Governing Principles of Alginate Microparticle Synthesis withCentrifugal ForcesHuseyin Burak Eral,†,‡,# Eric R. Safai,§,# Bavand Keshavarz,∥,# Jae Jung Kim,§ Jisoek Lee,⊥

and P. S. Doyle*,§

†Process and Energy Department, Delft University of Technology, Delft 2628 CD, The Netherlands‡Van’t Hoff Laboratory for Physical and Colloid Chemistry, University of Utrecht, Utrecht 3512 JE, The Netherlands§Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States∥Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States⊥School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, Korea

*S Supporting Information

ABSTRACT: A controlled synthesis of polymeric particles isbecoming increasingly important because of emergingapplications ranging from medical diagnostics to self-assembly.Centrifugal synthesis of hydrogel microparticles is a promisingmethod, combining rapid particle synthesis and the ease ofmanufacturing with readily available laboratory equipment.This method utilizes centrifugal forces to extrude an aqueouspolymer solution, sodium alginate (NaALG) through a nozzle.The extruded solution forms droplets that quickly cross-linkupon contact with aqueous calcium chloride (CaCl2) solutionto form hydrogel particles. The size distribution of hydrogelparticles is dictated by the pinch-off behavior of the extruded solution through a balance of inertial, viscous, and surface tensionstresses. We identify the parameters dictating the particle size and provide a numerical correlation predicting the average particlesize. Furthermore, we create a phase map identifying different pinch-off regimes (dripping without satellites, dripping with satellites,and jetting), explaining the corresponding particle size distributions, and present scaling arguments predicting the transitionbetween regimes. By shedding light on the underlying physics, this study enables the rational design and operation of particlesynthesis by centrifugal forces.

■ INTRODUCTION

With the development1 of the nanotechnology and bioengin-eering fields, interest in controlled synthesis of polymericparticles has seen a rapid resurgence.2,3 Applications rangingfrom medical diagnostics4 to anticounterfeiting technologies5

constantly challenge our capacity to produce polymericparticles efficiently.6 In response, scientists and engineershave developed creative methods to synthesize polymericparticles7 and to assemble them into more complex structures.8

Microfluidics9−12 and batch synthesis approaches13 are themost commonly used synthesis methods. A directed assemblyinto more complex particles is achieved by external fields suchas magnetic, electric, and hydrodynamic14,15 as well as throughasymmetric particle−particle interactions.16 Applications placeemphasis on various aspects of controlled synthesis ofpolymeric particles. Self-assembly studies require monodispersebuilding blocks with well-defined geometries, whereas medicaland pharmaceutical applications place strict biocompatibilityrestrictions on the materials and synthesis methods used.2,3,17

Polymeric particles manufactured using natural biopolymershave recently risen to prominence in biological andpharmaceutical applications.18,19 The biocompatibility, abun-

dance, and low-cost of natural polymers are the driving forcebehind this rapid expansion. Particularly, natural polymers, suchas sodium alginate (NaALG), κ-carrageenan, and carboxyme-thylcellulose, that can cross-link to form hydrogels have beenwidely used in numerous applications such as controlled releaseof actives, encapsulation of biomolecules, and scaffolding forcell culture.20,21 Notably, Lacy et al. used alginate (ALG)hydrogels to encapsulate islet cells capable of releasinginsulin.22

Lab-scale synthesis of ALG hydrogel particles and fibers hasbeen demonstrated using dripping,23−26 coextrusion,27 micro-fluidics,24,28,29 inkjet printing, and 3D printing.20,21 Bremond etal. also demonstrated encapsulation with very thin controlledlayers of ALG hydrogels.27 However, alternative methodscapable of producing relatively large amounts of particles withstandard lab equipment are still sought after. Among theaforementioned methods, centrifugal synthesis of ALG andchitosan hydrogels30,31 has attracted interest because of its

Received: March 16, 2016Revised: June 10, 2016Published: June 16, 2016

Article

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© 2016 American Chemical Society 7198 DOI: 10.1021/acs.langmuir.6b00806Langmuir 2016, 32, 7198−7209

ability to produce large amounts of hydrogel microparticles,low-cost nature, and ease of implementation with readilyavailable lab equipment (centrifuge, needle, and falcon tube).Compared with the standard dripping method that requires apump, the centrifugal synthesis method provides an alternativemeans to overcome pressure drops with standard labequipment. In this approach, the centrifugal force is used toextrude an aqueous NaALG solution through a nozzle of radiusRn. The NaALG solution either pinches off and breaks intodroplets or forms a jet after extrusion from the nozzledepending on the balance of capillary, inertial, and viscousforces. The aqueous NaALG droplets quickly cross-link uponcontact with aqueous calcium chloride (CaCl2) solution toform ALG hydrogel particles (Figure 1). The size distributionof hydrogel particles is controlled by the dynamics of the pinch-off and the cross-linking process in CaCl2 solution.The centrifugal synthesis approach has been used to

synthesize ALG hydrogel particles of various sizes andcompositions for a variety of applications.32,33 Lee and Kimsynthesized composite ALG particles containing polydiacety-lene liposomes for multitargeting.32 Maeda et al. demonstratedthe synthesis of composite particles and compartmentalizedencapsulation of different moieties such as cells and compositemagnetic colloids using multiple glass capillaries stackedtogether.33 However, all of these efforts have focused onsynthesizing ALG hydrogels empirically without providing anin-depth understanding of the phenomenon. Haeberle et al.used stroboscopic imaging techniques to visualize the pinch-offprocess under acceleration.34 These authors provided strobo-scopic images of filament formation and pinch-off along withreports on size distribution.In all of the aforementioned studies, predicted sizes of

synthesized hydrogel particles are based on a static forcebalance on a pendant droplet, Tate’s law.35 This static approachignores the pinch-off phenomenon.36 Studies on centrifugalsynthesis have so far focused on demonstrating the versatility ofthe technique. The lack of physical understanding of theprocess limits the repeatability of previous work, as well asgeneralization of centrifugal synthesis to other materials.In this study, a systematic analysis of the centrifugal hydrogel

microparticle synthesis process for predicting (i) the particle

size and (ii) the pinch-off regimes is provided. The datacollection is performed by measuring the average size and sizedistributions of cross-linked hydrogels by optical microscopyunder various experimental conditions. Experimental parame-ters dictating the size of the hydrogel particles are identified,and a correlation predicting the average hydrogel particle size ispresented. The proposed correlation takes into account thepreviously overlooked pinch-off phenomenon, and it is accuratewithin the dripping without satellites regime. On the basis of theobservation of particle size distributions shown in Figure 1c−e,we develop scaling arguments explaining the emergence ofdifferent pinch-off regimes (dripping without satellites, drippingwith satellites, and jetting). Incorporating the pinch-off processinto the physical model of centrifugal synthesis enables a betterunderstanding of the previously overlooked experimentalparameters such as the viscosity of the extruded solution,length of the nozzle, and height of the fluid. This improvedphysical understanding of the process can aid in rational designof experiments and opens the possibility of expanding thecentrifugal method into other polymeric materials. Utilizing thephysical insights of our study, we provide a step-by-step guideaimed to help scientists in designing experiments in theSupporting Information.

■ MATERIALS AND METHODSChemicals and Materials. NaALG (CAS: 9005-38-3), CaCl2

(CAS: 10043-52-4), sodium dodecyl sulfate (SDS, CAS: 151-21-3),Kolliphor P188 (KP188, CAS: 151-21-3), sodium hydroxide (NaOH,CAS: 1310-73-2), and trichloro(1H,1H,2H,2H-perfluorooctyl)silane(perfluorosilane, CAS: 78560-45-9) were purchased from SigmaAldrich. All chemicals were used without any further treatment ormodification. Blunt-end syringe nozzles of gauges (G) 21, 23, 25, and30 were purchased from Nordson, with inner radii (Rn) of 258, 168,130, and 80 μm, respectively. The length of the blunt nozzles L was 1.8cm. All nozzles used in the study were made of stainless steel and wereunmodified unless specified. Centrifugation was achieved with atabletop, swinging bucket centrifuge (Eppendorf 5702).

Experimental Procedure. A schematic of the experimental setupis shown in Figure 1. NaALG droplets are generated through stainlesssteel blunt-tip needles of varying gauges by centrifugal force. A rangeof centrifugal accelerations (1−500 g) drives fluid flow, with theaccelerated NaALG solution impacting a 500 mM CaCl2 bath. The

Figure 1. (a) Illustration of the experimental setup. Noncross-linked NaALG solution is extruded from a syringe nozzle of radius Rn by centrifugalacceleration a, forming droplets of radius Rd. The droplets cross-link and form hydrogels upon impact into the liquid bath. (b) Illustration of thegelation process where Ca2+ ions react with ALG to form hydrogels. Snapshots of ALG hydrogels produced at different accelerations where theconcentration of NaALG is 3% wt/wt NaALG is extruded at (c) 1000, (d) 1500, and (e) 2200 rpm.

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cross-linking of the NaALG polymer to form ALG hydrogels occursupon impact on the CaCl2 bath. Resulting hydrogel particles areanalyzed by image processing.Fabrication of the Nozzle-In-Centrifuge (NiC) Apparatus.

Falcon tubes, 50 mL, are utilized as supports (outer chamber) for thesyringe and needle (inner chamber) while also serving as the CaCl2bath. The volume of the liquid in the CaCl2 bath is used to adjust thedistance between the needle tip and the CaCl2 bath (H). Syringes (10mL) are cut to shape by hand and secured through a punctured tubecap using a hot melt adhesive to maintain needle positioning. ThisNiC apparatus provides accessibility to interchange the needle tip andall component specifications. The assembly and operation of the NiCapparatus are detailed in the Supporting Information.Needle Silanization. To hydrophobize the nozzle, untreated blunt

needles were soaked in 1 M NaOH solution for 1 h. They were thendried with compressed argon. The needles were coated withperfluorosilane under vacuum with an incubation time of 2 h. Thehydrophobicity was confirmed using bright field microscopy(Supporting Information).Droplet Generation and Observation. NaALG solutions were

prepared by mixing appropriate amounts of NaALG powder in waterand subsequently stirring using a magnetic bar. Higher concentrationsrequired longer agitation times to achieve homogeneous solutions. Allsolutions were prepared at room temperature. ALG and CaCl2solutions were injected into the inner and outer chambers, 2 and 8mL, respectively, prior to centrifugation. The cap securing the NaALG-containing syringe and nozzle was fixed at a height such that thedistance H between the nozzle tip and the CaCl2 bath was 3.6 mm.The length of needles, L, used as the nozzle was 18 mm, and thedistance, H, was kept constant at 3.6 mm throughout the study. Theimpact of varying H is elaborated in the Supporting Information.Centrifugation times ranged from <30 to 60 s. Sub-thirty second spintimes were used for less viscous NaALG solutions to minimize changesin H. NaALG concentrations varied between 0.5 and 8% wt/wt, with2.5% wt/wt being our canonical solution. SDS was used to modify thesurface tension of NaALG solutions.Cross-linked hydrogel microparticles were maintained in CaCl2

solution prior to and during imaging. ALG microparticles werecollected and imaged under bright field via an inverted microscope(Axiovert 200, Zeiss) equipped with a Nikon lens (2X to 20X). Imageswere processed using public domain software ImageJ (NIH) and acustom code was written in Matlab.

■ RESULTS

The centrifugal microparticle synthesis process can be dividedinto two distinct phenomena: pinch-off and impact with thereaction (Figures 1 and 3). In pinch-off, NaALG solution exitsthe nozzle and forms a stream of droplets with radius Rdf as aresult of the balance between surface tension, inertial, andviscous forces. In the impact with the reaction stage, theimpacting droplets penetrate into the CaCl2 bath. NaALGdroplets solidify into ALG hydrogel microparticles with radiusRp because of the reaction of NaALG with the divalent cationCa2+ (Figure 1b).37 The focus of this study will be the pinch-offprocess where the centrifugal acceleration drives the flow of thefluid through the nozzle. We systematically investigate thefactors dictating the hydrogel microparticle size (Rp) and thepinch-off regimes governing the microparticle size distributionsshown in Figure 1c−e.Dimensional Analysis. We first discuss factors dictating

the formation and the size of the droplets during pinch-offthrough dimensional analysis using the Buckingham-Pitheorem38 where ρ, γ, and μ are the fluid properties: density,surface tension, and viscosity of the extruded fluid, respectively.Rp is the particle radius, and Rn is the nozzle outer radius. θ isthe contact angle. U is the fluid velocity at the nozzle outlet, h isthe height of the liquid, and L is the length of the nozzle

(Figure 1). The dimensionless parameters pertinent to thisstudy are

θ

ργ

ργμ

ρ γ

=

=

=

=

⎛⎝⎜

⎞⎠⎟

R

Rf Bo We Oh

hL

LR

BoaR

WeU R

OhR

, , , , ,p

n n

n2

2n

n (1)

where Bo stands for the Bond number, which captures therelative strength of gravitational stress imposed by theacceleration to capillary stress. We is the Weber number,which is the ratio of inertial and surface tension stresses. TheOhnesorge number, Oh, relates the viscous stress to inertia andsurface tension stresses.39,40 θ is the advancing contact angle atthe solid−liquid−gas interface formed by the nozzle, ALGsolution, and air. The geometric parameters h/L and L/Rn arealso important in determining the speed of flow inside of thenozzle.The dimensional analysis suggests that the relative radius of

the extruded droplet (Rd/Rn) might depend not only on thebalance of the surface tension force with the centrifugal bodyforce as previously mentioned in the literature33,34 but also oninertial and viscous forces. Furthermore, it suggests thatpreviously overlooked parameters such as θ, h/L, and L/Rncan play a role in controlling Rd. Upon pinch-off, the dropletimpacts the CaCl2 bath and assumes the final size Rp as shownin Figure 1.

Derivation of Flow Inside of the Nozzle. The flow speedof the fluid while exiting the nozzle needs to be calculated toaccount for the inertial effects. The NaALG solution is extrudedby the pressure head created by the centrifugal force (a) actingon the total height of the fluid (h + L). This problem is aspecial case for the pressure drop in inclined pipes where thedriving force is the centrifugal force.38 The majority of pressuredrop occurs within the nozzle; we can assume a Hagen−Poiseuille form where spatially averaged velocity of the fluid atthe nozzle outlet is

ρμ

=+

Ua h L R

L( )

8ni

2

(2)

Equation 2 is valid in the laminar flow regime where theReynolds (Re) number is smaller than 2000. Rni is the innerradius of the nozzle. The Reynolds number is defined as Re =ρURni/μ where ρ and μ are the density and the viscosity ofNaALG solution, respectively. For all of the experimentsconducted in this study, Re is less than ten.

Static Force Balance on a Pendant Drop. A simple forcebalance can be written around the droplet and the nozzle wheresurface tension is balanced by the weight of the droplet. Thesurface tension force holding a pendant droplet (Figure 3) is2πRnγ, and the weight of the droplet is 4πRdi

3ρa/3. This simpleforce balance is called Tate’s law.35 Rn and Rdi are the outerradius of the nozzle and radius of the pendant drop. It isimportant to note that Tate’s law is only applicable to pendantdroplets, and it ignores the pinch-off process. Tate’s law can berewritten in a dimensionless form as

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= −⎛⎝⎜

⎞⎠⎟

RR

Bo32

di

n

31

(3)

The effect of the contact angle can be introduced into Tate’slaw by incorporating the contact angle into the surface tensionforce, holding the pendant droplet (2πRnγ cos θ) against theweight of the droplet, which is 4/3πRdi

3ρa. This equation canbe rewritten in a dimensionless form as

θ= −

⎛⎝⎜

⎞⎠⎟

RR

Bo1

cos32

di

n

31

(4)

Estimating the Size of Hydrogel Particles. The resultinghydrogel particle size is arguably the most important parameterin centrifugal hydrogel microparticle synthesis. For biomedicaland drug delivery applications, the size dictates the time scale ofmass transport of actives through diffusion along with networkproperties such as mesh size.25,26 Dimensional analysisdiscussed in the Dimensional Analysis section indicates thatthe relative size of the pinched-off droplet normalized by thenozzle radius might have a dependency on dimensionlessnumbers, Bo, We, and Oh, and θ as well as other geometricfactors given in eq 1.In Figure 2, we systematically investigate the effect of

acceleration (a), outer nozzle radius (Rn), surface tension (γ),and contact angle (θ) on the hydrogel particle size (Rp) whilekeeping the viscosity of NaALG solution and other geometricfactors in eq 1 constant. In Figure 2a, Rp is plotted against theacceleration for four different nozzle sizes (Rn). Two trendsappear in Figure 2a. Rp decreases with decreasing nozzle radius,Rn, and with increasing acceleration. Furthermore, below acertain acceleration, centrifugal synthesis did not produce

droplets (discussed in the No-Dripping to Dripping Transitionsection). Above a critical acceleration, satellite droplets andbroad droplet size distributions were observed (Figure 1d,e).We excluded the data points where satellites and broaddistributions are observed in Figures 2 and 3. The emergence ofaforementioned heterogeneous size distributions is discussed insections below.

Figure 2. (a) Effect of the nozzle size on the hydrogel particle size: radius of hydrogel particles (Rp) versus centrifugal acceleration (a) produced withfour different nozzle radii (Rn). (b) Effect of surface tension: radius of hydrogel particles produced by extruding noncross-linked ALG solutions withdifferent surfactant concentrations vs centrifugal acceleration (a). (c) Effect of the contact angle: radius of hydrogel particles (Rp) produced withhydrophobic (silanized) θ ≈ 100° and hydrophilic (untreated) nozzles (θ ≈ 0°) vs centrifugal acceleration. (d) Dimensionless particle radius cubedvs Bond number (Bo) for different radii nozzles given in panel a. (e) Dimensionless particle radius cubed vs Bo for ALG solutions with differentsurface tensions given in panel b. (f) Dimensionless particle radius cubed divided by cos θ vs Bo hydrophobic and hydrophilic surfaces given in panelf. The presented data are obtained with the canonical sample 2% NaALG, and they are limited to the dripping without satellites regime.

Figure 3. Ratio of the particle radius (Rp) to the nozzle radius (Rn)cubed divided by cos θ at different Bond numbers (Bo) for differentnozzle sizes, surfactant concentrations, and surface treatments. Thelines are Tate’s law35 (eq 3, red line) and the numerical predictionfrom Yildirim et al.43 (eq 6, black solid line). The presented data arelimited to the dripping without satellites regime for the canonicalsample. In the inset image, dotted green line indicates swelling/shrinking upon cross-linking.

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The effect of surface tension on the size of hydrogel particlesis shown in Figure 2b for Rn fixed at 80 μm. Increasing thesurfactant concentration decreases the surface tension(Supporting Information), which leads to smaller droplets.Figure 2c examines the role of the contact angle, demonstratedby comparing untreated metallic nozzles with silanized nozzles.Metallic nozzles have θ ≈ 0°. Silanized nozzles are morehydrophobic with a contact angle of θ ≈ 100°. For all nozzlesizes, silanized nozzles create smaller hydrogel particles,indicating that the contact angle is a parameter influencingthe size of ALG particles.For estimating the hydrogel size in centrifugal synthesis,

Tate’s law (eq 3) has been used extensively in the literature.33,34

Plotting the dimensionless droplet size (Rp/Rn) against theBond (Bo) number captures the overall trend shown in Figure2d−f. However, Tate’s law clearly overestimates the dropletsize, which emphasizes the need for developing more accuratecorrelations for estimating Rp.All of the experimental data for different nozzle sizes, surface

tension, and contact angle values given in Figure 2 can becollapsed onto a single experimental curve, shown in Figure 3,by plotting (Rp/Rn)

3/cos θ vs Bo. The modified Tate’s law in eq4 (red solid line) overestimates the hydrogel size at all Bovalues in the experimental range as mentioned before. In theliterature, it is well known that the radius of a pinched-offdroplet (Rd) from a dripping nozzle is smaller than the radius ofa pendant drop estimated by Tate’s law (Rdi) as a smallerpendant droplet remains behind after pinch-off (inset of Figure3). Harkins and Brown first observed this phenomenon in 1919while measuring the surface tension of liquid droplets byweighing the pinched-off droplets.41 They experimentallydetermined a correction factor (Φ) to Tate’s law for a liquidof known density extruded through a nozzle very slowly. Theyfound Φ to be independent of the nature of the liquid or thenozzle material and to be dependent only on the nozzle radius(Rn) and the volume of the pinched-off droplet (Vf = 4πRd

3/3).Lando and Oakley42 applied linear regression to theexperimental results of Harkins and Brown41 and provided acorrelation for Rn/Vf

1/3 as a function of Φ

π γ ρ= ΦR V g2 n f (5)

Along with the development of digital cameras andgoniometers that can accurately determine the size of pendantdroplets through curve fitting, the drop weight method wasreplaced with the pendant droplet method and the Du Nouyring method that enables more accurate measurements ofsurface tension.44 Interest in Harkins and Brown’s experimentalwork was renewed with the development of numericaltechniques capable of addressing the pinch-off problem.Yildirim et al.43 numerically validated the experimental resultsof Harkins and Brown and proposed an easier to use versiongiven below for low We and Oh numbers (We < 10−7 and Oh <10−3)

= −⎛⎝⎜

⎞⎠⎟

RR

Bo0.9372df

n

31.07

(6)

Yildirim et al. also studied the effect of the pinch-off processon the droplet size at largeWe and Oh numbers. In experimentspresented in Figures 2 and 3, the We and Oh numbers coveredwere relatively low (cf. Discussion section). Plotting eq 6provided by Yildirim et al. (solid black line) in Figure 3provides a better fit than Tate’s law (solid red line) in theexperimental regime. The improved fit compared with that ofTate’s law suggests that the pinch-off process has to be takeninto account while predicting Rp. We also considered thepossibility of swelling after impact. In this case, the cross-linkedhydrogel size Rp would be different than the size of thepinched-off droplet, Rdf. To investigate swelling, we introduceda swelling/shrinking parameter C where Rp = C × Rdf into eq 6.The resulting equation is given below

= −⎛⎝⎜

⎞⎠⎟

R

RC Bo0.9372p

n

33 1.07

(7)

Equation 7 provides a more general version of eq 6,considering materials that can shrink/swell upon cross-linking.Fitting eq 7 to experimental data in Figure 3 using C as a fittingparameter resulted in C = 0.99. We conclude that shrinking/swelling does not play an appreciable role for our canonicalsample (2% NaALG).

Operational Phase Diagram. The results in the previoussection clearly demonstrate that the pinch-off process needs to

Figure 4. (a) Experimental phase diagram showing different pinch-off regimes as a function of centrifugal speed (ω) and NaALG concentration byweight (NaALG%) for a nozzle size of Rn = 80 μm. (b) Illustrations of different pinch-off regimes with resulting hydrogel formations and summary ofconditions for transitions between different regimes. The thick green arrow indicates the transition between dripping without satellites to jettingregimes without entering the dripping without satellites regime.

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be taken into account in centrifugal microparticle synthesis. Inthis section, we demonstrate the interplay of viscous, inertial,and surface tension stresses on centrifugal hydrogel micro-particle synthesis with an operational phase diagram (Figure 4).We define scaling arguments for the no-dripping to drippingtransition, dripping to dripping with satellite formation transition,and dripping to jetting transition in the corresponding sections.Using the presented scaling arguments, experimentalists canplace themselves in the right operational window and controlsize distributions.In the centrifugal process, the extruded NaALG solution can

exhibit distinct pinch-off regimes that result in drasticallydifferent particle size distributions (Figures 1c−e and 8). As therotational speed (ω) is increased, the centrifugal acceleration(a) driving the flow velocity (U) increases and the balance offorces governing the flow is altered. The acceleration, a, is givenby a = ω2Rcent where ω is the rotational speed in rad/s and Rcentis length of the centrifuge arm. For a low viscosity fluid, Oh ≪O(1), the pinch-off behavior is dictated by the balance ofsurface tension and inertial stress. We observed that hydrogelsstart dripping into the CaCl2 bath above a critical acceleration,which we refer as the no-dripping to dripping transitiondiscussed in the Results section. This transition exists becauseof a balance between the gravitational body force pushing theNaALG solution out of the nozzle and capillary force holdingthe fluid filament at the nozzle. Once the fluid is extruded fromthe nozzle, three distinct hydrogel particle size distributions areobserved (Figure 1c−e). Spherical monodisperse droplets areformed at low a values (Figure 1c), indicating that the ALGdroplets are extruded as single droplets, and pinch-off behavioris classified as dripping without satellites. At intermediate avalues, satellite hydrogel particles with bimodal size distribu-tions appear (Figures 1d and 8). We refer to this pinch-offbehavior as dripping with satellites. At high a values, polydispersehydrogel particles are produced as shown in Figure 1c,suggesting that the fluid is extruded as a single liquid columnand breaks into polydisperse droplets either prior to or afterimpact. At high NaALG concentrations, the viscous effectscome into play and alter the centrifugal speeds where theaforementioned pinch-off regimes are observed in Figure 4.Pearl-like morphologies seen at high viscosities are attributed tothe jetting liquid column impacting on the liquid bath prior tojet breakup and discussed in detail in the Jet Breakup section.Different morphologies observed and the transitions betweeneach pinch-off regime are summarized in Figure 4b.No-Dripping to Dripping Transition. For dripping to

start, the hydrostatic pressure created by the centrifugal motionon the liquid inside of the nozzle and NaALG compartment(Figure 1) should overcome the Laplace pressure. Thissituation can be represented by a simple pressure balancewhere the capillary pressure of a hemisphere (2γ/Rn) isbalanced by the hydrostatic pressure (ρa(h + L)) as

γ ρ= +R

a h L2

( )n (8)

For dripping to start, the left-hand side of eq 8 has to besmaller than the right-hand side. Rewriting this equationprovides a simple argument for the onset of dripping.

+ >Boh L

RO

2(1)

n (9)

Figure 5 shows results of a set of experiments where a isgradually increased, and the transition a at which the first

hydrogel dripped is noted. Plotting the results of thisexperiment with the modified Bond number demonstrates atransition region shown in Figure 5 in accordance with eq 9.We attribute the large error bars to the instrumental inaccuracyin setting a and contact angle hysteresis.44 It is important tonote that the modified Bond number given in eq 9 has no termaccounting for the viscosity of NaALG solutions. This indicatesthat the no-dripping to dripping transition has to be observed atthe same ω for different NaALG concentrations in Figure 4.Indeed, the operational phase diagram corroborates thisprediction. However, longer centrifugation times are requiredfor the observation of dripping in high viscosity NaALGsolutions compared to that of low viscosity NaALG solutionswith identical a, Rn, h, and L values. At large Oh values, theobservation of this transition is slowed down because of longertravel times of the viscous fluid through the nozzle.

Dripping without Satellites to Dripping with Satel-lites Transition. To identify the dripping without satellites todripping with satellites transition, we followed the experimentalprocedure described in the Experimental procedure sectionwhere the centrifugal acceleration is gradually increased and theresulting hydrogel particles are imaged. The transition isidentified as the first centrifugal acceleration a at which satellitedroplets are observed. For a given NaALG solution, at lowcentrifugal accelerations below this critical value, the nozzle isin the dripping without satellites regime and at accelerationsabove this critical value, satellite droplets emerge.Figure 4a shows how the acceleration for this transition

varies with the viscosity of the ALG solutions. In the drippingwith no satellite regime, every droplet is detached from thenozzle in a breakup time scale τb that scales with liquidproperties (surface tension γ, density ρ, and viscosity μ) and thegeometry of the nozzle Rn. Each of these parameters can affectthe dynamics of the local flow in the thinning filament that isformed between the pendant drop and the nozzle. In theinviscid case, where viscous stresses are negligible, the imposedpressure from capillary stress leads to the acceleration of liquidelements in the fluid filament, resulting in the drainage of thefluid from the connecting neck into both the hanging drop andthe hemispherical cap at the nozzle. Thus, the capillary andinertial forces balance each other, leading to an inertia-capillary

Figure 5. Radius of the particle (Rp) normalized by the nozzle radius(Rn) with respect to the modified Bond number (Bo(h + L)/2Rn) isplotted along the no-dripping to dripping transition.

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balance. For the inviscid case, the breakup time in the nozzles c a l e s w i t h t h e i n e r t i a - c a p i l l a r y t im e s c a l e

τ τ ρ γ≈ ≡ R /b cap. n3 .45−47 This scaling for the breakup time

emerges also in the linear stability analysis for an inviscid liquidcolumn.48,49 In the presence of viscous effects, the local balancebetween capillary and inertial stresses will be affected by viscousforces. The extra viscous resistance in the liquid thread slowsdown the thinning dynamics, leading to a longer breakup timefor the filament. Several studies in the literature47,49 show thatfor a viscous thread linear stability analysis provides a newscaling for the breakup time τb ≈ τcap. f(Oh), in which

= +f Oh Oh( ) 2 2 6 is a linear function of the Ohnesorgenumber.39,40 This scaling can be easily derived from the long-wave dispersion relationship that is discussed in detail byEggers and Villermaux in their review on liquid jets.47 In thelimit of low viscosity, the viscous correction f(Oh) reaches aconstant value →

≪f Ohlim ( ) 2 2

Oh 1, and we recover the

inviscid scaling τb ≈ τcap.. For very viscous threads, the viscouscorrection f(Oh) is linearly proportional to the Ohnesorgenumber →

≫f Oh Ohlim ( ) 6( )

Oh 1and the breakup time scales

with the visco-capillary time τb ≈ τvisc.−cap. ≡ μRn/γ.To have a quantitative prediction for the transition

acceleration between the aforementioned regimes (drippingwith satellite and without satellite formation), we study theprocess by comparing the relevant time scales. The time neededfor each drop to detach from the nozzle is equal to the breakuptime scale τb = τcap. f(Oh). As the drop is pinching off from thenozzle, the liquid is delivered into the hanging thread throughthe nozzle. The time scale for the delivery of fluid scales withthe convection time scale in the nozzle τconv. = Rn/U where U =ρa(h + L)Rn

2/8μL is the average liquid velocity inside of thenozzle. For a given liquid, if the fluid elements are deliveredfaster than the natural rate of droplet breakup (i.e. τconv. ≤ τb),then the satellite-less dripping mechanism cannot anymoresupport the high rate of fluid delivery. This leads to an increasein the length of the connecting filament between the main dropand the nozzle exit. Consequently, the extended filament goesthrough a secondary pinch-off process and forms smallersatellite droplets, which follow the trajectory of the maindroplet and impact into the CaCl2 bath. This simplified viewcan give us a simple criterion for satellite formation

ττ

ττ

< →

> →

f Oh

f Oh

( )1 dripping without satellites

( )1 dripping with satellites

cap.

conv.

cap.

conv. (10)

This criterion is presented by a comparison between theinvolved time scales (τcap. f(Oh) and τconv.). By multiplying bothtime scales with the convection velocity U, the criterion can berewritten in terms of the length scales involved in the process

< →

> →

LR

LR

1 dripping without satellites

1 dripping with satellites

d

n

d

n (11)

where Ld = Uτb = Uτcap. f(Oh) is the length scale, whichdescribes the extension of the connecting filament between themain drop and the nozzle (the inset image in Figure 6a).R e p l a c i n g L d w i t h ( ρ a ( h + L ) R n

2 /

8μL) ρ γ μ ργ+R R/ (2 2 6 / )n3

n and using the liquid andgeometric properties, for every transition acceleration measuredand plotted in Figure 6a in a dimensionless form, one can findthe corresponding values of Ld/Rn. Figure 6b shows anotherdimensionless representation of the data in Figure 6a byplotting transition values of Ld/Rn for different ALG solutionsat different Ohnesorge numbers. It is clear that above a criticalvalue of Ld/Rn ≈ O(1) satellite formation is observed. Thus, thescaling shown in eq 11 predicts a transition criterion for satelliteformation, which is in quantitative agreement with observedtrends. This simple scaling suggests that for more viscousliquids the transition between the formation of single-sizedroplets and stretched filaments (that break into satellitedroplets) happens at higher We. Similar scalings from Hinzeand Milborn in their study of rotary atomization50 suggest thatwith increasing Oh through liquid viscosity, μ, the transitionbetween the drop and filament formation happens at higherWe.

Dripping to Jetting Transition. The dripping to jettingtransition is identified as the transition from the formation ofindividual droplets through dripping (with or without satellites)into the ejection of a liquid jet (Figure 4b and the inset of

Figure 6. (a) Bo number versus Oh plotted for data points along the dripping without satellites to dripping with satellites transition. The data points aretaken from Figure 4a. The bottom inset illustrates dripping without satellites. After the pinch-off, the remaining filament of length (LD) retracts, that is,LD/Rn < O(1). The top inset illustrates the dripping with satellites. After the pinch-off, satellite droplets are formed. (b) Length of the filamentnormalized by the radius of the nozzle (LD/Rn) versus Oh is plotted along the dripping without satellites to dripping with satellites transition.

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Figure 7) out of the nozzle. The transition points aredetermined experimentally by gradually increasing We through

a at fixed Oh and imaging the resulting hydrogel particles asdescribed in the Experimental Procedure section. Theobservation of polydisperse hydrogel size distributions (Figure8c,e) is associated with jet breakup prior to impact. Theformation of stretched columns with pearl-necklace structuresdiscussed in the Jet Breakup section is attributed to the fluid jetimpacting as a connected single jet into the CaCl2 bath (Figure4b). The dripping to jetting transition happens when themomentum of the incoming fluid at the nozzle exit exceeds theresisting capillary pressure. The incoming fluid momentum andthe body force on the pendant drop because of centrifugalacceleration favors the transition from dripping to jetting, but

capillary forces resist it. The balance of these three effects canbe represented by a combination of critical jetting Weber (Wej= ρUj

2Rn/γ) and Bond numbers. Clanet and Lasheras51 showed

both by experimental measurements and a theoretical modelthat the critical Weber number (Wej) for the dripping to jettingtransition is a function of the Bond number f(Bo)

= =

+ − + −⎜ ⎟

⎡⎣⎢

⎤⎦⎥

⎡

⎣⎢⎢

⎛⎝⎜⎛⎝

⎞⎠

⎞⎠⎟

⎤

⎦⎥⎥

We f BoBoBo

KBo Bo

KBo Bo

( ) 4

12

( ) 12

( ) 1

ji

1/2

i1/2

i1/2

2 1/2 2

(12)

in which Boi is the Bond number based on the inner nozzleradius and Bo is the Bond number based on the outer nozzleradius.This can be rewritten as a criterion for the transition from

dripping to jetting

> →

< →

We

f BoO

We

f BoO

( )(1) jetting

( )(1) dripping

j

j

(13)

Knowing that f(Bo) increases with the Bond number andconsequently acceleration, one can see that at higheraccelerations the transition happens at smaller We. Thisshows that in the presence of high acceleration (high Bo) theliquid will overcome the capillary pressures with an evensmaller initial momentum (smaller We). Figure 7 shows thecorrected values of the jetting Weber number plotted versus Ohnumber. As predicted by the model suggested by Clanet and

Figure 7. Corrected Weber number for jetting (Wej) plotted as afunction of the Ohnesorge (Oh) number along the dripping to jettingtransition. The top inset illustrates the jetting phenomenon, and thebottom inset illustrates the dripping with satellites regime.

Figure 8. Panels a−c show microscopy images of hydrogel particles at different accelerations corresponding to different regimes: (a) dripping withoutsatellites, (b) dripping with satellites, and (c) jetting. The scale bar is 200 μm Panels d and e show the observed size distributions in different pinch-offregimes. The NaALG concentration is 2.0% ALG corresponding to Oh = 0.0145.

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Lasheras,51 the critical Weber number for the jetting transitiondecreases with centrifugal acceleration. Furthermore, in thelimit of large accelerations (Bo > 1), one can expand eq 12 into

≈>

−f Bo Bo Bo K BoBolim ( ) 4( / )( )Bo 1

i2

ni2, which scales as a−2.

Thus, the suggested model by Clanet and Lasheras51 predictsthat the critical Weber number for the dripping to jettingtransition scales as f(Bo) and decreases with acceleration as Wej≈ a−2. Figure 7 shows a plot of Wej/f(Bo) values versusOhnesorge number for all liquids tested in this study. It is clearthat the transition from dripping to jetting does not show arecognizable trend with changes in the viscosity over a widerange of Ohnesorge numbers, and within the experimentalerrors, the transition occurs at a constant value of Wej/f(Bo) ≈O(1). Thus, by replacing gravitational acceleration withcentrifugal acceleration, a simple model based on theinteraction between capillary, inertia, and gravitational effects(suggested by Clanet and Lasheras51) can be used to provide anapproximate criterion for the transition from dripping to jettingin our rotary configuration (eq 12).Jet Breakup. To understand why the broad hydrogel

particle size distributions and pearl-necklace geometries areobserved at high accelerations (Figure 1e), we estimate the jetbreakup length (Lj) using a relationship that is proposed byMiddleman52

= +L

RWe Oh

219.5( (1 3 ))j

nj

0.85

(14)

Middleman showed that a Newtonian liquid jet characterizedby the corresponding values of Weber and Ohnesorge numbers(Wej and Oh) breaks into a series of droplets in air at a length Ljaway from the nozzle exit described by eq 14. By comparing Ljto the gap height H between the nozzle and the CaCl2 bath, wecan conclude whether the jet breaks up into individual dropletsbefore impacting into the bath (Lj ≤ H) or it enters the bath asa connected jet ((Lj ≥ H)). One can estimate lower limits for Ljfrom eq 14 by inserting the Wej and Oh values at the drippingto jetting transition (Figures 4 and 7). The lower estimates forLj values vary from 32Rn to 360Rn, whereas the distance H iskept constant at 3.6 mm ≈ 45Rn. This simple scaling suggeststhat in the current geometry, for most liquids, right after thedripping to jetting transition, the jet impacts the bath as aconnected column of the liquid, and because of the inertia ofthe impact, the fragmentation of the liquid column results intoa group of individual droplets with a relatively polydisperse sizedistribution. This explains the polydispersity that is observedfor the size distributions in Figures 1e and 8e as well as thecylindrical columns with pearl-necklace geometries that havebeen observed for high NaALG concentrations shown in Figure4b. At low NaALG concentrations where Lj ≈ H, jet breaks upprior to/during impact into the liquid bath, and thefragmentation dynamics are faster than those of the gelationprocess (lower viscous resistance), leading to a polydispersesize distribution observed in Figure 8. At high NaALGconcentrations where Lj > H, the jet impacts onto the liquidbath as a liquid column and the extra resistance from viscousstresses delays the fragmentation process, forming corrugatedliquid columns that go through gelation before they break upinto individual droplets. Thus, gelation freezes the breakupprocess in time and creates pearl-necklace morphologies thatare observed in Figure 4b.Particle Size Distributions. Figure 8 shows the size

distributions of hydrogel particles synthesized at different

pinch-off regimes. Panels a−c show the microscopy images ofALG hydrogel particles corresponding to dripping withoutsatellites, dripping with satellites, and jetting regimes, respectively.The hydrogel droplets shown in Figure 8 are synthesized at afixed value of the Ohnesorge number Oh = 0.0145 but atdifferent values of centrifugal acceleration a. Panel d comparesthe size distributions between two hydrogel particle sets thatare prepared in dripping without satellites (blue data points) anddripping with satellites (green data points) regimes. For hydrogeldroplets synthesized in the dripping with satellites regime, twodistinct peaks are visible in their corresponding sizedistribution. The satellite droplets are approximately 5 timessmaller than the main droplets. Figure 8d compares thecorresponding size distribution for hydrogel particles betweenthe jetting regime (red data points) and dripping withoutsatellites regime (blue data points). It is clear from the sizedistributions plotted in Figure 8e that the jetting regime leadsto relatively broad size distributions, which is a natural outcomefor the multi-length-scale and multi-time-scale process of jetfragmentation upon a liquid bath at high Weber numbers.53

Phase Diagram for Centrifugal Synthesis. For research-ers interested in manufacturing hydrogel microparticles, it ishelpful to know the limits of different regimesthat aredescribed in our studywithin the context of a dimensionlessphase diagram. Such a phase diagram for different regimes ofpinch-off in the centrifugal synthesis of hydrogel droplets isshown in Figure 9. The dimensional parameters used in Figure

4a can be replotted in a dimensionless form, developing a phasemap in which the transitions between different pinch-offregimes are controlled by the scaling arguments. Figure 9 is aplot of the corrected We number, We/f(Bo) versus theOhnesorge number, and shows the four pinch-off regimesobserved in our study separated from each other by thecorresponding criteria.The transition between no dripping to dripping without

satellites is set by the competition between the hydrostaticpressure created by the centrifugal acceleration and the resistingcapillary pressure in the pendant drop at the nozzle exit (eq 9).The transition between dripping without satellites and drippingwith satellites is explained by eq 11. The dripping to jettingtransition is governed by the interaction between inertia,capillary, and centrifugal forces and a corrected value of the

Figure 9. Dimensionless phase diagram for centrifugal synthesis. We/f(Bo) vs Oh demonstrates the different pinch-off regimes predictedfrom the scaling arguments and the transitions between them. Theexperimental points are from Figure 4a.

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Weber number We/f(Bo) described by eq 13 provides anapproximate for this transition.

■ DISCUSSION

Our work provides a detailed study of the centrifugal synthesisof hydrogel particles and identifies critical parameters thatcontrol the size of synthesized hydrogel particles, as well asdifferent pinch-off regimes governing the corresponding sizedistributions.Previously Overlooked Pinch-Off Regimes & Exper-

imental Parameters. Previous studies32−34 observed theemergence of bidisperse or polydisperse particle size distribu-tions, yet a physical description was not provided. Scientiststrying to reproduce the reported experiments previouslystruggled to synthesize monodisperse particles and had tooperate by a trial and error methodology. With the scalingarguments provided, experimentalists can now rationally chooseoperating conditions to be in the desired pinch-off regime andhence achieve monodisperse particle size populations.Experimental parameters such as the contact angle, θ, and the

liquid viscosity, μ, and geometrical parameters such as thelength of the needle, L, the height of the fluid, h, and the nozzleto CaCl2 bath distance, H, were not studied systematically inprevious studies.33,34 Our results indicate that these parametersinfluence the pinch-off regime and particle sizes. For instance,both h and L influence the flow speed, U (eq 2), and hence alsoaffect We and Bo. For instance, slightly reducing h or increasingL can move an experiment from the dripping with satellitesregime to the dripping without satellites regime, hence avoidingthe emergence of satellites. H is also found to influence theparticle shape at low We. Maeda et al. also observed theformation of asymmetric hydrogel particles with larger H.33 Weplaced the nozzle as close as possible to the CaCl2 bath, that is,the smallest H experimentally accessible to minimize shapedeformations. At large We, a jet is ejected from the nozzle. Hdictates whether this jet will impact the bath before or after thejet breakup (Jet Breakup section). Further details on thegeometry of the setup and a detailed discussion of the influenceof H are provided in the Supporting Information.Influence of the Pinch-Off Process on the Particle

Size. Previous studies33,34 relied on Tate’s law, which ignoresthe pinch-off process (eq 3), to estimate the average size ofhydrogel particles. Figure 3 demonstrates that Tate’s lawunderestimates the average particle size. We hypothesize that aportion of the pendant drop should stay behind once thependant droplet pinches off as the volume of the pinched-offdroplet is smaller than the volume of the pendant droplet.Along with the proof provided by the phase diagram, weconclude that the pinch-off process needs to be taken intoaccount. The numerical correlation by Yildirim et al. (eq 6)predicts the average droplet size within the experimental regimecovered in this study. Equation 6 is only valid for small We andOh where the impact speed on the CaCl2 bath is small.43

Influence of Shrinking/Swelling after Impact on theParticle Size. A droplet of radius Rdf can shrink/swell its sizeto Rp upon cross-linking. The degree of cross-linking dictatesthe extent of swelling/shrinking. Fitting eq 7 where C is ashrinking/swelling parameter to Figure 3 resulted in C ≈ 0.99for the canonical sample. This result indicates that the pinched-off droplet shrinks slightly yet it is not statistically significant.Therefore, we conclude that the shrinking is not significant forour canonical sample.

We expect shrinking to be more pronounced with higherNaALG concentrations as previously reported in cross-linkingwith dripping or bulk experiments.25,26 Furthermore, othercross-linking materials such as chitosan may shrink or swelldepending on the formulation and cross-linking solutionconditions.2,4 Therefore, determining C prior to experimentsis important for shrinking/swelling materials. The fittingparameter C can be determined in simple dripping experimentswhere the Rdf and Rp can be measured by video imaging priorto and after impact. Once C is determined for a givenformulation, semiempirical eq 7 can predict the particle sizeaccurately.

Behavior at Finite We and Oh Numbers. Equation 6holds within the dripping without satellites regime where We andOh are small. However, more accurate correlations consideringfinite values of We and Oh can be developed. Particularly, forlarge Oh and We, we expect deviations from eq 6. Once specificvalues of We and Oh numbers are known, corrections to eq 6can be introduced using numerical simulations.54

Differences between Dripping Faucet Experimentsand Centrifugal Synthesis. It is important to mention thatthe experimental system used by Harkins and Brown,41 thedripping faucet,55 has fundamental distinctions from the NiCsetup used in centrifugal synthesis. In dripping faucetexperiments, the average fluid velocity, U, can be independentlycontrolled by controlling the pumping rate; hence, Bo and Weare independent of each other. In centrifugal synthesis, both Boand We are dependent on the centrifugal acceleration, a;therefore, the numerical solutions of the 1D slender jetequation56 given in Yildirim et al.43 for the dripping faucet hasto be used with caution. The experiments by Harkins andBrown41 are dripping faucet experiments with diminishinglysmall We numbers, and the Bo number governed bygravitational acceleration, g, is constant for a given Rn andfluid properties. Yildirim et al.43 provided the numericalsolutions connecting Rdf/Rn to Bo for a given We, whereas inexperiments shown in Figure 3, the We changes with Bo and anew numerical solution is required for every Bo, which is atime-consuming process. For predicting the hydrogel particlesize in Figure 3, we utilized the correlations for low We in eq 6,which does not account for the full coupling of Bo and We. Inthe experiments presented in Figure 3, Oh varies between 0.15and 0.25 because of changes in Rn and γ. We varies between0.01 and 0.1. We attribute the variations at high Bo > 10−1

observed in Figure 3 to inertial effects, that is, non-negligibleWe numbers.From a fundamental fluid mechanics point of view, the

pinch-off process in the centrifugal synthesis of ALG hydrogelsis analogous to the dripping−jetting transition in the flow of aliquid through a nozzle51,54 yet subtle differences exist. Indripping nozzle studies, the flow rate of the fluid is controlled,whereas the Bo is defined by the gravitational acceleration andhence is approximately constant. In other words, We and Bonumbers can be independently varied. In centrifugal synthesis,the centrifugal acceleration drives the flow and both We and Bodepend on a; therefore, they are interconnected. Thecorrection given in eq 12 developed by Clarnet and Lasheras51

becomes more important for centrifugal synthesis because ofvarying and significantly larger values of Bo. Furthermore, theimpact of the pinched-off droplet and the reaction aspectincreases the complexity of experiments compared to thedripping nozzle problem.

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Experimental Issues. In dripping faucet experiments, thepinch-off process is directly observed, which allows for accuratemeasurements of droplet shape, size distribution, and exitvelocity. In our study, the presented predictions are based onthe average hydrogel size and size distributions acquired byimage processing after cross-linking. This is due to experimentaldifficulties in imaging at high centrifugal speeds and the needfor developing a dedicated centrifugation apparatus. Haeberle etal. used stroboscopic imaging techniques to visualize the pinch-off process under centrifugal acceleration.34 We predict thatemploying stroboscopic imaging techniques in future studiescan enable a better insight into the pinch-off process underacceleration.The non-Newtonian behavior of NaALG solutions also has

to be taken into consideration. As demonstrated by Haeberle etal.,34 the rheological behavior of NaALG solutions gives rise tothe formation of very long filaments at large stain rates withconcentrated NaALG solutions. For our canonical sample, wedid not observe a significant effect of the shear-thinningbehavior of NaALG solutions that comes into play at large Weand Oh numbers. This effect can manifest itself by decreasingthe viscosity and increasing U at a given Bo, therefore inducingjetting at lower a values than predicted in eq 12 where We iscalculated using zero shear viscosity.

■ CONCLUSIONSCentrifugal synthesis of hydrogel particles is a promisingmicroparticle synthesis method. It enables the rapid manu-facturing of relatively large quantities of hydrogel particles withstandard lab equipment. Despite its promise, the lack of aphysical understanding of the method has limited its wide-spread use. Previous studies predicted an average droplet sizeusing a simple force balance over a pendant drop, ignoring thepinch-off process. Furthermore, the observations of non-monodisperse particle size distributions were not connectedto different pinch-off regimes.33,34

In this study, we improved the overall physical understandingof the centrifugal hydrogel synthesis method. We provided acorrelation taking into account the pinch-off phenomenon forpredicting the average size of hydrogel particles accuratelywithin the dripping without satellites regime at low We and Ohnumbers. Furthermore, we explained the emergence of differentpinch-off regimes (dripping without satellites, dripping withsatellites, and jetting) governing size distributions and presentedscaling arguments predicting the transition between regimes.Our systematic study unveiled the importance of previouslyoverlooked parameters and connected them to pinch-offregimes. The presented results can guide the rational designof centrifugal synthesis hydrogels and polymeric particles forvarious applications.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.6b00806.

Guide for experimentalist: design of a nozzle-in-centrifuge (NiC) apparatus, influence of the distancebetween the nozzle and the liquid bath on the particleshape, density of NaALG as a function of NaALGconcentration, surface tension of NaALG with SDS, andhydrophobization of nozzles (PDF)

■ AUTHOR INFORMATION

Corresponding Author*E-mail: pdoyle@mit.edu.

Author Contributions#H.B.E., E.R.S., and B.K. contributed equally.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by the MIT-Novartis Center forContinuous Manufacturing. ERS acknowledges the LordFoundation for the MIT undergraduate researcher opportunityprogram. The content of the information does not necessarilyreflect the position or the policy of the Government, and noofficial endorsement should be inferred.

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Langmuir Article

DOI: 10.1021/acs.langmuir.6b00806Langmuir 2016, 32, 7198−7209

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