Article pubs.acs.org/IECR
Engineering Micro/Nanoparticles by PPRGEL Process through Parametric Analysis Mriganka Mondal, Sandip Roy,* and Mamata Mukhopadhyay Department of Chemical Engineering, IIT Bombay, Mumbai 400076, India ABSTRACT: The present work investigates the formation of micro/nanoparticles by precipitation by pressure reduction of gasexpanded liquid (PPRGEL) using carbon dioxide (CO2). Rapid depressurization of the GEL solution results in very rapid evolution of CO2 bubbles and a concomitant large temperature drop (∼50−70 K). Consequently, the solid solubility is lowered, leading to heterogeneous nucleation at the CO2 bubble−GEL interface. A thermodynamic model based on the total entropy change of the depressurizing system is used for computing the time-variant reduction of the CO2 mole fraction in GEL for the CO2−acetone−cholesterol system. This, in turn, is used in a combination with a kinetic model for predicting the variation of nucleation rate and the resultant solute particle size. The model is used to analyze the effects of the pre-depressurization pressure and the depressurization time, the key process parameters, on the average particle size. The predicted particle size compares well with reported experimental data.
1. INTRODUCTION Production of micro/nano particles of uniform size is a necessity for a large section of the food and pharmaceutical industries. In recent years, processes using either subcritical or supercritical fluids, especially CO2, have been accorded preference in the production of micro/nanoparticles of uniform size over the other conventional processes, like crystallization, spray drying, and liquid antisolvent precipitation. These novel processes use CO2, as a solvent, cosolvent, or antisolvent, and are based on the principles of depressurization crystallization, antisolvent crystallization, and thermally induced crystallization. Examples include rapid expansion of supercritical solutions (RESS), particles from gas saturated solutions (PGSS), gas antisolvent (GAS), supercritical anti-solvent (SAS), solutionenhanced dispersion by supercritical fluids (SEDS), and aerosol solvent extraction system (ASES).1 These processes differ only in their modes of attaining very high and rapid supersaturation of the solid solute, required for formation micro/nano particles.2 Yet another recently developed process is precipitation by pressure reduction of gas expanded liquid (PPRGEL).3 This process uses subcritical CO2 to attain sufficiently high, rapid, and uniform supersaturation by depressurization of the CO2 gas expanded liquid (GEL) solution. The solid solute to be micronized is dissolved in a suitable solvent, and the solution is introduced in a closed vessel. Subcritical CO2 is next introduced, which progressively dissolves in the solution to form GEL. After attaining the desired pressure and temperature, the GEL is depressurized rapidly. The resultant vigorous evolution of CO2 gas bubbles from GEL leads to a drastic reduction in temperature followed by precipitation of particles. The main advantages of this process over other CO2-based processes for particle production are (a) use of subcritical CO2 at near ambient initial conditions (e.g., 4.0−7.0 MPa and 25− 30 °C), (b) operational simplicity, as it obviates the need for specially designed nozzles for spraying, (c) rapid attainment of thermally induced supersaturation as the GEL temperature drops by about 50−70 K during depressurization, and (d) © 2015 American Chemical Society
intrinsic generation of CO2 gas bubbles in large numbers, which enables attainment of uniform supersaturation of the dissolved solid solute. There are mainly two disadvantages of this process, namely, (a) possible prevalence of residual solvent in the final product and (b) the products obtained are crystalline in nature. However, these may be overcome by suitable engineering strategies. Despite its distinct advantages, the mechanistic aspects of the PPRGEL process remain inadequately explored. The present work attempts to address this gap by advancing a comprehensive mathematical model of the PPRGEL particle formation process. In particular, the model is applied to an illustrative system comprising subcritical CO2 (1), acetone as solvent (2), and cholesterol as solute (3). One of the critical parameters of the model is solid solute solubility, which requires the knowledge of both the temperature and instantaneous GEL CO2 mole fraction. Both are estimated using the present model. In previous work,4,5 the CO2 mole fraction was computed on the basis of enthalpy balance of the GEL solution during depressurization. However, in the present work, this has been calculated on the basis of total entropy change of the depressurizing system, an approach more appropriate to the PPRGEL process. Formation of particles in any precipitation process occurs in two steps: (a) the formation of nuclei and (b) their growth to form larger particles. It is well-known that the nucleation of the solid solute may occur by means of both homogeneous and heterogeneous nucleation.4,6 In the related literature,7−10 most of the nucleation and growth mechanisms have been described largely considering homogeneous nucleation of particles. In addition, the characteristic physical properties of the system are assumed to be invariant with time. However, in this work, it is Received: Revised: Accepted: Published: 3451
December 22, 2014 March 6, 2015 March 13, 2015 March 13, 2015 DOI: 10.1021/ie504960u Ind. Eng. Chem. Res. 2015, 54, 3451−3461
Article
Industrial & Engineering Chemistry Research Where
envisaged that heterogeneous nucleation plays the dominant role due to the availability of a large number of CO2 gas bubbles, which provide a gas−liquid interface. This facilitates heterogeneous nucleation even at low degrees of supersaturation, as the Gibbs free-energy barrier for the precipitation of solid solute in the solution is lowered. The present study focuses on computation of supersaturation, nucleation, and growth of the solid particles in the GEL solution during depressurization, which is further employed to predict the final average particle size. A key feature of these computations is that it also considers variations of the three-phase contact angle and of transport and other physical properties of the GEL solution over the depressurization time. In particular, the effects of the initial pressure and depressurization time on the particle size are predicted and analyzed. Finally, the model of particle formation is validated by comparing the estimated average particle size with the reported experimental values.4
s = θs Lmix + (1 − θ )sg mix
Using eq 2 and the above expression gives θ, may be expressed as θs, θs =
θV =
(3)
n nL = L nL + ng nt
(4)
Where nL and ng are the instantaneous number of moles of the liquid and gas phases, respectively. Though the liquid phase is a ternary mixture (of CO2, acetone, and cholesterol), the gas phase may be considered as a binary mixture of CO2 and acetone, since the cholesterol content in GEL is very low. Furthermore, from conservation of initial number of moles of acetone available, prior to depressurization, one can write nL =
n2i − ng y2 1 − x1
(5)
ni2
where = the initial number of moles of acetone charged, and y2 is the equilibrium vapor phase mole fraction of acetone at a given P and T. The instantaneous number of moles of liquid phase, nL, and gaseous phase, ng, are calculated from the total vessel volume, V (m3), and the molar volumes of the liquid solution and vapor phase mixture, vL and vg, respectively, as nLvL + ng vg = V
(6)
Thus,
ng =
V − nLvL vg
(7)
n2i
First considering and V, the values of nL and ng are calculated at the initial condition (t = 0), from P, T, x1, and y1 (equilibrium) data, using eqs 5 and 7, respectively. The value y2 is relatively small and is assumed to remain constant at its initial (pre-depressurization) value throughout depressurization (for example, at 5.5 MPa and 303 K, y2 = 0.006). Next, θ is calculated from eq 4. The required molar volumes are calculated using all relevant physical properties, and the ZL− Pr correlation reported by Dalvi and Mukhopadhyay.12 Following this, for the prevalent value of θ, the initial molar entropy of the system is calculated employing eq 3. While utilizing eq 3, the molar entropies of the liquid and gaseous mixtures are calculated using the pure component entropies and by assuming regular solution behavior for computing entropy of mixing at the prevalent values of P, T, and phase compositions. This particular computational procedure is explained further in the next subsection. 2.1.1. Estimation of Molar Entropy of GEL Liquid Phase Mixture (sLmix). Since the liquid phase is a mixture, for computing its molar entropy, a solution thermodynamic model is needed. As noted earlier, we assume here the regular solution behavior (i.e., ΔsE = 0). Thus, the molar entropy of the
(1)
nti
where is the total initial number of moles (before depressurization) of the solution, nt is total number of moles present in the system at any time, while si and s are the corresponding total system molar entropy (J/mol K) values. Neglecting entropy change of the vessel, nvΔsv (where nv = moles of vessel material), one obtains: si = s
s L mix − sg mix
where sLmix and sgmix are the molar entropies (J/mol K) of the liquid phase and gaseous phase mixtures, respectively. However, by definition θ can also be expressed as (denoting it as θV):
2. METHODOLOGY OF CALCULATIONS This section presents the detailed methodology for calculations of time-dependent variation of the following process parameters: CO2 and solid solute mole fractions in GEL, equilibrium solute solubility, supersaturation, and nucleation rate of the solid solute. These are, in turn, utilized in a mass transfer model to estimate the final particle size distribution, and hence, the average size. As in the experimental system,4,5 for all computations in this work, the following are considered: the vessel volume is 0.00109 m3, the initial solvent volume is 0.0001 m3 (i.e., 1.36 mol of acetone), and the initial solute (cholesterol) mole fraction is 0.00032. Carbon dioxide is dissolved in the solution such that the initial (i.e., predepressurization) pressure of the solution is less than the critical pressure (
