Dynamics of Complex- and Bio- Fluids

 

My research explores the interrelation between microstructure dynamics and macroscopic flow behavior (rheology) of soft complex fluids: emulsions, polymer blends and biological suspensions. My studies combine theoretical analyses, numerical simulations, and experiments to advance our understanding of the flow behavior of these soft materials.

 

Introduction

 

Emulsions, polymer blends and biological fluids such as blood are heterogeneous materials, where micron-sized particles (drops, cells) are dispersed in another liquid.

 

Micrograph of an emulsion (Iza and Bousmina, 2000)

Droplet size ranges from 1mm to 1mm.

Blood.  

 

The microstructure imparts “softness” in these materials, i.e.,  their response to applied stress can be  solid-like or liquid-like depending on the time scales of microstructure relaxation and the external forcing. The microstructure continuously changes in a flowing dispersion. For example, under a simple shear flow emulsion drops deform and elongate; if the applied shearing force is not very strong drops orient at an angle of about 45 degrees with respect to the flow direction.

 

Simple shear flow            

(flow between two  parallel plates)

 

 

Deformed emulsion drops in shear flow (Iza and Bousmina, 2000).

 

Soft materials find a wide range of industrial and practical applications – paints, foods, personal care products, pharmaceuticals, to name just a few. Fundamental knowledge of the interplay between the microstructure and macroscopic dynamics of complex fluids is crucial for the rational design of materials with tailored properties and performance.   The goal of my research is to develop a systematic study of dispersion rheology. Current projects address problems with increasing level of complexity –  from  single-particle dynamics to concentrated dispersions.  

 

 

Projects

 

1. Deformation and dynamics of a single particle in flow: drops and vesicles

 

As a first (and essential) step towards elucidating dispersion rheology, one needs to understand the particle-level microhydrodynamics. However, even a single particle in flow poses a challenge. Dynamics of deformable particles such as drops and cells in flow is a difficult  problem because the shape of these “soft” objects is not given a priori but is governed by the balance between interfacial forces, e.g. due to stretching and/or bending of the interface, and fluid viscous stresses. The interfacial properties, therefore, play a crucial role in the dynamics of soft particles. Drop interface governed by the interfacial tension and the interfacial area can change. In contrast, in the case of artificial cells made of phospholipid bilayer membrane (so called vesicles), the interface is governed by bending stresses and its area is fixed. Consequently drops and cells (vesicles) have very different physical behavior.

 

For example, the equilibrium shape of a drop is a sphere (the surface tension minimizes the area), while vesicles exhibit variety of shapes corresponding to minima of the bending energy for a given volume-to-area ratio. 

 

                 

 

Images of giant vesicles (phase contrast microscopy) (Rumiana Dimova, MPI-KG)

 

 Given the rich phase diagram of vesicles at rest, it is not surprising that under non-equilibrium conditions such as flow, vesicles exhibit even more complex behavior. In simple shear, three different types of dynamics have been observed experimentally and explained theoretically (1) tank- treading, where the vesicle deforms into a prolate ellipsoid inclined at a stationary angle with respect to the flow direction; (2) tumbling, where the vesicle undergoes a periodic flipping motion; and (3) breathing, where the vesicle is trembling in the flow direction with periodic shape deformations. 

 

The microscopic cell dynamics gives a clear signature on the macroscopic properties of a vesicle suspension or blood. Namely, the suspension viscosity attains a minimum at the tank-treading to tumbling transition, which recently has been confirmed experimentally by Vitkova et al. (2008).

 

References:

 

   P. M. Vlahovska, R. Serral Gracia, “Dynamics of a viscous vesicle in linear flows”,  pdf , Physical Review E 75, 016313 (2007)

   G. Danker, P. M. Vlahovska, C. Misbah, “Migration and shape coexistence of vesicles in a Poiseuille flow” ,pdf , Physical Review Letters (submitted)

 

 

Ongoing and future work:

 

  1. Effect of shear elasticity on vesicle dynamics in shear flow: understanding  the swinging red blood cells in shear flow
  2. Effect of thermally induced membrane undulations on the vesicle dynamics
  3. Drops and vesicles in complex (time-dependent, quadratic, etc.) flows
  4. Effect of confinement on vesicle dynamics: understanding the enhanced Farhaeus effect and its implications to microcirculatory blood flow and resistance.

 

 

2.  Electro-hydrodynamics of drops and vesicles

 

Electric fields are widely used for cell manipulation. Weak fields influence cell signaling, wound healing, and cell growth. Strong pulsed fields can induce transient perforation of the cell membrane, which enables the delivery of exogenous molecules (drugs, proteins, and plasmids) into living cells. Biological cells exhibit various frequency-dependent behaviors in AC electric fields, e.g., translation (dielectrophoresis) and rotation. Vesicles are widely used as a model system to study electric effects on cells.

 

 Vesicles exhibit quite intriguing behavior in electric fields, which is not fully understood at present time.

 

 

 

 

Vesicles subjected to DC pulses. Riske and Dimova (2006)

 

Vesicles in AC electric fields. Aranda et al. (2008)

It is generally argued that electrostatic pressure pulls the vesicle at the poles, where the electric field is maximal, which results in a prolate shape. However, the oblate shapes remain an open problem, in particular, the fact that they are observed only when the conductivity ratio of inner and outer fluids is less than one. We are developing theoretical models that explain the morphological transitions of vesicles in electric fields. It has emerged that the electrohydrodynamic coupling at the membrane interface is responsible for the oblate shapes. 

 

 

References:

 

 P. M. Vlahovska, R. Serral Gracia, S. Aranda and R. Dimova,  “Electrohydrodynamic model of vesicle deformation in alternating electric fields “, pdf, Biophysical Journal (submitted)

 

Ongoing and future work:

 

  1. Vesicle deformation in DC electric fields
  2. Electroporation of lipid membranes
  3. Electrodeformation of surfactant-covered drops
  4. Electrorheology of emulsions

 

 

 

 

3. Concentrated dispersions

 

Dispersions contain many hundreds of particles. A common simplification is to model the heterogeneous system as a homogeneous material with effective properties. In dilute dispersions, particles are far away from each other; each one of them feels alone in the flow. Therefore, the dispersion effective stress is just a sum of all single-particle stress contributions. In concentrated systems, particles experience hydrodynamic interactions with each other and with the walls of their container.

 

3.1. Hydrodynamic interactions of soft particles (drops, vesicles)

 

The pair-wise hydrodynamic interaction of deformable drops or vesicles show a cross-flow displacement after the particles have passed each other, which gives rise to self-diffusion. A collaborative research with Prof. Young (NJIT) and Prof. Biros (Georgia Tech) investigates the correlation in the motion of two vesicles due to hydrodynamic interactions, and in particular, how the trajectory asymmetry depends on the shape and dynamic state of the isolated vesicles.

 

 

Two vesicles in shear flow (Numerical simulations by G. Biros)

 

 

3.2. Surfactant-laden emulsions

 

 

Surface active agents (soaps, proteins, block copolymers) are often employed to control emulsion properties.  Flow convects the surfactant  along the drop surface and the surfactant distribution becomes non-uniform. A simple shear flow stretches the drop shape and surfactant distribution along the straining axes of the flow.

 

Experimental visualization of the surfactant distribution in extensional flow (Jeon et al (2003 )

 

Nonuniformities in the surfactant distribution give rise to gradients in the interfacial tension the so called Marangoni stresses. Marangoni stresses can have rather profound effect – for example in weak flows surfactant-covered drops behave as rigid spheres. Consequently a surfactant-laden emulsion is more viscous than a surfactant-free emulsion with the same volume fraction. There are of course other factors such as drop deformability and hydrodynamics interactions. The coupling of all these effects gives rise to very rich non-Newtnoian rheological behavior, for example the effective viscosity may decrease with the shear rate (shear thinning).

 

I have systematically explored the behavior of a single surfactant-covered drop in flow. Current efforts focus on the hydrodynamics interactions between drops and drop dynamics in wall-bounded flows.

 

References: