Jet Breakup and Droplet Formation in Near-critical Regime of Carbon

Chemical Engineering Science 63 (2008) 3366 -- 3378

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Chemical Engineering Science

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Jet breakup and droplet formation in near-critical regime of carbondioxide--dichloromethane system

Lai Yeng Leea,1, Liang Kuang Lima,1, Jinsong Huab, Chi-HwaWanga,∗aDepartment of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, SingaporebInstitute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn Singapore Science Park II, Singapore 117528, Singapore

A R T I C L E I N F O A B S T R A C T

Article history:Received 8 December 2007Received in revised form 7 April 2008Accepted 7 April 2008Available online 11 April 2008

Keywords:ComputationSupercritical fluidVisualizationDroplet formationParticle formationMultiphase flow

The jet breakup and droplet formation mechanism of a liquid in the near-critical conditions of asolvent--antisolvent system is examined with high-speed visualization experiments and simulated usinga front tracking/finite volume method. The size of droplets formed under varying system pressure atvarious jet breakup regimes is measured with a Global Sizing Velocimetry, using the shadow sizingmethod. A stainless steel nozzle with 0.25mm I.D and 1.6mm O.D was used in this study. Experimentswere performed at fixed temperature of 35 ◦C and system pressure in the range from 61 to 76bar inthe near-critical regime of the DCM--CO2. At the near mixture critical regime for DCM--CO2 mixture, themiscibility between the two fluid phases increases and the interfacial tension diminishes. This phasebehavior has important applications in particle formation using gas antisolvent (GAS) and supercriticalantisolvent (SAS) processes. The jet breakup and droplet formation in the near-critical regime is stronglydependent on the changes in interface tension and velocity of the liquid phase. An understanding of thedroplet formation and jet breakup behavior of DCM--CO2 in this regime is useful in experimental designfor particle fabrication using SAS method.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Particle formation is an important application of supercriticalfluid technology (Jung and Perrut, 2001). Properties of supercriticalfluids that favor particle formation include liquid-like density andgas-like viscosity (Richard and Dechamps, 2004). The well knowntechniques for particle formation using supercritical fluids includethe rapid expansion of supercritical solutions (RESS) (Jung andPerrut, 2001; Richard and Dechamps, 2004; Tom and Debenedetti,1991; Debenedettiet al., 1993) and the gas/supercritical antisolvent(GAS/SAS) processes (Jung and Perrut, 2001; Richard and Dechamps,2004; Tom and Debenedetti, 1991; Randolph et al., 1993;Subramaniam et al., 1997; Chattopadhyay and Gupta, 2001a,b,2002a--c; Reverchon et al., 2003; Henczka et al., 2005).

Carbon dioxide (CO2) is used extensively as a supercritical fluidin particle fabrication and pharmaceutical applications, which isattributed to its desirable properties such as relatively accessiblecritical point at temperature of 31.1 ◦C and pressure at 73.8 bar,

∗ Corresponding author. Tel.: +6565165079; fax: +6567791936.E-mail address: [email protected] (C.-H. Wang).1 The authors have equal contributions to this work.

0009-2509/$ - see front matter © 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2008.04.015

abundance and its low toxicity (Jung and Perrut, 2001; Richard andDechamps, 2004; Tom and Debenedetti, 1991). Since most organicsolvents are miscible with CO2 at supercritical conditions, a lowresidual solvent content can be easily achieved in the final productwithout extensive downstreampurification to remove excess organicsolvent (Ruchatz et al., 1997). In particular, the SAS process has beenused in numerous studies for pharmaceutical products. In the SASprocess, the substrate of interest is first dissolved in a suitable organicsolvent. The organic solution is then injected into supercritical fluidwhich acts as an antisolvent by rapid mass transfer, resulting inprecipitation of the substrate.

Several factors may affect the particle size and propertiesachieved from SAS process. This includes the phase behavior of theternary mixture and the hydrodynamics of the solution injected intothe supercritical phase. Considerable literature suggests that thecontrolling parameter for particle size in the SAS process is the rateof mass transfer (Reverchon et al., 2003; Henczka et al., 2005). Thisis influenced by both the spray hydrodynamics of the organic solu-tion and thermodynamic properties of the supercritical fluid phase.Perez de Diego et al. (2005) reported the mechanism of particleformation in subcritical and supercritical regimes for precipitationfrom compressed antisolvent (PCA) process. The jet disintegrationmechanism for operation in subcritical and supercritical conditions

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L.Y. Lee et al. / Chemical Engineering Science 63 (2008) 3366 -- 3378 3367

was different and hence particles properties were also different. Theeffect of flow rate on particle size in the subcritical regime wasreported. Carretier et al. (2003) investigated the hydrodynamics ofthe SAS process by evaluating the macro and micromixing withinthe precipitation vessel.

It was observed that most studies on SAS were carried out inatomization of a gaseous plume mode in the turbulent jet regime(Carretier et al., 2003; Shekunov et al., 2001). Varying parameterssuch as nozzle diameter, solution flow rate, pressure and temper-ature have no significant effect on the size and size distribution offinal particles obtained. Final particle size achieved is mainly depen-dent upon the extent of mixing between the organic solvent and CO2phases. Smaller and more uniform sized particles could be achievedusing coaxial (Henczka et al., 2005) and ultrasonic nozzles (Randolphet al., 1993; Subramaniam et al., 1997) which provides better mixingbetween the two phases.

The dichloromethane (DCM)--CO2 system is one of the most com-monly used for fabrication of polymeric particles using SAS process(Perez de Diego et al., 2005; Gokhale et al., 2007; Obrzut et al., 2007),and the various flow regimes in the free jet of DCM in CO2 have beenreported (Kerst et al., 2000). DCM is a good solvent for Poly L lactide(PLA) and several other pharmaceutical compounds. The mixturecritical pressure of DCM--CO2 at 35 ◦C is 78bar (Gokhale et al., 2007)with a composition between 1.0 and 1.9mol% DCM in CO2 (Reaveset al., 1998). In this work, the droplet formation and breakup of DCMjet in CO2 is studied. By operating in the regime close to the mixturecritical point (MCP) of DCM--CO2 system, and with careful manipu-lation of the Reynolds number of the liquid phase, it is possible toachieve dripping or Rayleigh disintegration of droplets where moremonodispersed droplets could be achieved. In the dripping mode,the droplet size is a very strong function of the interface tension be-tween the two phases. In the Rayleigh disintegration mode or jettingmode, droplet size is approximately 1.5 times the jet diameter.

2. Materials and methods

2.1. Materials

Compressed CO2 (Air Liquide Paris, France) was purchased fromSoxal (Singapore Oxygen Air Liquide Pte Ltd.). DCM (DS1432, HPLCgrade) was purchased from Tedia (Fairfield, OH, USA). PLA was pur-chased from Sigma Aldrich (St. Louis, MO, USA).

2.2. Experimental setup and visualization

The experimental setup used in this study is shown in Fig. 1.Liquefied CO2 (C1, Polyscience refrigerating circulator) was intro-duced into the high pressure vessel (HP, Jerguson 12-T-32, 70 cm3)by means of a high pressure pump (P2, Jasco HPLC pump) to the re-quired pressure. The temperature in the vessel was controlled and

P1

V1BPRF2

CO2

P2

C1

C2

HP

V2

Fig. 1. Experimental setup. P1, P2: pumps for the polymer solution and liquifiedCO2, respectively. HP: high pressure vessel. C1, C2: temperature controllers. BPR:back pressure regulator. F2: flowrate regulator. Temperature of the setup for dropletand particle formation studies was fixed at 35 ◦C.

maintained at 35 ◦C by use of a circulating heated water bath (C2,Polyscience 712 circulator). The system pressure used lies in thenear-critical regime of DCM--CO2 from 61 to 76bar. The compositionof the antisolvent phase in the vessel is maintained at 0--1% DCM inCO2 at all times.

The high pressure vessel used in this study has two parallelborosilicate glass windows which allow visualization along the en-tire length of the vessel during the antisolvent process. Highmagnifi-cation images were captured with a digital SLR camera (D2H, Nikon,Japan) with a macro lens (105mmMicro Nikkor, Nikon, Japan). High-speed camera was (FastCam PCI, Photron Inc., USA) used with thesamemacro lens to capture consecutive snapshots during the dropletformation process. The high-speed camera can capture images up to2000 frames per second. Shadow sizing system (Dantec Dynamics,Denmark) is used for measurement of DCM droplet size during theSAS process. This system is equipped with a high sensitivity cam-era (Highsense MKII, Dantec Dynamics, Denmark) and is operatedbased on backlighting with laser light and image analysis softwarewith an advanced edge detection algorithm (FlowManager PC, Dan-tec Dynamics, Denmark).

2.3. Numerical simulation

In order to aid the current investigation, numerical simulationwas employed to study the formation process of the dripping modeand the Rayleigh disintegration mode. The two-fluid system consist-ing of a liquid jet emerging from a nozzle into a gaseous mediumis modeled in this study. A two-dimensional (2D) axis-symmetriccylindrical-coordinate system was used, and the numerical simula-tion was done using a front tracking/finite volume method.

2.3.1. Front tracking/finite volume methodThe recent development of a front tracking/finite volume method

for multiphase flow simulation has provided a novel and robustmethod to treat the moving interface between two fluids with largedensity difference (Unverdi and Tryggvason, 1992; Hua and Lou,2007). In this study, the front tracking/finite volume method pro-posed by Hua and Lou (2007) is modified to take into account thechanges in the surface tension when the MCP of the DCM--CO2 sys-tem is approached. In this method, a stationary fixed backgroundmesh is used throughout the whole computational domain, and aset of adaptive front mesh is used to mark the moving interface.Only one set of the momentum and continuity equations is solved inthe whole computational domain by treating the different phases asone single fluid with variable material properties. The distributionsof physical properties such as density and viscosity are calculatedaccording to the position of the interface and the property differ-ence between two fluid phases. The physical properties of the bulkphases of DCM and CO2 (at 35 ◦C) used in this study are summarizedin Table 1. The surface tension stress is computed on the front meshand then distributed to the fixed background mesh through the useof a dirac-delta like distribution function as a body force term inthe momentum equation. The position of the interface is advectedexplicitly with the velocity interpolated from the flow field on the

Table 1Summary for physical parameters of CO2 and DCM at 35 ◦C

DCM properties at 35 ◦CDensity, �L (kgm−3) 1289Viscosity, �L (Pa s) 3.7 × 10−4

61bar 71bar 76bar

CO2 properties at 35 ◦CDensity, �G (kgm−3) 160 220 270Viscosity, �G (Pa s) 2.81×10−4 3.83×10−4 4.24×10−4

Interfacial tension coefficient, � (Nm−1) 5.359×10−3 2.230×10−3 1.126×10−3

3368 L.Y. Lee et al. / Chemical Engineering Science 63 (2008) 3366 -- 3378

background gird. Such method has been applied successfully to var-ious interfacial flow problems (Tryggvason et al., 2001).

2.3.2. Governing equations and boundary conditionsThe flow field simulation is formulated by solving the govern-

ing equations of mass conservation and the momentum equations.Assuming the system to be isothermal, both liquid phase and gasphases can be considered as incompressible. Hence, the mass con-servation of the whole domain for both the gas phase and the liquidphase can be expressed as

∇ · ⇀u ∗ = 0 (1)

where⇀u ∗ is the velocity of the fluid.

To take into account the surface tension on liquid--gas inter-face (F∗

ST), an additional interfacial force term is included in the

Navier--Stokes equation. The governing equation for momentum

conservation can be expressed as

��∗ ⇀u ∗

�t∗ + ∇ · �∗ ⇀u ∗ ⇀

u ∗ = − ∇p∗ + ∇[�∗(∇ ⇀u ∗ + ∇ ⇀

u ∗T)]

+ (�∗ − �∗g)

⇀g ∗ + F∗

ST (2)

where �∗ is the density of the fluid, p∗ is the pressure, �∗ is the

viscosity of the fluid,⇀g ∗ is the gravitational acceleration. Subscript

g refers to the gas phase (CO2).The surface tension force on the twophase interface can be cal-

culated as follows on the front mesh:

F∗ST,f

=∫f�∗�∗

f

⇀n f �(x∗ − x∗

f)�(y∗ − y∗

f)ds∗

f(3)

where �(x∗ − x∗f) and �(y∗ − y∗

f) are the dirac-delta functions in the

x and y directions of the space coordinate system. �∗ is the surfacetension coefficient, �∗

fis the curvature of the interface.

2.3.3. Interface treatment and trackingTo solve the momentum equation in the whole domain, the vary-

ing physical properties of the fluid, which includes the gas phase andthe liquid phase, must be taken into account. Although the physicalproperties are considered to be constant in each phase, there is achange in the physical properties across the interface. The novelty ofthe front tracking/finite difference method, proposed by Tryggvason,is that the interface, i.e. the moving front, is considered to have afinite thickness of the order of the mesh size, instead of having zerothickness with sharp jump of fluid properties. In the region nearbythe interface, the physical property changes smoothly and continu-ously from the value on one side of the interface to the value on theother side of the interface. The thickness of the interface thus de-pends on the grid size and is kept constant during the computation.Thus, the governing equations could be solved in the whole domainswith variable property for both liquid and gas phases. In the fronttracking method, the field distribution b( x⇀, t) of the physical fluidproperties throughout the whole domain can be calculated through

b( x⇀, t) = bg + (bl − bg) · I( x⇀, t) (4)

where bl is the properties in the liquid phase (DCM), bg is the proper-ties in the gas phase (CO2) and I( x⇀, t) is an indicator function whichhas a value of one in the liquid phase and 0 in the gas phase. The

indicator function can be written in the form of an integral over theregion where the liquid phase lies

I( x⇀, t) =∫�

�(x − x′)�(y − y′)dx′ dy′ (5)

where �(x − x′) is a delta function that has a value of one on theinterface and zero everywhere else. x and y represent the two spatialcoordinates in the system. dx′ dy′ is the differential area that coversthe region (�) where the inner liquid phase exists.

It is well known that it is difficult to implement the dirac-deltafunction numerically. Hence, a distribution function D( x⇀) is used toapproximate the delta function and to estimate the fraction of thephysical properties distributed across the artificial thickness ofthe interface. As a result, there is no sharp jump in the value of thephysical properties crossing over the interface. In this study, thedistribution function given by Peskin (Peskin, 1977; Peskin andPrintz, 1993) is used:

D( x⇀ − x⇀f) =

{(4h)−2

(1 + cos

( �

2h(x − xf )

))·(1 + cos

( �

2h(y − yf )

)), if |x − xf | <2h; |y − yf | <2h

0, otherwise(6)

where h is the grid size.Taking the gradient of the indicator function I(x, t), a gradient

function G( x⇀, t), showing the changes cross the interface (), is givenas follows in an integral form:

G( x⇀, t) = ∇I( x⇀, t) =∫

�(x − x′f)�(y − y′

f)⇀n f ds′

f

=∑f

D( x⇀ − x⇀f , t)⇀n f �sf (7a)

where⇀n f is the unit normal vector at the interface at an interfacial

elementwith an area of �sf whose centroid is x⇀f . Thus, the followingPoisson equation can be used to reconstruct the indicator functionI( x⇀, t), which will be used in Eq. (4) to calculation fluid propertydistribution on the background mesh for the fluid flow:

∇ · ∇I( x⇀, t) = ∇ · G( x⇀, t) (7b)

In a similar manner, the interface tension force calculated usingEq. (3) on the front mesh can be distributed to the backgroundmesh using the distribution function for the solution of momentumequation (2):

F∗ST ( x⇀) =

∑F∗ST,f

D( x⇀ − x⇀f ) (7c)

With the calculated distribution of fluid property and also the inter-facial force source in governing equations, the velocity field is ob-tained on the fixed background mesh. The moving velocity of theinterface could be interpolated from the velocity field at the fixedgrid so that the interface is ensured to move at the same velocity asthe surrounding fluids. The distribution function given by Peskin isused to interpolate the velocity of the interface from the backgroundfield using

⇀u f =

∑D( x⇀f − x⇀)

⇀u (8)

Then, the interface is advected in a Lagrangian fashion

x⇀ n+1f

− x⇀ nf

= �t⇀u f (9)

After the interface is advected, the mesh size and quality on theinterface may be deteriorated due to the deformation. Hence, frontmesh adaptation has to be performed to improve the front meshquality.


2.3.4. Numerical methodTo solve the above equation numerically, normalization is needed

to improve the numerical calculation accuracy. In this study, thefollowing normalizations are applied to the characteristics variables:

x = x∗R∗0

, u = u∗(g∗R∗

0)1/2, t = t∗

R∗1/20 g∗−1/2

, � = �∗�l

P = P∗�∗lg∗R∗

0, � = �∗

�∗l

, � = �∗

R∗−10

(10)

R∗0 is defined as the radius of the inner diameter of the nozzle,

and subscript l represents properties of the liquid (organic solution)phase.

The re-formulated momentum equation can be re-expressed as

�(�⇀u)

�t+ ∇ · �

⇀u

⇀u

= −∇P + (1 − �)⇀g + 1

Ar∇ · [�(∇ ⇀

u +∇T ⇀u)]

+ 1Bo

∫f�f

⇀n f �(x − xf )�(y − yf )dsf (11)

where Ar is the Archimedes number, defined by (Bonometti andMagnaudet, 2006)

Ar = �∗lg∗1/2R

∗3/20

�∗l

(12a)

Archimedes number is the ratio of gravitational force to viscous forcewhich characterizes the motion of liquids due to density differences.This may be taken as the Reynolds number based on the gravitationalvelocity (gR∗

0)1/2. (Note: the relevant velocity scale is actually (1 −�g/�l) (gR∗

0)1/2. Since the �g/�l value is in the order of 0.001, this

velocity scale is approximated by (gR∗0)1/2.)

Bo is the Bond number, defined by

Bo = �∗lg∗R∗2

0�∗ (12b)

The Bond number is written as a ratio of the gravitational force to thesurface tension force. The relative importance of these three forcesdictates the mode where droplet formation occurs.

In this work, using a fixed, Cartesian, staggered grid, the momen-tum equation is discretized with the finite volume method. As thefront is advected explicitly, the physical properties and surface ten-sion are updated subsequently. Then the coupling of fluid velocityand pressure is updated by solving the momentum equations andthe continuity equation using a SIMPLE scheme (Patankar, 1980).The simulation process is thus robust even for large density ratiobecause of the semi-implicit algorithm:

The procedures implemented are listed as shown in Fig. 2:

1. Based on the velocity field and the interface position at time stept, the velocity of the moving interface on the front mesh can becalculated according to Eq. (8).

2. The interface is moved to a new location for the next time stept +�t using Eq. (9). And the surface tension stress for each pointon the interface is calculated according to Eq. (3).

3. With the new interface location, the indication function I(x, t+�t)

can be reconstructed. And the fluid physical properties such asdensity and viscosity are redistributed in the simulation domainonto the background mesh using Eq. (4) with appropriate valuesfor the liquid phase and the gas phase, respectively. The inter-face tension force is also redistributed to the background meshusing Eq. (7).

2. Advect interface (Eq. 9) to the newposition and calculate the interface

tension (Eq. 3)

3. Redistribute fluid physical properties(Eq. 4) and interfacial tension (Eq. 7c)to the background mesh for fluid flow

4. Solve Navier-Stokes equation for newvelocity field (Eq. 2)

1. Calculate velocity of interface on thefront mesh (Eq. 8)

Fig. 2. Flow chart for the iterative numerical procedure.

4. The equation for the conservation of mass and the momentum,with the inclusion of the surface tension stress, are then solvedto get the new velocity field and pressure field for the next timestep (t + �t).

5. Steps 1--4 are repeated to continue with the calculation for thenext time step.

The radius of the domain where the simulation is performed has adimensionless length of 8, while the length of the domain is depen-dent on the type of simulation performed so as to make the simu-lation computationally efficient. Typically, the dripping mode has ashorter domain, while the Rayleigh disintegration mode has a longerdomain. There are 20 grid points per dimensionless length. The ge-ometry of the nozzle is set to mimic the actual physical geometryof the setup and the liquid attachment point on the nozzle wall isdetermined through experiments. Simulation was performed on theIBM supercomputer p575 in the Institute of High Performance Com-puting, Singapore.

3. Results and discussion

3.1. Interfacial tension of DCM--CO2 system

The interaction between high pressure CO2 with organic solventssuch as ethanol, acetone and DCM, provides favorable conditions forparticle formation using SAS process. The miscibility of organic sol-vents in CO2 is strongly dependent on the pressure and compositionof the system. Sun and Shekunov (2003) investigated the surfacetension of ethanol in CO2 using laser interferometric microscopy,and belowMCP, stable droplets with surface tension decreasing withincreasing CO2 pressure is observed. Badens et al. (2005) also mea-sured the pure dynamic interface tension of water, ethanol and DCMin CO2 using the hanging drop method.

In this work, the interface tension of DCM in CO2 is determinedusing image analysis of a pendant drop using the image analy-sis method described by Hansen and Rodsrud (1991). Fig. 3 showsthe pendant drops of DCM in CO2 at varying CO2 pressures. Thesize of pendant drop decreases with increasing system pressure,which shows a decrease in interface tension at higher pressures.The calculation of DCM--CO2 interface tension at varying pressuresfrom ambient to near MCP is shown in Fig. 4. The results obtainedare very similar to the interface tension measurements by Badenset al. (2005). The interface tension of DCM in CO2 has important


Fig. 3. Pendant drops of DCM in CO2 taken using digital SLR at (a) 1bar; (b) 21bar;(c) 41bar and (d) 61bar. The temperature of the system was fixed at 35 ◦C.

y = -0.3129x + 24.446R2 = 0.9914

0

5

10

15

20

25

30

0 20 40 60 80 100

CO2 Pressure (Bars)

Inte

rfac

ial t

ensi

on (

mN

/m) Badens et al. (2005)

Present study

Fig. 4. Comparison of measurements for DCM--CO2 interfacial tension at 35 ◦Cbetween present study (DCM--CO2 interfacial tension at 308K) and Badens et al.(2005) (DCM--CO2 interfacial tension at 308K). x: CO2 pressure (bar). y: interfacialtension (mN/m).

Fig. 5. Different jet disintegration regimes observed in a high pressure CO2--DCMsystem. (a) Dripping mode; (b) Rayleigh disintegration mode; (c) wavy disintegra-tion/sinuous wave mode; (d) atomization/turbulent jet mode. The temperature andpressure of the system was 35 ◦C and 61bar, respectively. Flowrate of DCM is in-creased from 0.5 to 5ml/min to achieve the corresponding transitions from drippingto turbulent jet modes.

implications on the various modes of droplet formation at varyingCO2 pressures. This in turn provides insights to the design of oper-ating parameters to be used for particle fabrication experiments.

3.2. Jet break up regimes

The disintegration of a jet may be described by various regimesin the stability curve (Grant and Middleman, 1966) Various flow

0

10

20

30

40

50

60

70

80

0 500 1000 1500 2000 2500 3000

ReL

L/d

51 Bars61 Bars

Fig. 6. Jet stability diagram for CO2--DCM system at 35 ◦C and pressure of 51 and61bar, respectively. L: jet length before disintegration, d: nozzle diameter, ReL=Ud/,where U is the characteristic velocity of the jet and is the kinematic viscosity ofthe supercritical CO2. For each point on the graph, the sampling size is n = 3 andthe L/d value reported is the mean value of the measurements, and the error barrepresents the standard deviation.

Fig. 7. Axis-symmetric modes of jet disintegration in a DCM--CO2 system at 61barand 35 ◦C simulated using front tracking/finite volume simulations. (a) Drippingmode at a flowrate of 0.5ml/min; (b) Rayleigh disintegration mode at a flowrate of0.8ml/min.

regimes of free jets at high ambient pressure have been reported inthe studies by Kerst et al. (2000). Fig. 5 shows the variousmodes of jetdisintegration that can be observed for the injection of DCM into CO2.At very low flow rates, dripping of DCM from the tube is observedand no jet with a definable breakup length is formed (dripping mode,Fig. 5a). As the flow rate of the liquid phase increases, a jet is formedand the jet breakup is mainly influenced by surface tension forces.The jet is predicted to be unstable only to symmetrical disturbances(Rayleigh disintegration mode, Fig. 5b). Further increase in flow rateshifts the jet disintegration mechanism from symmetric breakup totransverse wave breakup (wavy disintegration mode, Fig. 5c). At veryhigh flow rate, the jet is turbulent at the nozzle exit and a turbulentjet is formed (Fig. 5d).

The drop sizes obtained at various jet formation modes are verydifferent. In the dripping mode, the mass of droplet is proportionalto the surface tension of the liquid (Lefebvre, 1989). In the Rayleigh


Fig. 8. Axis-symmetric modes of jet disintegration DCM--CO2 system obtained using front tracking/finite volume simulation. Transition from the dripping mode to theRayleigh disintegration mode at CO2 pressure of 71bar and temperature of 35 ◦C as the flowrate of DCM increases. The flowrate of DCM for a1--a3 is 0.500ml/min, whilethe corresponding one in b1--b3 is 0.525ml/min. Panels a1 and b1 illustrate the outline of the flow from the simulation results. a2 and b2 show the contours for excesspressure (relative to environmental pressure), while a3 and b3 show the velocity vector, plotted against the streamline of the flow in the system.

disintegration mode for viscous fluids, the diameter of droplet isapproximately twice the diameter of the jet, and droplet sizes arefairly uniform. In the wavy disintegration mode, droplet sizes areless uniform and observed to be less than or about the same asthe jet diameter. In the turbulent jet mode, typical droplet sizesare much smaller than the jet diameter. The jet stability curve (L/dvs. ReL) for DCM in high pressure CO2 is shown in Fig. 6 (L: jetlength before disintegration, d: nozzle diameter). ReL is the Reynoldsnumber of the liquid leaving the nozzle. ReL = Ud/, where U is thecharacteristic velocity of the jet and is the kinematic viscosity ofthe supercritical CO2. This figure is prepared by performing an imageanalysis of the jet at 35 ◦C at CO2 pressures of 51 and 61bar, usinghigh magnification pictures obtained from the digital SLR mentioned

in Section 2.2. As CO2 pressure increases, the transition betweenvarious jetting modes shifts to the left of the curve.

The droplet formation of DCM in CO2 at elevated pressures inthe dripping and Rayleigh disintegration modes is investigated us-ing both image analysis and front tracking/finite volume simula-tion to understand the droplet formation mechanism in these tworegimes and to assess their application to particle fabrication usingSAS method. Figs. 7a and b show a snapshot of the axis-symmetricdroplet formation process simulated using the front tracking methodfor the dripping mode and Rayleigh disintegration mode, respec-tively. At high pressure of 61bar, it was observed from the simula-tion that increasing the flowrate from 0.5 to 0.8ml/min changes thedroplet formation from dripping to Rayleigh disintegration modes.


Fig. 9. Axis-symmetric modes of jet disintegration DCM--CO2 system obtained using front tracking/finite volume simulation. Changing from the dripping mode to the Rayleighdisintegration mode when the CO2 pressure is at 76bar and temperature at 35 ◦C. The flowrate of DCM in a1--a3 is 0.400ml/min, in b1--b3 is 0.425ml/min, and in c1--c3 is0.450ml/min. Panels a1, b1 and c1 show the outline of the flow from the simulation results. a2, b2 and c2 show the contours for excess pressure (relative to environmentalpressure). Panels a3, b3 and c3 show the velocity vector, plotted against the streamline of the flow in the system.


Fig. 10. Dripping mode of DCM in CO2 at different pressures obtained using fronttracking/finite volume simulation: (a) at 61bar and 35 ◦C, � = 5.36 × 10−3 N/m,Deqv =2.27mm; (b) 71bar and 35 ◦C, �=2.23×10−3 N/m, Deqv =0.75mm; (c) 76barand 35 ◦C, � = 1.13 × 10−3 N/m, Deqv = 0.50mm.

Figs. 8 and 9 show the transition from dripping mode to Rayleighdisintegration mode at CO2 pressures of 71 and 76bar, respectively.At higher pressures, the transition between dripping and Rayleighmodes occur at lower DCM flowrates which is attributed to the cor-responding decrease of interfacial tension close to the MCP. Also,at the same flow rate but with decreasing surface tension, the sys-tem that has a smaller surface tension will produce smaller dropletsdue to the increasing relative strength of the gravitational effect ascompared to the surface tension effect, and the frequency of dropletformation will increase.

3.3. Droplet formation in dripping mode

Fig. 10 shows the changes in the droplet size (at the point of pen-dant drop breakage) in the dripping mode when the CO2 pressureis increased from 61, 71 to 76bar. An increase in CO2 pressure in-creases the miscibility of CO2 and DCM phases and consequently, areduction in the interface tension between DCM--CO2 is observed.Thus the Bond number of the system is increased in magnitude. Thesize of the droplets in the dripping mode is a strong function of theBond number. This can be explained by the fact that at this mode,the size of the pendant drop that is attached to the nozzle beforepinch-off is determined by the balance between the gravitationalforce (it pulls the liquid downward in the direction of gravity) andthe surface tension force (it holds the droplet in place, resisting mo-tion). From Fig. 10, the size of droplets obtained from simulationdecreased from 2.27, 0.75 to 0.50mm with increasing pressure from61, 71 to 76bar. Accompanying the increase in pressure, the gravi-tational effect also became increasingly important, as shown by anincrease in the Bond number from 0.039, 0.093 to 0.183.

Fig. 11 shows the pinch-off process when the weight of the pen-dant drop is too large for the surface tension to hold it in place.Comparing Panels a1--a3, b1--b3, c1--c3, d1--d3 and e1--e3, it wasobserved that the numerical simulation result matches well withthe experimental observation, showing the pinch-off of the liquiddroplet. Panels a2, b2, c2, d2 and e2 show that pressure contours inthe system. The point of greatest pressure before droplet pinch-offis at the neck (see Panels a2 and b2). After the pinch-off of droplet,there is a gradual dissipation of the built-up pressure in the droplet,while a large pressure is built-up in the retracting liquid columnthat is attached to the nozzle (see Panels c2 and d2). The observedpressure contour profile can be explained by analyzing the balanceof the pressure inside and outside the DCM--CO2 interface,

‖P∗ + �∗(∇ ⇀u ∗ + ∇ ⇀

u ∗T) · n‖ = �∗�∗ (13)

where the square bracket represents the difference between"outside'' and "inside'' of the interface.

The pressure difference is strongly dependent on the surface ten-sion and the curvature of the interface. In the axis-symmetric cylin-drical coordinates, the surface curvature is a function of the radius ofthe liquid column. Therefore, it can be seen that the point of highestpressure is located at the region where the radius of a liquid col-umn is the smallest. The velocity vectors are shown in Panels a3, b3,c3, d3 and e3 of Fig. 11, plotted against the corresponding stream-lines. As the droplets are formed and transported in the direction ofthe gravity, the corresponding fluid phase velocity is in the down-ward direction. Due to the confined nature of the chamber wherethe droplets are flowing downwards, circulation in the surroundingfluid can be found in the vicinity of the droplets. This phenomenonis clearly visible with reference to the streamline plots illustrated onthe right-hand side of each of the figure panels.

To determine the size of the droplet, the shadow sizing system isdeployed. By analyzing the shadow image of the droplets (Figs. 12aand b), the length of the major and minor axes of the droplets canbe obtained, and the size of the droplet can be calculated. Takinginto account the axis-symmetric nature of the system, the equiv-alent diameter (Deqv) of the droplets is then calculated (Fig. 12c).The corresponding equivalent diameter at 66 and 71bar is 1.31 and1.07mm, respectively. Fig. 12d illustrates the close match betweenof the sizes of droplets achieved at different pressures during thedripping mode.

3.4. Droplet formation and jet breakup in Rayleigh disintegration mode

As the inlet velocity is increased while the surface tension isdecreased by increasing the CO2 pressure, the dominant term in themomentum equation (Eq. (11)) shifts from the fourth term (relatedto the interface tension, involving 1/Bond number) to the third term(related to the viscous stress, involving 1/Archimedes number). In theRayleigh disintegration mode, there is no formation of the pendentdrop. A thin jet is first formed as the liquid leaves the nozzle, andthen droplets are formed through the jet-breakup process.

One point to note is that due to the affinity of DCM to stainlesssteel nozzle in the subcritical CO2 environment, the jet diameter isweakly dependent on the surface tension (the point of contact ofthe interface on the stainless steel nozzle and the contact angle isdetermined by the balance of the stainless steel--DCM surface ten-sion, stainless steel--CO2 surface tension, and the varying DCM--CO2surface tension).

Results of the simulation show that the droplet size is very weaklydependent upon the interfacial tension (Fig. 13). The above observa-tion may be explained as the limit where the viscous effect is small,the dominant jet-breakup wavelength is only dependent on the ra-dius of the jet (Rayleigh, 1878, 1879). The surface tension has noeffect on the jet-breakup wavelength, and only plays a part in de-termining the instability growth rate of the dominant jet-breakupwavelength. Since the dominant wavelength is not affected by thechanges in the surface tension, it can be shown that the final dropletsize (D∗

droplet) of an inviscid jet in such Rayleigh disintegration pro-

cess is related to the jet diameter (D∗jet) through the following simple

function:

D∗droplet = 1.48D∗

jet (14)

The above expression was derived by noting that the dimensionlesswavenumber of Rayleigh disintegration of the inviscid jet is around0.69 (non-dimensionalized by the jet circumference) (Rayleigh, 1878,1879), and subsequently through the conservation of mass for thesection of the jet that is broken off to the formation of a spheri-cal droplet. Further work to correlate the size (Lefebvre, 1989) has


Fig. 11. Comparison of experimental and simulated pendant drop formation in the dripping mode. Panels a1, b1, c1, d1 and e1: snapshots of the pinch-off point in drippingmode at 71bar and 35 ◦C and DCM flowrate of 0.4ml/min (time between each consecutive snapshots from top to bottom row is 0.001 s). Panels a2, b2, c2, d2 and e2:outline of the pinch-off process obtained through the numerical simulation, and the contours for excess pressure (relative to environmental pressure) of the system. Panelsa3, b3, c3, d3 and e3: velocity vectors of the successive snapshots are plotted against the streamline of the flow in the system.

suggested that the ratio of diameter of droplet to the diameter of jetis around 1.89 for the case of a viscous jet. The ratio of the jet diam-eter to the droplet diameter from Fig. 13 for the simulated case of61bar is around 1.75 (dimensionless jet radius=1.50, dimensionless

droplet radius=2.63), for the simulated case of 71bar is around 1.67(dimensionless jet radius=1.35, dimensionless droplet radius=2.25)and for the simulated case of 76bar is around 1.70 (dimensionlessjet radius = 1.13, dimensionless droplet radius = 1.93). The surface


Fig. 11. (continued).

tension of the DCM in CO2 at 61 and 71bar is 5.36 × 10−3 and2.23 × 10−3 N/m, respectively. The surface tension of DCM in CO2at 71bar is less than half the value at 61bar, however, there are nosignificant differences in the jet and droplet diameter as shown inFig. 13. This shows that surface tension has negligible effect on thedimensionless wavenumber of the Rayleigh disintegration of the jet,and is close to the expected value. This, together with the slightlychanging affinity of DCM to the stainless steel nozzle, explains therather weak dependence of the changes of surface tension on thedroplet size, since only the jet diameter is weakly dependent on thesurface tension.

If a glass nozzle was used in place of the stainless steel nozzle,different droplet size will be expected in the dripping mode as bothsurface tension forces and liquid attachment area play importantroles on drop size in this regime. Using the stainless steel nozzle,upward force balancing the weight of the drop is higher due to theaffinity of the drop to the nozzle wall and also the larger area wherethe liquid is attached to the surface of the nozzle, resulting in largerdrop size. However, in the Rayleigh disintegration mode, drop size islikely to be unaffected by change in the nozzle material as the dropsize is dependent on the jet diameter which is mainly similar to theinner diameter of the nozzle.

3.5. Particle formation

The SAS process is commonly used in pharmaceutical applicationsfor micronization of biodegradable polymers and drugs. In this work,it was observed that the initial drop size of DCM in high pressure CO2is strongly dependent upon the pressure in the dripping mode due toa variation in the interface tension of the system. Particle fabricationin SAS processes is affected by both the thermodynamic conditions(pressure, temperature and composition, etc.) of the system as wellas the hydrodynamics of the organic phase into the high pressureCO2 (flowrate, nozzle diameter, nozzle design, etc.).

Figs. 14a and b show the fabrication of PLA particles from a solu-tion of 2% (w/v%) polymer in DCM into CO2 at 71 and 76bar, respec-tively. Dripping flow was observed at both pressures at a flowrate of0.05ml/min. From Fig. 14, it can be observed that at 71 and 76bar,operating at a dripping flow yields fairly uniform sized particles.However, at lower pressure (71bar), it was also observed that parti-cles formed tend to agglomerate. At an even higher pressure closerto the MCP of the system (76bar), much higher miscibility betweenDCM and CO2 is achieved as shown in the snapshot of the dropletformation process at 76bar. The particles formed at this conditionwere found to be more discrete and spherical, and generally in the


50

55

60

65

70

75

80

0 0.5 1 1.5 2 2.5

Equivalent diameter (Deqv)

Pres

sure

(ba

r)

SimulationExperimental

zr

B

A

1mm

Fig. 12. Measurement of droplet size of DCM in CO2 at 35 ◦C and at different pressures using shadow sizing system: (a) 66bar, Deqv = 1.31 ± 0.02mm; (b) 71bar,Deqv = 1.07± 0.06mm; (c) calculation of equivalent diameter (Deqv) of droplet using an axis-symmetric model. Taking into account the axis-symmetric nature of the dropletand the system, Deqv is calculated based on Deqv = 3√

A2 · B and (d) comparison of experimentally determined Deqv with numerical simulation in the dripping mode.

Fig. 13. Simulation of Rayleigh disintegration of DCM jet in CO2 at 35 ◦C andhigh pressure. (a) Typical Rayleigh disintegration droplet formation process, 76bar,flowrate of DCM = 0.5ml/min, D∗

droplet/D∗jet ≈ 1.75; (b) simulated case, 61bar,

flowrate of DCM = 0.8ml/min, D∗droplet/D

∗jet ≈ 1.75; (c) simulated case, 71bar,


∗jet ≈ 1.67; (d) simulated case, 76bar,


∗jet ≈ 1.70.

range of 2--5�m. Fig. 14c illustrates particles fabricated at conditionsof 76bar and flowrate of 0.2ml/min (left panel) and 3ml/min (rightpanel). At 0.2ml/min, the particle size distribution achieved is similaras observed in Fig. 14b. However, when operating in the turbulentjet mode at higher flowrate of 3ml/min, the particle size becomesignificantly more polydispersed.

Figs. 15a and b show PLA particles obtained from solution of 2%(w/v%) polymer in DCM at a flowrate of 0.05ml/min into CO2 at 81and 91bar, respectively. At these conditions above the MCP of thesystem, it was observed that particle size distribution is more non-uniform than the particles shown in Figs. 14a and b. At this operatingregime, the interfacial tension between DCM and CO2 diminishedand axis-symmetric dripping mode is not observed. The solutionenters the vessel as a gaseous plume. Figs. 15c and d show particlesobtained at flowrate of 4ml/min at 81 and 91bar, respectively. Oncomparison with particles from Figs. 15a and b, it was observed thatat the conditions above MCP, solution flowrate has no obvious effecton the final particle size and size distribution.

4. Conclusions

The droplet formation process of DCM in high pressure CO2 isinvestigated in this work. It was observed that the interface ten-sion of the DCM--CO2 system is significantly affected by the pres-sure of the surrounding CO2 gas phase, especially at pressures closeto the mixture critical point. Dripping, Rayleigh disintegration, wavydisintegration and turbulent jet were clearly observed using high-speed visualization of the DCM--CO2 system at elevated pressures.The dripping and Rayleigh disintegration modes yield more mono-disperse droplets in contrast to the wavy disintegration and tur-bulent jet modes. The axis-symmetric modes of droplet formationwere simulated using a front tracking/finite volume simulation codeand compared with experimental observations. Very close match of


Fig. 14. PLA particles fabricated from the SAS process at 35 ◦C at (a) 71bar with DCM flowrate of 0.05ml/min into CO2; (b) 76bar with DCM flowrate of 0.05ml/min intoCO2; (c) 76bar with DCM flow of 0.20ml/min into CO2 (left panel) and 3.00ml/min into CO2 (right panel).

Fig. 15. PLA particles fabricated from the SAS process at 35 ◦C with a DCM flowrate of 0.05ml/min into CO2 at (a) 81bar; (b) 91bar; and with a DCM flowrate of 4.00ml/mininto CO2 at (c) 81bar; (d) 91bar.


the simulation with high-speed camera results were obtained in thedripping mode.

In the dripping mode, the droplet size decrease with increasein CO2 pressure due to a corresponding decrease in the interfacetension. This was observed in the droplet size measurements usingthe shadow sizing system as well as in the simulation results. In theRayleigh disintegration mode, the droplet size is weakly dependenton the interface tension of the system and is proportional to thediameter of the jet. The operation of SAS process in the windowclose to the mixture critical point at low flowrate provides a meansof particle fabrication with possible size control. Operating in thedripping mode near the mixture critical point, the initial droplet sizecan be manipulated by small changes in the pressure of CO2.

Notation

Ar Archimedes numberBo Bond numberdS∗

finterface length element

f variables in the fluid phaseg variables in the outer gas phase⇀g acceleration due to gravity, ms−2

l variables in the inner liquid phaseP pressureReL Reynolds numberR0 inner radius of the capillary tube⇀u velocity vector∗ dimensional quantity

Greek letters

�∗f

curvature of the interface

� dynamic viscosity� density�∗ surface tension coefficient

Abbreviation

CO2 carbon dioxideDdroplet droplet diameter, mmDeqv equivalent diameter, mmDjet jet diameter, mmDCM dichloromethane

Acknowledgments

This research was supported by Agency of Science, Technologyand Research (A*STAR) and National University of Singapore (NUS)under the Grant number R279-000-208-305. The authors acknowl-edge the scientific discussion and inputs from Professors Kenneth A.Smith and Yen Wah Tong during various phases of this project.

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Jet Breakup and Droplet Formation in Near-critical Regime of Carbon

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