Shelley L. Anna Carnegie Mellon University

Pittsburgh, PA

Using Mass Transport to Control Microscale Emulsion Formation

Symposium in Honor of Bob Bird on the occasion of his 90th birthday

1997 Society of Rheology Meeting, Galveston, TX

The Transient Extensional Rheology of Polystyrene and Polyacrylamide Boger Fluids

and the Effects of Salt Concentration on the Extensibility of PAA

Macromolecules

as Q0 increases

(and CaFF)

Microfluidics Allows Formation of Uniform Emulsions

Microfluidic flow focusing

(Anna & Mayer Phys. Fluids 18 (2006) 121512)

(Anna Bontoux & Stone, Appl. Phys. Lett. 2003) QuickTime™ and a

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(Lee, Walker, Anna Phys. Fluids, 2009)

Re = ρUDµ

<10

Caliper Technologies

US Genomics

10-100 micron length scales

Enhanced transport

Droplet-Based Microfluidic Processing Strategies

Droplets as chemical reactors: •generate precise volumes •interface protects encapsulated materials •easy to manipulate droplets

Continuous Flow PCR in Microfluidic Droplets Schaerli et al, Anal. Chem. (2009)

f ~ 1000+ s-1 d ~ 5-100 µm

Chen, Gerdts and Ismagilov, J. Am. Chem. Soc. (2005)

Protein Crystallization in Microfluidic Droplets

Surface Active Materials at Microscale Interfaces

τ D ∝

l 2

D

•Surfactants, polymers, and particles stabilize bulk emulsions •In droplet-based microfluidics, typically loaded with surfactant •Surface active species impact: formation, stability, barrier properties, mobility

Kinetic exchange

αβ

Diffusion D

Flow Marangoni Stress

Γ

C∞

(microstructure) τ conv ∝

lU

Two Ways Transport Matters in Synthesis of Novel Multiphase Materials

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Example 1: Generating submicron droplets

Small molecule surfactants diffuse rapidly Kinetics of adsorption competes with microfluidic formation times

Tipstreaming of tiny droplets

Students & Collaborators: Professor Lynn Walker, Wingki Lee, Nick Alvarez, Anthony Kotula, Todd Moyle, Chris Nelson, Hans Mayer

Example 2: Stable, Non-spherical Pickering Foams

Nanoparticles diffuse slowly Diffusion competes with microfluidic residence times

Control coverage of particles on interface

Controlling the Properties of Emulsions and Foams

Desired Qualities: droplet size/shape, particle loading, stability...

Bulk methods

• Homogenization

• Mixing

Break up

Particle adsorption

Coalescence

No independent

control of desired

properties

Cannot separate emulsification processes

Microfluidics: Control size, volume fraction in 10-100 µm size range

Challenges: Make droplets a lot smaller? Control coverage on interface?

Example 1: Making Droplets Smaller than the Device

Submicron drop formation in microfluidic flow focusing (Anna Bontoux & Stone, Appl. Phys. Lett. 2003)

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Taylor (1934), DeBruijn (1993), Eggleton, Tsai and Stebe (2001), etc

Tipstreaming

• Surfactants are necessary • Droplet size ~100X

smaller than orifice

(Anna & Mayer Phys. Fluids 2006) (Lee, Walker, Anna Phys. Fluids 2009)

C∞ M[ ]

Qo mL hr[ ]

Observations of Surfactant Mediated Tipstreaming

Key Observations •Surfactants are necessary •Droplet size ~100X smaller than device orifice •We can’t control process for arbitrary surfactants •Oil-water-surfactant transport parameters not known

(Anna & Mayer Phys. Fluids 18 (2006) 121512) (Lee, Walker, Anna Phys. Fluids (2009) 032103)

Tipstreaming is a kinetic limited phenomenon

∂Γ∂t

+ ∇s ⋅ Γv s( )+ 2HvnΓ − Ds∇s2Γ = jn

∂c∂t

+ v ⋅∇c = D∇2c

ja /d = βCs Γ∞ − Γ( )−αΓ

jD = −D n ⋅∇c s

surface compression

surface dilution

surface diffusion

advection-diffusion flux to interface from bulk

kinetic exchange of surfactant near

interface

• Mass balance of surfactant on interface

Controlling dimensionless parameters

•If Bi(Peh) << 1, then kinetically controlled

•If Bi → 0, then approaching insoluble limit

Bi = αG

Pe = Ga2

D

h =Γeq

C∞a

Biot number

Peclet number

adsorption depth

Milliken & Leal (1994); Eggleton & Stebe (1998)

C12E8: Bi(Peh) ≈ O(10-6 to 10-3)

C12E8: Bi ≈ O(10-9 to 10-7) • Allows for simplifications, but equations still nonlinear and difficult to

solve • For our systems, something still needs to adsorb for tipstreaming to

occur!

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∂ öΓ∂öt

+ ö∇s ⋅ öΓöv( )+ 2 öH n ⋅ öv( )öΓ − 1Pes

ö∇s2 öΓ =

jn

Γ∞G

µoaGRTΓ∞

öTo− λ öT

i( )⋅n+ ö∇söγ − öγ n ö∇s ⋅n( )= 0

Modeling Interfacial Flows

Diffusion

Desorption Adsorption

Convection

Stokes flow

stress balance on interface

surfactant mass balance on interface

fluid flow interface geometry

surfactant effects

Alvarez, N. J., et al. J. Colloid and Interface Sci. (2011)

Interfacial Concentration

Gradients

Goal:

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• Cone shaped interface – relatively steady during thread generation

• Very little normal motion of interface

A Simplified Model for Tipstreaming Key Experimental Observations

θc

2a

L

(Anna & Mayer Phys. Fluids 18 (2006) 121512)

Axisymmetric Stokes flow, radial motion requires:

vs ≈ −2Qorc

2

worh1r2

• Model: axisymmetric conical interface

with cutoff radius at point of thread generation

θc

(Moyle, Walker, Anna in preparation)

Predicting the Operating Parameters for Tipstreaming Normal & Tangential Force Balances on Interface

τ o − τ i( )⋅n( )⋅ t − ∇sγ( )⋅ t = 0

pi − po( )+ τ o − τ i( )⋅n( )⋅n + γ ∇ ⋅n( )= 0 ‣Use to obtain pressure jump across interface

‣Use to obtain γ(r)

• Surface tension profile requires a surface concentration distribution • Determined by surface equation of state

surface tension plunges to zero near thread

surface concentration increases steeply near thread

• Integrate to find out how much surfactant is needed

• Equate to amount adsorbed in time for drop formation

Nneeded = Γ r( )2πr sinθc drrc

S

∫

Nads = βC∞Γ∞τ d 2πa2( )τ d ≈ 0.15DH

3 QdCaff

(Lee, Walker, Anna Phys. Fluids (2009) 032103) (Moyle, Walker, Anna in preparation)

Physical constraint boundaries Experimental tipstreaming observations

_

_ Applying Additional Constraints to Determine Boundaries

Geometry limit for the apex angle of a cone

Transition to jetting boundary These constraints limit conditions where a cone can be maintained and allow for rapid estimation of the tipstreaming region

Boundaries arise separating physical from unphysical operating conditions

Transition to jetting

Global Surfactant Balance Tipstreaming

viable

Global surfactant balance boundary

Cone geometry boundary

θc

Geometry

Henry's law boundaries Generalized Frumkin boundaries Experimental tipstreaming observations

A more realistic adsorption isotherm adjusts the boundaries

Generalized Frumkin equation of state

(Moyle, Walker, Anna Phys Fluids 2012)

Controlling the Interface Shape to Eliminate Large Droplets

200 μm

Utilizing this control scheme, thread formation has been sustained for several hours

200 μm

Electric to pneumatic transducer

Pressurized vessel

Dispersed phase liquid

Compressed Nitrogen

Characterizing the Tipstreaming Droplet Size and Polydispersity

Tipstreaming can be used to generate monodisperse, submicron droplets

Size range: 180 - 1200 nm

More polydisperse with controller

Flow conditions dramatically impact size

Example 2: Control Particle Coverage at a Bubble Interface

S. Crossley et al., Science, 327, 2010.

M. Cui et al., Science, 342, 2013.

Fluid storage & delivery

Catalysis

Particle stabilized foams to create porous monoliths

I.Akartuna et al Adv Mater (2008)

Experimental Set-Up

Center for Complex Fluids Engineering 19

Microcapillary device • Borosilicate glass (circular or square) R = 250 – 300 μm • Single slug bubble or drop generated at nozzle

Syringe Pump (0.1-1 mL/hr)

or Air Pressure (10-20 kPa)

Syringe Pump (1-5 mL/hr)

Nozzle Reservoir

Syringe Pump (1-5 mL/hr)

Continuous Particle Size Dispersed Reason

3% latex suspension + 18 mM lysine-HCl 1.9 μm Octanol Direct particle

observation at interfaces

2% silica + 0.2mM CTAB 12 nm Air Particle-stabilized

bubbles 10% silica + 0.2mM CTAB

Microfluidic Generation Methods for Particle-Stabilized Emulsions

Center for Complex Fluids Engineering 20

Microfluidic methods • Monodisperse • Control over droplet dynamics • Particle adsorption rates • Slug bubbles exhibit neck – related to surface coverage • Modeling – relating coverage to residence time

Kotula and Anna, Soft Matter, 342, 2013.

Bubbles in nonequilibrium shapes

Flow N2 Aqueous

nanoparticle suspension

A.R. Studart et al., J. Phys. Chem. B, 12, 2009.

Modeling Particle Adsorption to Slug Bubbles

Center for Complex Fluids Engineering 21

Particle Transport Model • Assumption – rear lobe is close-packed with particles

a

L

Mass flux

Surface area for

adsorption

Covered length

Kotula and Anna, Soft Matter, 342, 2013.

Particle coverage is directly related to residence time!

No direct particle observation

Determining Particle Coverage of Nanoparticle Suspensions

Center for Complex Fluids Engineering 22

12 nm Silica + CTAB • Air bubbles generated •Mass balance at interface

Cannot visually observe coverage during flow

Can observe effects through jamming at interface

Ain

Γin

Aout

Don’t know Ap Determine relative Γ

Γout

Γout

Aout

Γout = Γc

Γout unknown

Surface areas

Surface concentrations

Calculate Γin/ Γc for jammed systems

(Assumed constant)

Critical jamming conc.

Measuring Surface Areas In and Out of Confinement

Center for Complex Fluids Engineering 23

Measure length in capillary - surface area of known geometry

L

D

Bubble exits confinement

Measure surface area of jammed bubble • Assume axisymmetric • Rotate arc length around centroid

Kern and Bland, Solid Mensuration with Proofs, 1948.

Measure surface area ratios at two different particle concentrations

Surface Area Ratios Correlate with Residence Time

Center for Complex Fluids Engineering 24

Relative particle conc. • Increases with increasing residence time • Increasing bulk concentration particle loading

Γin = Γc

Γin = 0

Indirect measure of particle loading versus residence time

No jamming Jamming

Using Residence Times to Control Particle Coverage

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Microfluidic control of residence time allows control of bubble size, volume fraction, and interfacial coverage

Conclusions

Knowledge of detailed transport mechanisms and timescales in droplet-based microfluidic devices enables synthesis of novel multiphase materials

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Happy Birthday, Bob!!