FieldField--and Shearand Shear--Driven Collective Phenomena in Driven Collective Phenomena in Suspensions Suspensions Boris KhusidNew Jersey Institute of TechnologyAndreas AcrivosThe Levich Institute at CUNYSupportNASA, NSF, DARPADielectrophoresis Dielectrophoresis The force acting on a particle subject to a gradient electric field is Electrophoresis is the motion of a charged particle in a DC field Dielectrophoresis is the motion of a neutral particle in gradient DC and AC fieldsThe time average dielectrophoretic force in an AC fieldEPEF)(Qe∇⋅+=( )23rms)Re(a2f0EFd∇ωβεπε=PositivedielectrophoresisNegativedielectrophoresis0)Re(>β0)Re(<β()()( ) ( )ωε+ωεωε−ωε=β*f*p*f*p2FieldField--induced Phase Transitioninduced Phase Transition0E=TkWBel≥A variety of orderedaggregation patternsA homogeneous random arrangement of particlesElectrorheological fluidsDussaud, Khusid, Acrivos, J Appl Phys, 88, 2000Measuring the Particle Polarization Measuring the Particle Polarization Validated the equation for dielectrophoretic force for E~ 1 kV/mm Dielectric spectroscopy for measuring particle polarization for E~ 1 V/mm The Maxwell-Wagner modelDielectric Spectroscopy DS measures the relation between time-varying voltage and currentthrough a samplesampleE~1 V/mmNJIT W.M. Keck Laboratory()( )( )ωβ=ε+ωεε−ωεc2c,c,*f*s*f*sMicroscopic theory for field-induced phase transitionsFieldField--induced Phase Separationinduced Phase SeparationPhase Diagramrelative field strength UNSTABLEMETASTABLEspinodalcoexistencecurvea=1 µma=1 nmparticle volume fractioncrϕϕTkvEBp2f0εε=λKhusid & Acrivos, Phys Rev E, 1995, 1996, 1999cccr10V0VSandia’s SwIFTTMprocess monolithic multilayer device10 Vptp, 15-30 MHz()()()Lµm570Hµm6Wµm40 ××FlowElectrodes0V10Vµm6Dielectrophoretic gates2rmsE∇GateDielectrophoretic Particle ConcentratorDielectrophoretic Particle ConcentratorSource: Bennett, Khusid, Galambos, James, Okandan, TRANSDUCERS'03, Boston, MAExperimental ResultsExperimental Resultspolystyrene spherical beads in DI water, 0.1% (v/v) µm10.27i0.45ß−−=Particle polarization Flow rate 0.24 pL/s to 9.6 pL/s; Re~10–5-10–3Source: Bennett, Khusid, Galambos, James, Okandan, Jacqmin, Acrivos, ApplPhys Lett, 2003Dielectrophoretic gatesFlowElectrodes10V0Vµm6dF2rmsE∇10Vptp, 30 MHzFlowGate10s70s120s 180sm20µPhase transitionFlowing Heterogeneous MixtureBeads and bacterial cells (heat-killed staphylococcus aureus)10 Vptp, 15 MHz Flow rate 0.24 pL/s to 9.6 pL/sSource: Bennett, Khusid, Galambos, James, Okandan, Jacqmin, Acrivos, ApplPhys Lett, 2003m20µBeadsCellsFlowElectroElectro--hydrodynamic Modelhydrodynamic ModelSuspension flowChemical potential (Phys Rev E, 1995-9)2cdcdfvTk2ts00pBpcEω∂ε′∂ε−=µ()0*=∇ωrD()0*=×∇ωrE()**s0*c,ωωωεε= EDQuasi-steady electrodynamic equations0=∇v( )gsvvvfppvissccptρ−ρ+µ∇−∇+−∇=∇+∂∂ρParticle balance( )0ctcp=+∇+∂∂jv∂∂+∂∂η=ijjisvisijxvxvs2mfscc1c5.11−+η=η()( )[ ]gjfppsp2pa6vc1cρ−ρ+µ∇−ηπ−=Shear stress( )2*221rEEω=ViscosityElectric displacementEntropic factor( ) ( )[ ]∫−+−=c00dcc1Zc1clncfThe particle polarization can be measured at low fields)Re(βModelingModeling0.1%(v/v)-suspensionFlow rate 8.64 pL/sVoltage 10Vptp10s 10s70s 70s180s 180s120s 120sFlow velocity Particle velocityAverage flow velocity 36 µm/ssm8.49 µsm2.45 µsm3.106 µsm8.78 µsm4.110 µsm4.151 µsm9.139 µsm6.171 µ1, concentration2, field strength8.73%45.4%56.4%Two bolusesSingle bolusDussaud, Khusid & Acrivos, J Appl Phys., 88, 2000Electric Field Configuration Electric Field Configuration 0y=∂ϕ∂0y=∂ϕ∂Computational cell80 mm3 mm160 mmElectric fieldElectrodes+/-xyFlow0x=∂ϕ∂0x=∂ϕ∂1=ϕ1=ϕ0=ϕ02=ϕ∇0=ϕElectrodesSuspensionElectricElectric--field Strengthfield StrengthLog E2(Vrms/d)2Neutrally buoyant suspensionPolyalphaolefin spheres (0.92 g/cm3 , 90 µm) in corn oil (0.92 g/cm3, 0.06 Pa·s, eps=2.2)()( )( )ωϕβ=ε+ϕωεε−ϕωε*f*s*f*s2,,The Maxwell-Wagner model15.0)Re(−=βfor 100-1000 HzParticle polarization in low field ~ 1V/mm Channel cross-sectionLow Field Region3 mmd=2mmGR HVHVSource: Kumar, Qiu, Khusid, Jacqmin, Acrivos, Phys. Rev. E, 20045kv, 100Hz, without flowFieldField--induced Segregationinduced Segregation0s 45s90s300s150s2325sGRHVGRHVGRHV3.6mmVrms/d =2.5 kV/mmTop view, 10%Neutrally buoyant polyalphaolefinspheres in corn oil 15.0)Re(−=βfor 100-1000 HzSource: Kumar, Qiu, Khusid, Jacqmin, Acrivos, Phys. Rev. E, 20045kV, 100Hz, without flow10%,38min15%,30min20%,28min25%,36min30%,30min5%,41minGRHVGRHVGRHVGRHVGRHVGRHV3.6mmFront FormationFront FormationTop viewmmkVrms2.5d=VSource: Kumar, Qiu, Khusid, Jacqmin, Acrivos, Phys. Rev. E, 2004Comparison with Experiments0 10 20 30 40 50 60 70 80 90 1001101201300.150.200.250.300.350.400.450.500.5515%10%5%Front Position, L/D5% (5kV/2kHz)5% (3kV/2kHz)10% (5kV/100Hz)10% (3kV/100Hz)15% (5kV/2kHz)15% (3kV/2kHz)GRHVD=3.6mmL( )( )2rmsf02f4dVRead3ωβεεη=τDielectrophoretic timed/t τSource: Kumar, Qiu, Khusid, Jacqmin, Acrivos, Phys. Rev. E, 2004Field Strength and Frequency Effects5kV, 100Hzt=20.5min4.63td=τ3kV, 2000Hzt=52.5min6.58td=τ3kV, 100Hzt=54.5min8.60td=τTop view, 10% suspensionSource: Kumar, Qiu, Khusid, Jacqmin, Acrivos, Phys. Rev. E, 2004MultiMulti--Channel ApparatusChannel Apparatuselectrodesinletoutlet150 chambers on the 4” waferH = 30 µmSilicon WaferAl electrodesTransparentGlass CoverinletoutletinletoutletElectrodesparallel tothe flowElectrodesperpendicularto the flow3 mm6 mmElectrode spacing = 2, 5, 10 µmNJITNJITSource: Markarian, Yeksel, Khusid, Farmer, Acrivos, Appl Phys Lett, 82, 2003Model for Dilute SuspensionsModel for Dilute Suspensions§ The balance of drag, dielectrophoretic, and gravitationalforces§ The field-induced particle displacementur=dtd00trr==( )( )evu ga34E)Re(a2a63fp2rms3f0fρ−ρπ+∇βεπε=−πηfQiu, Markarian, Khusid, Acrivos, J Appl Phys, 92, 2002 Dussaud, Khusid, Acrivos, J Appl Phys, 88, 2000The particle polarization can be measured at low fields)Re(β§ The asymptotic expression for the spinodal1≈Ψϕλω()2Re3~ βΨωTkvEBp2f0εε=λ0 secZXGRHVHVHVHVGRGRGR160 µm900 secGRHVHVHVHVGRGRGRExperimental Results Experimental Results 10 µmFlowAC Field: 20V, 1kHzelectrodes à lightGL = GL0 particles à darkGL < GL0 240 µm0.1% (v/v); Q = 0.05 µl/min; Re=10–5Measurement ofGray Level