iaoyi Li United Technologies Research Center Advisor: Dr. Kausik Sarkar Mechanical Engineering, University of Delaware Andreas Acrivos Dissertation Award Presentation 62 nd APS DFD meeting, Minneapolis, MN, Nov 24 th 2009
Overview of dissertation Navier-Stokes Deforming interface Front-tracking Dynamics of drop Oscillating extensional flow (OE) Phys. Fluids Vortex flow J. Fluid Mech. Rheology of emulsion OE flow J. Non-Newtonian Fluid Mech. Phys. Rev. Letters Shear flow J. Rheology Mechanics of cell In unbounded shear J. Comp. Phys. In shear near a wall Cell adhesion... R http://bme.virginia.edu/ley/ 2
Emulsions: applications and challenges Material Energy Biology Food processing Polymer manufacturing Oil recovery & refinement Blood diagnosis Interfacial restoring force Effective stress Complex microstructure Dynamic & inertial environment 3 Iza & Bousmina (2000) J. Rhoelogy Rheology
Oscillating extensional (OE) flow Computer-controlled four-roll mill Taylor (1932), Bentley & Leal (1986) Inertia & time-dependency: less investigated Turbulent flow oscillatory forcing Drop in oscillating extensional flow Stokes flow analysis Asymptotic: small deformation Taylor (1932), Cox (1969) BEM: arbitrary deformation Rallison & Acrivos (1978) Amplitude Frequency Oscillating four-roll mill 4
D Drop deformation and phase in OE flow Drop in OE: complex 3D flow with moving interface B L L B D L B Taylor (1932) Deformation D 0.14 0.13 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Initial zero strain rate, flow-center Initial maximum strain rate, flow-center Initial maximum strain rate, non flow-center 0 0.5 1 1.5 t' D max Time forcing 5 Time Deformation Phase Rheology
Deformation Computational result Reduced-order analysis Resonance 6 D max 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 Re=0.1 Re=1.0 D max 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.01 Re=0.1 k=45 10 0 10 1 10 2 Re=1.0 k=200 St St -1 Re=0.1 k=45 Re=1.0 k=200 0.02 Natural frequency St St -1 Frequency 0.01 10 0 10 1 10 2 10 1 2 2 R^e=0 1 St ˆ ˆRe k^=200 ˆ 2 2 2 ( kr^e=0.1 St ˆ Re ˆ ) k^=45 St ˆ R^e=1.0 k^=200 10 0 10-1 10-2 10 1 R^e=0 k^=200 R^e=0.1 k^=45 R^e=1.0 k^=200 10 0 10-1 10-2 Re increase 10 0 10 1 10 2 S^t 10 0 10 1 10 2 S^t
Resonance breakup Deformation Drop breakup Inertia increases Efficient energy transfer at appropriate frequency Frequency selective breakup in turbulence!!! Gas bubble breakup in turbulence Risso & Fabre (1998) Frequency 7
Rheology computation Assume dilute emulsion: Excess stress: n A V σ Interface tensor q excess d σ 1 nn I da V 3 Drop-shape Stress A d excess q d Stress Strain Strain rate Elastic stress ~ flow strain Viscous stress ~ flow strain rate 8
1.5 1 0.5 0 ^ non-dimensional moduli Rhoelogy in OE flow (Re=0.1) Modulus (stress/strain) 10 3 Phase (behind strain rate) π/2 1.5 Viscous Elastic 1 10 2 E Re=0.1 Re=1.0 0.5 0 10 1 E E d ' int E d '' int E d int ' Oldroyd and Bousmina E d int '' Oldroyd and Bousmina 10 0 10 0 10 1 10 2 St Re=0.1 Flow frequency -0.5-1 Re=0.1 k=45 Re=1.0 k=200-1.5 10 0 10 1 10 2 St -0.5-1 -1.5 Flow frequency 9
non-dimensional moduli Negative elasticity (Re=1) Modulus (stress/strain) 1800 1600 1400 1200 1000 800 600 400 200 0-200 E d int ' E d int '' E d ' Oldroyd and Bousmina int E d '' Oldroyd and Bousmina int Resonance E Re=1 E Effective property Due to inertia induced microstructure change Elastic response in the same direction as forcing 10 10 0 10 1 10 2 Negative Elasticity! St Flow frequency
Rheology in shear 2 1 In Stoke s flow of emulsions N 3 int 1 11 22 >0 N int 2 22 33 <0 Choi and Schowalter (1975) 11
Interfacial normal stress difference ( o ) Sign change of normal stress difference 2 1 2 0.05 0.1 0.15 0.2 2 1.75 1.75 N 1.5 1.5 int 1 11 22 1.25 1.25 1 1 Re=0.1 Re=1.0 0.75 0.75 0.5 0.5 int 2 22 33 0.25 0.25 0 0 3 N 0.05 0.1 0.15 0.2 45 45 40 40 Re=0.1 35 35 Ca=0.02 Ca=0.05 Ca=0.2 30 30 Orientation Angle Re=1.0 25 25 12-0.25-0.25 0.05 0.1 0.15 Ca Ca 0.2 R 0 20 20 0.05 0.1 0.15 0.2 Ca Ca
Cell modeling: membrane and bond Lipid-bilayer + network of proteins Elastic membrane http://bme.virginia.edu/ley/ Leukocyte (WBC) adhesion Molecular bond Elastic spring Stochastic formation and rupture 13
Cell adhesion: effects of cell deformation Equilibrium rupture rate k r0 k = k exp(γf/k T) r r0 b Bell (1987) k r0 10 3 ADS Simulation by Hammer's group CFD Simulation EG =33.3 h =100 CFD Simulation EG =133 h =400 CFD Simulation EG =333 h =1000 10 2 10 1 10 0 10-1 10-2 Deformable Detachment No Adhesion Deformable particle in shear flow near a wall 10-3 10-4 10-5 Adhesion 5E-06 1.5E-05 Sensitivity of rupture rate to forces γ Hydrodynamic LIFT Pushing particle from wall Leal (1980) 14
Summary Drop deformation Rheology Oscillating extensional flow (OE) dynamic & inertial : turbulent flow Drop in OE at finite inertia resonance breakup in turbulence negative phase negative elasticity in emulsion Drop in shear at finite inertia orientation angle > 45 o sign change of normal stress difference in emulsion Effects of cell deformation Lift force Adhesion 15
amplitude Current activities: High Re two-phase flow Propulsion /power generation Fire suppression Models at various levels of fidelity Lubrication High fidelity direct Simulation filmer Mesoscale CFD Simulation Dynamic Reduced Order Modeling 6 4 2 16 0 0 5000 f [Hz]
Acknowledgement Dr. Kausik Sarkar, University of Delaware Dr. Gretar Tryggvason, Worcester Polytechnic Institute Dr. Antony Beris, Dr. Lian-Ping Wang, Dr. Ajay K Prasad, University of Delaware Dr. Marios Soteriou, Dr. Marco Arienti 17