COST MP1305 - Flowing matter 2014 Instituto para a Investigação Interdisciplinar, Universidade de Lisboa 15-17 December 2014 Flow-induced deformation of droplets, vesicles and red blood cells Stefano Guido Simona Capecchi LABORATORY OF CHEMICAL ENGINEERING @ µ-scale DEPARTMENT OF CHEMICAL, MATERIALS AND PRODUCTION ENGINEERING NAPOLI, ITALY
Background Flow behavior of deformable particles, both individual and collective, is relevant in a range of applications Droplets yalemedicine.yale.edu Blood cells jmgreer71.wordpress.com Vesicles www.inspired.ca Emulsions, polymer blends www.nnin.org Lab-on-chip diagnostics, single cell analysis www.incubelabs.com Drug delivery C. Misbah, J. Phys. Conf. Series 392 (2012), R. G. Winkler, D. A. Fedosov, G. Gompper, Current Opinion in Colloid and Interface Science 19 (2014)
Droplets Flow-induced morphology evolution of droplets is governed by two (apparently) simple processes Drop deformation and breakup Collision and coalescence 50 µm Our starting point is an isolated droplet (or a binary collision) under simple (laminar) shear flow in the small deformation limit
Some issues on (laminar) flow behavior of droplets How do isolated droplets deform and breakup under steady and transient (unbounded) shear flow? How does geometrical confinement affect droplet deformation and breakup? What is the effect of viscoelasticity of the component fluids? What can we learn from isolated droplets on collective flow behavior of concentrated systems (e.g., emulsions and polymer blends)? How can coalescence be investigated under shear flow? What is the effect of surfactants?
Starting point: small deformation theory Nondimensional parameters governing drop deformation Ca = η γ R c σ Capillary number V γ = δ V δ λ η η = d c Viscosity ratio Main theory predictions (under steady state conditions) r MAX r0 r MIN r0 r z = r 0 1 ( λ 2 ) Ca + f ( λ ) = 1 + f Ca 1 ( λ 2 ) Ca + f ( λ ) = 1 f Ca 3( λ 2 ) 1 + f Ca σ interfacial tension η c and η d viscosities of continuous and droplet phase Experiments show that droplets take an ellipsoidal shape under shear flow Taylor G I, Proc. R. Soc. London A, 138 (1932) 41-48, Taylor G I, Proc. R. Soc. London A, 146 (1934) 501-523. Maffettone P L and Minale M, J. Non-Newtonian Fluid Mech., 78 (1998) 227-241 Greco F., Phys. Fluids, 14 (2002) 946-954. 2 2 S. Guido and M. Villone, J. Rheology, 42, 395-415 (1998)
Effects of confinement Wall effects tend to stabilize shape and hinder breakup h 150 µm h 2R Unbounded 50 µm Data in agreement with small deformation theory (Shapira and Haber, Int. J. Fluid Mechanics, 1990) h 2R, Ca = 0.5 V. Sibillo, G. Pasquariello, M. Simeone, V. Cristini, S. Guido, Phys. Rev. Lett., 97(5), 054502 1-4, (2006)
Viscoelastic effects Rheological properties of the fluid components can be another source of viscoelasticity apart from the interfacial tension Additional physical quantities New nondimensional parameter N = T T = Ψ N T T γ 2, = = Ψ γ 2 1 11 22 1 2 22 33 2 W ψ 1σ p = 2 2 Ca 2r η 0 ( 1 for significant non-newtonian effects) Outer fluid: non-newtonian (Boger), Inner fluid: Newtonian Ca = 0.4 λ = 1 Small deformation theory shows that drop orientation is directly linked to N 1 Inner fluid: Newtonian, Outer fluid: non-newtonian (Boger) V. Sibillo, M. Simeone and S. Guido, Rheol. Acta, 43, 449-456 (2004)
From isolated droplets to concentrated systems Isolated droplet deformation predictions hold true also in a concentrated system provided that the actual system viscosity is used to calculate Ca Ca* = η blend Rγ σ Shear banding D 0.6 0.5 0.4 0.3 0.2 Taylor 2,5% 0.1 5% 10% Isolated drop 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Ca* Vorticity 1.0 η/η 0 Flow 0.9 0.8 0 10000 20000 Strain S. Caserta, M. Simeone, and S. Guido, Shear banding in biphasic liquid-liquid systems, Phys. Rev. Lett., 100(13), 137801 1-4 (2008)
Binary collisions and coalescence Drop collisions is irreversible mechanism for drop dispersion Coalescence between two droplets The resulting drop is broken up and the daughter drops are made to collide again S. Guido and M. Simeone, J. Fluid Mech., 357, 1-20 (1998)
High deformations: droplet breakup in shear flow Upon increasing Ca, a critical condition (Ca cr ) is reached where shape becomes unstable λ = 1 Ca>Ca cr Ca>>Ca cr Scaling arguments show that breakup time scales as and that daughter drop size scales with critical drop size, but fragment distribution is still an open issue Cristini V, Guido S, Alfani A, Blawzdziewicz J and Loewenberg M, J. Rheol., 47 (2003) 1283-1298.
Effect of surfactants Emulsions are often made with high surfactant (and co-surfactants) concentration to improve stability or performance High surfactant concentrations are associated with complex microstructures and a strong interfacial viscoelasticity, which make measurement of interfacial properties quite difficult with classical methods Microfluidics tensiometry A simplified binary system could be just surfactant and water (surfactant droplets or vesicles)
Surfactant multilamellar vesicles (SMLVs) Most work in the literature is devoted to equilibrium microstructures (e.g., micelles, bicontinuous sponge phase, lamellar phases and vesicles) as a function of concentration and temperature Main issue: how can SMLVs deform and breakup under the action of flow? HLAS surfactant γ. A. Pommella, S. Caserta, V. Guida, and SG, PRL 108, 138301 (2012)
Analogy with droplets and capsules Scale bar: 40 µm 1 σ = 10-4 N/m Ca = ηγ R σ λ = η d η Small deformation theory R. G. Cox, J. Fluid Mech. 37, 601 (1969) Vesicles deform at constant volume, but not at constant area A. Pommella, S. Caserta, V. Guida, and SG, PRL 108, 138301 (2012)
SMLV microstructure under flow Scale bars = 100 µm Parabolic Focal Conic domains (a defect of smectic A liquid crystals) Ch. S. Rosenblatt et al., Le Journal De Physique 38, 1105 (1977) A. Pommella, S. Caserta, SG,Soft Matter, 9(31), 7545-7552 (2013)
Red blood cells in microcirculation RBC cells can be regarded as fluid-filled sacs with an excess area, enclosed by a lipid bilayer (inextensible) membrane with an underlying protein network Flow-induced phenomena: clustering, deformation and aggregation Fluidity of Blood as a Consequence of Fluidity of Erythrocytes Author: Schmid-Schönbein, Holger (Aachen) Cluster Isolated cell What is the relative importance of RBC membrane parameters, including membrane viscosity? How do RBCs interact with endothelium and with microparticles (margination)? What are the pathological effects of altered RBC deformability and aggregability?
RBC stationary shape RBC flow behavior in a microcapillary is well described by (T. W. Secomb, R. Skalak, N. Ozkaya and J. F. Gross, J. Fluid Mech., 1986, 163, 405 423) considering the cell as axisymmetric using lubrication theory to model flow in the gap between cell and walls accounting for elastic deformation only (no viscous contribution) taking unstressed shape as that of an inflated sphere Theoretical predictions, Secomb et al. 1986 At high velocities only an isotropic in-plane tension is considered (bending and shear being negligible) S. Guido and G. Tomaiuolo, Comptes rendus Physique, 2009, 10, 751-763 G. Tomaiuolo, M. Simeone, V. Martinelli, B. Rotoli and S. Guido, Soft Matter, 2009, 5, 3736-3740
RBC transient shape: effect of (membrane) viscosity 10 µm Time, s Different shapes depending on initial RBC position and orientation Characteristic relaxation time of about 0.1 s (healthy cells) It decreases with increasing cell rigidity G. Tomaiuolo and S. Guido, Microvascular Research, 2011, 82, 35-41 G. Tomaiuolo, M. Simeone, V. Martinelli, B. Rotoli and S. Guido, Soft Matter, 2009, 5, 3736-3740
RBC flow in a diverging channel 10 µm 25 µm tension acting on the membrane due to the flow field µ=0.006 dyn/cm η=0.055 cp RBC deformation is well described by a Kelvin-Voigt model with a shear modulus µ and a membrane viscosity η elastic response of cell mebrane viscous response of cell mebrane Kelvin-Voigt model Membrane viscous contribution is dominant over inner cell viscosity (µ int r/µ = 0.015, Secomb and Hsu, 1996) and over elasticity at time scales < η/ µ = 0.1 s µ G. Tomaiuolo, M. Barra, V. Preziosi, A. Cassinese, B. Rotoli, S. Guido, 2011, Lab on Chip
Effect of a glycocalyx model system Glycocalix Layer of glycopolymers bound to endothelial cells membrane Thickness of 100 1000 nm Influence on the resistance to flow in microcirculation Involvement in microvascular diseases Polymer brushes phema RBCs velocity decrease in hairy capillaries is higher than expected from lumen reduction Highlighted in Physics Today, April 2014 Lanotte et al., Biomicrofluidics 2014 Lanotte et al., Langmuir 2012
Conclusions The flow behavior of deformable particles, such as droplets, vesicles and red blood cells, shows several analogies from the phenomenological point of view Particle deformation can be modelled in terms of one (or more capillary) number(s), depending on the rheological properties of the interface Measurement of interfacial viscoelasticity is a complex task
Acknowledgements Sergio Caserta Giovanna Tomaiuolo CEINGE Advanced Biotechnologies Napoli, ITALY National Interuniversity Consortium of Materials Science and Technology