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Rheology of non-Newtonian liquidMixtures and the Roleof Molecular Chain LengthSean ParliaColumbia University, Dispersion Technology Inc.Dr. Ponisseril SomasundaranColumbia UniversityDr. Andrei DukhinDispersion Technology Inc.Center for Particulate and Surfactant Systems (CPaSS)Summer 2019 IAB MeetingColumbia University, New York, NYAugust 6-7, 20191

Rheology of Non-Newtonian MixturesResearch Team: Sean Parlia, Dr. Andrei Dukhin, Dr. PonisserilSomasundaranOverview: We employ two methods for studying the rheology ofmixtures of nonpolar media mixed with surfactant: ShearViscosity and Longitudinal Viscosity measurements.StressTechnical Information: Effect of chain length on rheology ofnonpolar mixtures; Energy of molecular interactions for shortchain surfactants, volume-based mixing rule for long-chainsurfactants, Expanding-collapsing of flexible long-chain surfactantmoleculesIndustrial Relevance: Industrial Relevance: Personal Care,nanotechnology, paints and pigments, food industry, oil industry2

Classical Mixing Rules Arrhenius Mixing Rule (1887):ln m x1 ln 1 x2 ln 2Symbolsη – viscosityx – mole fractionV – molar volume Grunberg-Nissan Mixing Rule (1949):ln m x1 ln 1 x2 log 2 x1 x2 d Katti-Ghaudhri Mixing Rule (1964):Molecular energyrelating to structureln mVm x1 ln 1V1 x2 ln 2V23

Classical Mixing Rules, ContinuedSymbols Excess Activation Energy of the Viscous Flow: R– gas constant G i x xijE ijjT – absolute temp.E – intermolecular energybetween components Eyring’s Representation of Liquid Viscosity:Nln mVm xi ln iVi i GRT Combining above equations for 2-component mixture:ln mVm x1 ln 1V1 x2 ln 2V2 x1 x2E12RT4

Materials and MeasurementsMaterials Newtonian Liquid:Non- Newtonian Liquids: Toluene Short Chain Surfactants: Molecular Weight: 92.14 g/mol Sorbitan Monolaurate (SPAN 20) – Molecular Weight: 346.5 g/mol Sorbitan Monooleate (SPAN 80) Molecular Weight: 428.6 g/mol Long Chain Surfactants: Xiameter OFX-5098 Molecular Weight: 3,255.9 g/mol Xiameter OFX-0400 Molecular Weight: 3,101.1 g/molMeasurements Shear Viscosity – Translational & Oscillational* Motion Longitudinal Viscosity – Oscillational Motion5

Shear Rheology – Short Chain SurfactantTheoretical vs Measured Viscosity of SPAN 20/Toluene Mixtures10000Measured ViscosityArrhenius ViscosityKatti-Ghaudhri Viscosity100 Final Visc, E 16,131.78 J101Simple Mixing Rules FailExcess Activation Energy MixingRule fits data Indicates strongintermolecular interactions0.10102030405060708090100Concentration of SPAN 20 (wt. %)Theoretical vs Measured Viscosity of SPAN 80/Toluene Mixtures10000Measured Viscosity1000E12 Values: SPAN 20: 16,131 J SPAN 80: 21,293 JViscosity (cP)Viscosity (S/m)1000Arrhenius ViscosityKatti-Ghaudhri Viscosity100Final Visc., E 21,293.92 J1010.10102030405060708090100Concentration of SPAN 80 (wt. %)6

Intermolecular Forces E12 Consistent with HLBHLB Numbers: SPAN 20 – 8.6 SPAN 80 – 4.3 SPAN 80 is more hydrophobic than SPAN 20, so it has higher affinity fornonpolar Toluene.E12 is higher for SPAN 80 than SPAN 20, confirming higher affinity fortoluene.ΔG Values (at 50% Surfactant concentration):SPAN 20 : 4040 JSPAN 80: 5040 JThese values are 2x higher than values reported by Monsalvo[1] for mixtures of1,1,1,2-tetrafluoroeethane (HFC-134a) with tetraethylene glycol dimethylether[1] - Monsalvo M.A., Baylaucq A., Reghem P., Quinones-Cisneros S.E., Boned C. “Viscosity measurements andcorrelations of binary mixtures: 1,1,1,2-tetrafluoroeethane (HFC-134a) tetraethylene glycol dimethylether(TEGDME), J. Fluid Phase Equilibria, 233, 1-8 (2005)7

Classic Mixing Rules Fail for Long ChainsTheoretical vs Measured Viscosity of OFX-5098 Mixtures1000MeasuredViscosity (cP) Standard mixingrules, based onmole fractions,fail in all casesArrhenius - Mol. Basis1001010.10.10.20.30.40.50.60.70.80.91Volume Fraction of OFX-5098Theoretical vs Measured Viscosity of OFX-0400 Mixtures1000Measured DataArrhenius - Mole Basis Even whenconsidering excessactivation energy,theories still fail.100Viscosity (cP)01010.100.10.20.30.40.50.60.70.80.91Volume Fraction of OFX-04008

Vol. Fraction Based Rule Works for Long ChainsViscosity Ploted on Volume Fraction Basis1000MeasuredVolume fraction-basedmixing rule:ln m (1 ) ln 1 ln 2Vol. Basis100Viscosity (cP)Arrhenius - Mol. Basis1010.100.10.20.30.40.50.60.70.80.91Volume Fraction of OFX-5098Viscosity Ploted on Volume Fraction Basis1000Measured DataVol. BasisWhy does this theorywork, but not the others?Viscosity (cP)100Arrhenius - Mole Basis1010.100.10.20.30.40.50.60.70.80.91Volume Fraction of OFX-04009

Hypothesis for Long Chain SurfactantsDistanceInitial StateExpansion under longitudinal stressPressure GradientPxStressReturn to initial state, movedtranslationally Surfactant is initially bound in placeto nonpolar media (toluene) Under stress the molecule stretches When molecule is sufficientlystretched, it can release from initialmolecule, and return to original shapein new position, movingtranslationally. Longitudinal rheology data used forexploring this hypothesis10

Hypothesis for Long Chain Surfactants Think: Slinky Molecule experiences consecutive cycles ofexpansion and collapsing. In addition, it progressesforward driven by the stress. Such motion can be presented as superposition of oscillation andtranslation. Consequently, the two degrees of freedom that are involvedtranslational and oscillational. According to this model, viscosity of the mixture depends solely on theamount of the non-Newtonian surfactant, hence:ln m (1 ) ln 1 ln 211

Longitudinal Rheology: Role of OscillationLongitudinal ultrasound-based rheometer: Measures attenuation at multiple frequencies from 1 – 100 MHz: Molecules undergo mostly oscillational motion when such device is employed. This would allow us to characterize this degree of freedom individually,separately from the translational degree of freedom. Also can use to characterize mixtures as Newtonian or Non-Newtonian: Newtonian liquid viscosity is independent of frequency.12

Short-Chain Surfactants always Non-NewtonianSPAN 20Longitudinal Viscosity vs.Frequency PlotsSPAN 80 Short-chained surfactants (SPAN) formnon-Newtonian liquid mixtures even atvery low concentrations Only at VERY low concentrations dothe mixtures transition to Newtonian(below 1%)13

Long-Chain Surfactants: Unique BehaviorOFX-5098Long-chain surfactantmixtures become Newtonian atMUCH higher concentrations: OFX-5098 – Below 12.5 % OFX-0400 – Above 25 %OFX-0400Oscillation of long-chained molecules in anultrasound wave does not contribute to thelongitudinal viscosity indicates that the long chainedmolecules that we study here arepractically purely elastic.Their oscillation is thermodynamicallyreversible and does not lead to energydissipation.14

Conclusions Classic Mixing rules successfully model viscosity for mixtures withshort-chain surfactants Allows for calculation of excess activation energy betweensurfactant and toluene Volume-fraction based mixing rule succeeds in predicting viscositydata Hypothesized that energy dissipation for long-chained surfactantscaused by expanding-collapsing of flexible long-chain surfactantmolecules (slinky) Longitudinal rheology data implies that oscillational motion doesnot result in energy dissipation for long-chain surfactants Molecules are effectively elastic All energy dissipation comes from translational motion15

AcknowledgementsThis material is based upon work supported by the National Science Foundationunder Grant No. 0749481/1362060 and by CPaSS industry members.Thanks to: Dr. Andrei Dukhin, Dispersion Technology Inc. Dr. Ponisseril Somasundaran, Columbia University Members of Dr. Somasundaran’s Lab Group.DisclaimerAny opinions, findings, and conclusions or recommendations expressed in this materialare those of the author(s) and do not necessarily reflect the views of the National ScienceFoundation/Sponsors.16

Consistent with HLB 7 HLB Numbers: SPAN 20 – 8.6 SPAN 80 – 4.3 SPAN 80 is more hydrophobic than SPAN 20, so it has higher affinity for nonpolar Toluene. E 12 is higher for SPAN 80 than SPAN 20, confirming higher affinity for toluene. ΔG Values (at 50% Surfactant concentration): S

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