particles and a narrower distribution of sizes, given that, with increased pressure, the intermolecular distances diminish, in turn augmenting CO 2 density (viz.Table 1).The difference in density between pure ethanol and pure CO 2 decreases which results in a better mixture between the solution and the SCF, forming smaller particles (Boschetto, 2013;Franceschi et al., 2008;Reverchon et al., 2007).Contradictorily, according to Franceschi (2009) the increased pressure can result in larger particles when low levels of solvent and CO 2 flow rate are considered, as well as low initial concentration of solute in the organic solvent.
Thus, given the experimental complexity, the use the numerical simulation arises as a suitable alternative to determine the influence of operational parameters in the fluid dynamic behavior of flows within the SAS process, increasing its performance.This is an innovative approach concerning the FSC precipitation process, and it demands low cost and has the advantage of obtaining satisfactory results over a short time period (Bałdyga et al., 2010;Martín and Cocero, 2004;Sierra-Pallares et al., 2012;Werling and Debenedetti, 2000).
The numerical studies employing Computational Fluid Dynamics (CFD) seek to find appropriate conditions for spherical particle precipitation on a nanometric scale (Bałdyga et al., 2010;Cardoso et al., 2008;Erriguible et al., 2013b).However, within this scope there remains a lack of specific publications referring to the influence of operational temperature and pressure parameters upon the dynamics of the supercritical mixture.Some authors do consider the SAS process in the isothermal regime (Cardoso et al., 2008;Erriguible et al., 2013a;Martín and Cocero, 2004), while others have emphasized the influence of temperature variation (Jerzy et al., 2004;Sierra-Pallares et al., 2012).
In this sense, Martín and Cocero (2004) describe the SAS process according to a two-dimensional isothermal regime approach, modeling it as a turbulent mixture employing the standard k-ε turbulence model of completely miscible fluids, coupled to a model that predicts particle growth.In so doing, they evidenced that the flow rates and the mixture dynamics strongly influence the precipitation that occurs in an environment of great compositional variance.
Sierra-Pallares et al. (2012) also proposed a twodimensional and non-isothermal mathematical model coupled with a populational balance equation (PBE) associated with a closure model for the micromixing to describe particle sizes of β-carotene and concluded that temperature is quickly homogenized upon capillary exit.In that region there is approximately 4 K of variation; the flow pattern near the capillary exit is determined by the solution injection velocity; and the vortex generated in this region promotes the formation of intense mixture and is responsible for the mixture on macro scales.
Based on a non-isothermal approach coupled with a PBE and comparing with experimental data, Henczka and Shekunov (2005) pointed out the importance and better accuracy of models to predict particles sizes that consider the micro-mixing when compared to simulations that do not consider this physical process.
According to Erriguible et al. (2013b) in their study on the influence of pressure in subcritical conditions, increasing pressure has moderate impacts upon viscosity and significant impacts upon mixture density.They conjecture that this effect tends to remain under supercritical conditions.However, there are works in computational simulation which have modeled the SAS process in an incompressible regime (Cardoso et al., 2008;Erriguible et al., 2013a).Thus, the compressibility of the mixture in the process, as well as the impacts of pressure and temperature upon physical properties and flow patterns, has not yet been sufficiently examined and outlined.
In the cited numerical studies, there is no reference to modeling of the physical properties of the mixture, except Cardoso et al. (2008) who consider the dependence of the viscosity with the mass fractions of the solvent and the antisolvent; Sierra- Pallares et al. (2012) employed the method of Chung et al. (1988) for the thermal conductivity and the viscosity and the method of He and Yu (1998) for the diffusivity.However, there are no reports about the Brazilian Journal of Chemical Engineering influence of these assumptions on the flow dynamics or the size of the precipitated particles.
In particular, small diameter particle precipitation is directly associated with low viscosity (Bałdyga et al., 2010), and high levels of mixture diffusivity and thermal conductivity is required for proper thermal fields (Yamamoto et al., 2011).Thus, given the lack of relevant literature references concerning this aspect, it becomes important to investigate the influence of T 0 and P 0 upon these properties.
Given viscosity, thermal conductivity, and the diffusivity coefficient in the region near the Critical Point of the Mixture (CPM) as well as where 1 < Tr m < 1.5 and P > Pc m (as the conditions considered in this study), pressure exerts an effect on the mixture viscosity, which may diminish with increased temperatures.Increases in thermal conductivity in the supercritical mixture also showed themselves to be particularly sensitive to increases in pressure and diminished with temperature increases.The diffusivity coefficient is significantly affected by variations in mixture composition and high pressures with respect to the ideal gas condition (Poling et al., 2004).Thus, in typical supercritical conditions, it is important to investigate if the fluidynamic modeling of the SAS process requires consideration of adequate models in order to describe the mixture's physical properties.
In this work a mathematical model is presented to describe the SAS process fluid dynamics coupled to the turbulence model k-ε.Initially, based on Peng-Robinson's cubic equation solution, this study presents the density dependence of the mixture with respect to incremental pressure and temperature variations around their operational values.Then, based on the model's solution, the influence of values P 0 and T 0 on transport properties and upon the dynamic of flow of the binary mixture of CO 2 and ethanol was analyzed.In such analysis, the process is operated in the region of the phase diagram above CPM.In this region the mixture is found as a single phase.Finally, analysis is provided concerning the sensitivity to T 0 and P 0 on a molecular level.

METHODOLOGY
The model is represented by the system of Equations (1)-( 19) in order to describe the flow from the SAS process in steady state, considering it as compressible, non-isothermal, and in the turbulent regime because the transition from a laminar jet to a turbulent jet occurs at low Reynolds numbers (Silveira-Neto, 2002).Under the conditions considered in this study: 300 Re  for the ethanol inlet and 1500 Re  for the CO 2 inlet.ANSYS FLUENT 13.0 software was used to solve the system of equations.The chamber utilized in this study has cylindrical geometry and couples with a capillary tube in the center of the lid in a coaxial system in order to inject the ethanol and CO 2 .A two-dimensional axis-symmetric approach was considered due to the geometric circumferential symmetry, with a non-uniform cartesian mesh composed of 115.5 thousand of elements.A preliminary comparison with a three-dimensional approach employing a tetrahedral mesh with approximately 4.2 million elements presented a prohibitive computational effort in a serial run due to computational time.In a parallel run, with 5 partitions of a cluster, it took almost 90 hours when compared with the two-dimensional mesh, which took 16 hours in a serial run on a single Intel Core-i5@2.5GHzCPU and 4GB of RAM memory.

Equation of State PVT
The density of the CO 2 and ethanol mixture was described by the Peng-Robinson equation of state (PREOS), employing the van der Waals quadratic mixing rule.

  , (
) where P is the absolute pressure, V [m 3 mol -1 ] is the molar volume, T is the temperature, a m and b m are the PREOS mixing parameters calculated using the following rule of mixture: , , y i is the mole fraction of component i and the parameters a ij and b ij are calculated using the following combination rules: Chemical Engineering Vol. 33, No. 01, pp. 73 -90, January -March, 2016 k ij and l ij are the binary interaction parameters.Here, the following literature values obtained from (Franceschi, 2009) were used: k 12 =0.0703and l 12 = -0.0262.In the above equations, a i and b i are the parameters of the pure species.These parameters were determined using: where Tc and Pc are the critical temperature and pressure of species i, respectively; i i Tr T Tc  is the reduced temperature; and i  is the acentric factor of species i.

Viscosity
Each component's viscosity was calculated for each T 0 and P 0 as displayed in Table 1 based on Chung's rule as described by Chung et al. (1988).Chung's method takes density and high pressures into consideration.The mixing rule given by Equation (6) (Bałdyga et al., 2010) was employed in order to obtain the mixture viscosity.

Thermal Conductivity
To calculate the thermal conductivity of the mixture, , Chung's method was used (Chung et al., 1988), as it considers density at high pressures and viscosity at low pressures: where M is the molecular weight of the mixture, 0 [ .] Pa s


is the low pressure viscosity; ω m the acentric factor of the mixture and c v is the heat capacity at constant volume; R is the universal constant for gases; 6 y Vc V  with Vc being the critical volume of the mixture in [cm 3 mol -1 ].The factors

 
, , , , , are correction functions described in Chung et al. (1988), and D i are functions dependent on the mixture's acentric factor, as well as a correction factor for polar substances as described in Poling et al. (2004).

Diffusivity
According to Riazi-Whitson's equation (Riazi and Whitson, 1993), one can determine the diffusivity coefficient.This relationship, which considers viscosity of the mixture µ m as in Eq. ( 6), density of the mixture at low ρ 0 and density of the mixture at high pressures ρ, is given by: Here x 1 and x 2 are the mole fractions of ethanol and CO 2 , respectively.Also, in Eq. ( 8) Pc m is the critical pressure of the mixture, D 0 is the diffusivity coefficient of the mixture at low pressure.For simplicity, the mixture density at high pressures was established using Eq. ( 1), setting the operational pressure and the temperature to be T 0 and P 0 for each case of Table 1 and varying the mixture composition.Then, each case was described by a sixth-degree polynomial as a function of the CO 2 mole fraction obtained by polynomial interpolation.

Governing Transport Equations
With the intent to describe the SAS process, a model based on the mass-weighted Reynolds-averaged Navier-Stokes equations (RANS) was proposed.Some fundamental assumptions can be taken into account to correctly describe the fluidynamics of the formed jet and the mass transfer:  the supercritical fluid phase under turbulence conditions can be represented by the mass-weighted Reynolds-averaged Navier-Stokes equations (massweighted RANS);  the compressible flow can be analyzed under steady-state;

Brazilian Journal of Chemical Engineering
 there is a complete miscibility between the organic solvent and antisolvent;  the eddy viscosity hypothesis is assumed;  energy and chemical species balance equations were included;  Wilcox, 1993), Based on the hypotheses presented above, the conservation equations are given as follows: where  represents the density of the mixture and  i u are the velocity vector coordinate.
Momentum Balance Equation where the term ij  represents the Reynolds stress tensor and 2 3 where  h is the enthalpy of mixture is the effective thermal conductivity and k J  is the diffu- sive flux of the species.In this study, the energy variation due to the mixture enthalpy variation is accounted for in Eq. ( 11) by the source term S h (Jerzy et al., 2004): The dependence of mixture heat Q m with the concentration is calculated using the Peng-Robinson equation.S h is inserted as part of the energy equation in a subroutine as a user defined function (UDF) (ANSYS, 2010).

Chemical Species Balance Equation
where Y i is mass fraction of the i ih specie, is the turbulent diffusivity coefficient, Sc T is the turbulent Schmidt number equal to 0.7.The turbulence model incorporates two differential transport equations into the resulting system of equations, one is for turbulent kinetic energy k and the other is for the dissipation rate of turbulent kinetic energy ε (Wilcox, 1993), for the k-ε turbulence model Transport equation for the mixture fraction In Eq. ( 14) f is the mixture fraction, which represents the mass fraction of fluid fed into the system from a chosen point (Fox, 2003) and is given by: Brazilian Journal of Chemical Engineering Vol. 33, No. 01, pp. 73 -90, January -March, 2016   , can be understood as the deviation from the locally perfect mixture state, that is, the mixing process can be understood as the dissipation of such variance (Fox, 2003;Jerzy et al., 2004).The transport equations 2  are consid- ered and inserted into the system of equations as user defined scalar -UDS -transport equations (ANSYS, 2010).Such equations are given, respectively, by: Transport equation for the mixture fraction variance The term S  in Eq. ( 16) was entered via a subroutine as a UDF in the ANSYS FLUENT software.
The k-ε turbulence model transport differential equations based on turbulent viscosity are (Launder and Spalding, 1974): and Dissipation rate of turbulent kinetic energy ε In Eqs.(17 and (18) P k is a production term of turbulence due to the viscous forces; the constants, , and are closure constants found based on the correlation of experimental data.All mathematical derivations and the physical basis of the model can be found in detail in Rezende, R. V. d.P. (2008).

Operational Conditions and Boundary Conditions
Operational temperature values were considered in the range of 308 -320 K. Operational pressure 0 P was tested at 80 bar and 120 bar per conditions displayed in Table 1.The values for density calculated using the Peng-Robinson equation employed in Eq. ( 8) of the diffusivity coefficient and the values calculated for pure component viscosities, using the Chung method for Eq. ( 6) of the mixture viscosity are also listed in Table 1.
Under all cases, inlet boundary conditions considered were operating temperature T 0 and mass flows rate: 1.1x10 -4 kg/s for CO 2 and 1.2x10 -5 kg/s for ethanol and the outlet boundary condition was considered to be zero pressure.Turbulence intensity was considered to be 5% (medium intensity) as the inlet and outlet boundary conditions.The finite v solve the sy LUENT 13.0 sted of solvin riable one at non-lineariti gregated solu The SIMPL essure-veloci iteria were im RMS) of less osure for m fferences bet tes were of th gure 3: Solu ted solver (A The solutio d presented g the comple obtain conv ally adding Almeida, 2013 Step 1 -on omentum eq es transport e Step 2 -if c Step 3 -onc vate the equ mixture fractio

RES ensity Depen ifferentials
The Peng-R ons (1)-( 5   From entr or turbulent rees) for cir rofile follow 2013).In the he jet was de Figure 5 and The aperture Table 1 was

Pressure Var
Under bot idered, P 0 = ressure was ated.This v apillary, as s he chamber, The greate ube under bo urred at the Pressure varia een well stud ion and grow

Physical Prop ty and Diffu
Viscosity, oefficient of These three pr he small regio  The k-ε tu nto account btained with Analyses of hermal cond atio, were pe etween the e.,     In

a
Newtonian fluid was considered.It is convenient for compressible flow, to consider the density-weighted Favre average.Given a ϕ flow variable, one considers  represents the Reynolds temporal average for density.The field variable can be decomposed as the sum of its mean value and its fluctuation " ' Y  are the mass fractions of CO 2 in the CO 2 inlet and in the solvent inlet, respectively.Mixture fraction variance, 2 Figure 4 temperatu Figure 5: 2013) and

Figure
Figure 9: Pr within the cha Figure 11 Fig rat for ringVol.33, No.
Fig inj (b) ser Dynamic viscosity of the mixture [Pa.s] ρ Mixutre density [kg m -3 ] ω m Acentric factor of the mixture