Microrheology: A review

Rheology and Microrheology

Rheology is a science that deals with the deformations, the flow, and more generally the viscosity of the materials under the effect of an applied constraint. This science encompasses the study of all substances, whether liquid, “soft solids” or solids.

The rheological response of complex fluids can be linear or non-linear as a function of the applied stress. Since most industrial processing occurs in non-linear regimes, nonlinear rheology is of extreme practical importance. However it is very difficult to make general models of non-linear behavior. Much attention has been focused on the linear rheology of complex matter, which is simpler, but in many cases, a strong link can be made between the system’s linear response and the underlying structure.

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Microrheology is a technique used to measure the rheological properties of a medium, such as viscosity and viscoelasticity. Microrheology is a term that does not describe one particular technique, but rather a number of approaches that attempt to overcome some serious limitations of traditional bulk rheology [1] using rheometer. There are two types of microrheology: passive microrheology and active microrheology. In its “passive” implementation, it relies on measuring the motion in the system as caused by thermal noise or weak induced stresses. In contrast, “active” microrheology relies on inducing controlled external stresses, usually stronger than the ones resulting from thermal forces.

Microrheology: Methods of measurement

Light scattering: DLS and DWS

Dynamic light scattering (DLS) is the ancestor of today’s microrheology. It can be usedwith or without the addition of tracer scattering particles. Requiring more than 90% of light to be transmitted unscattered, this technique is limited to quite transparent samples, in order to avoid the complication of multiple scattering [2]. The measurement of the scattered light’s time-correlation function can be used to extract not just the viscosity but also the elastic modulus of viscoelastic material.

Diffusive wave spectroscopy (DWS) is the evolution of DLS, extended to opaque systems.This method has the additional advantage of extending measurements to very high frequencies and very good spatial resolution. However it is still a bulk technique, with the limitations of large (milliliter) sample sizes and inability to resolve spatial heterogeneity [3].

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Video-particle tracking

This method relies on the motion of a tracer particle within a material that needs to be characterized. Video tracking allows to measure the compliance and can yield a complete characterization of the linear viscoelasticity of the matrix.

The most challenging aspects of a video tracking experiment are often the process of acquiring the trajectory of a number of particles and the image analysis [4], which consist in:

  1. Analyze individual frames to extract the coordinates of all the particles in the frame
  2. Match the particles through subsequent frames to produce data of trajectories

Particle tracking of multiple objects imaged using a microscope is very convenient and enables to gather good statistic. However, this method has its drawbacks. Frame rate is limited by camera and computer technology, and this data has to be stored and analyzed offline [5].

Two-particle correlation

This method, which consists in tracking one or two particles at a time, constitutes an improved method from the previous one. With this alternative, very high sampling frequency is available, and the data acquired presents less redundancy, leading to fewer problems with data storage and the possibility of online analysis. Spatial resolution is also extremely good and the position of a particle can be measured to better than 10 nm. Moreover, these 2-particle correlations are not affected by the local environment around each bead [6], thus providing an unbiased probe. However, this method has its downside. To track only 2 particles, a larger amount of video data needs to be recorded and analyzed in order to obtain reliable statistics.

Comparison of microrheology vs traditional rheology

AdvantagesDownsides
  • Extremely wide frequency range, extended in particular towards high frequency.
  • Local probe, ideally suited to spatially heterogeneous systems or multiphase solutions
  • Samples can have very low viscosity (like water) and very low elasticity (tenuous gels).
  • Applicable to small volumes( ~ 100 µl vs. 1ml)
  • Non-conventional geometries: thin films, interior of biological cell, membranes etc.
  • Price of equipment (~ $30 000 vs. $100 000)
  • Study the non-linear response.
  • Limited to materials that are at least partially transparent to light.
  • Computationally intensive (no real-time analysis for now)
  • Challenging to apply to very stiff or viscous materials.

Microfluidic and microrheology

The development and growth of microfluidics over the last few years has increased the need for rheological information, but presents also new opportunities for material property measurement. Many of the multiple applications in microfluidic devices involve handling fluids that have a complex microstructure, and the flow of these materials may give rise to non-Newtonian phenomena. The behavior of complex liquids can be studied in micro-scale geometries and provide a rich platform for rheometric investigations of non-Newtonian phenomena at small scales [7]. Microfluidic systems also present a number of new opportunities for the rheologist interested in measuring material properties in shear, shear-free and mixed kinematics.

Among a range of techniques situated at the junction of microfluidics and rheology are the microfluidic devices for the measurement of bulk rheological properties in shear and extensional flow.

Microfluidic capillary devices

Microfluidic rheometry is naturally predisposed to exploiting capillary viscometry due to the simplicity of the design combined with the ease of microfabricating this type of geometry.

Capillary viscometry can be an extremely reliable and accurate technique for measuring shear viscosities [8]. Microfluidic capillary viscometers use both flow rate and pressure drop to measure the shear viscosity, following two main approaches:

Pressure monitoring

Imposing a pressure drop and measuring the flow rate

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For pressure driven flows, a variety of methods have been exploited, including capillary pressure [9], electro-wetting [10], controlling upstream hydrostatic pressur [11] and decreased downstream pressure [12]. Techniques for measuring the flow rate include micro particle image velocimetry [13] and the observation of the fluid-free surface by video microscopy [14]. With this technique, the limited dynamic range of many optical-based techniques constrains the capabilities of the microfluidic rheometer.

Flow rate monitoring

Imposing the flow rate and measuring the resulting pressure drop

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For the controlled flow rate studies, the volumetric flow rate is usually imposed using a syringe pump and the pressure drop can be monitored using either traditional pressure sensors [15] or microfabricated pressure sensors [16]. The principal challenge here is to construct and calibrate on-chip pressure sensors with good linearity and wide dynamic range.

Microfluidic stagnation point flows

The vorticity-free state of the flow near a stagnation point can result in large extensional deformation and orientation of the microstructural components of complex fluids [17]. Rheological information can be analyzed by exploring the optical properties of flows in the region of stagnation points (ex: extensional properties by monitoring birefringence [18]). Two methods for exploring these flows exist: microfluidic implementations of the four-roll mill [19] and the “cross-slot” flow geometry [20].

Four-roll mill devices allow rotational as well as irrotational flows to be established with varying degrees of vorticity [21]. With this technique, the behavior of macromolecules in flows with mixed shear and elongational characteristics can be investigated.

However, there are difficulties in measuring the global pressure drop or stress field in such devices.

Four-roll mill flow

Cross-slot flow

Microfluidic contraction flows

Contraction flows enable to study the extensional properties of complex liquids by relating the measured pressure drop across a contraction to the imposed flow rate [22]. Contraction flows are of mixed kinematic type and typically contain both strong shear and elongational components. This is important, as coupling between the extensional (“irrotational”) and shearing (“rotational”) deformations may lead to a significantly different microstructural response compared to a pure irrotational extensional deformation.

Two main approaches can be identified: experiments using abrupt contractions, easier to design and to build, and those using hyperbolic contractions, providing a better approximation to a uniform extension rate [23]. Unlike macroscopic studies, microfluidic devices offer the potential to apply these techniques to low viscosity solutions [24].

From an appropriate global force balance across the contraction [25] it is possible to evaluate an apparent elongational viscosity, to evaluate the Trouton ratio of a complex fluid (ratio of extensional viscosity to shear viscosity). The apparent extensional viscosity is found by separating the pressure drop due to shear stresses from that due to extensional stresses.

Other key approaches using microfluidics

  • To estimate the local rheological response, the motion of nano-scale particles can be studied [26]. Systems can be “passively driven” where the motions of particles due to thermal fluctuations are analyzed [27] or “actively driven” where forces exerted on beads are measured using optical traps [28] or magnetic tweezers [29].
  • The dynamics of single polymers, especially fluorescently labeled DNA, freely undergoing shear or extensional flow can be directly observed under certain conditions [30] and related to the macroscopic rheological response measured in conventional rheometers.
  • Microfluidic devices can also be used to control the creation of droplets in a repeatable manner [31], allowing the dynamics of single  droplets or groups of droplets to be explored, an important step in understanding the rheology of multiphase liquids.
  • Microfluidic studies of ordered complex fluids, such as liquid crystals, can be used to impose well-defined structural and orientational boundary conditions on length-scales comparable to the dimensions of the observed order [32].

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AUTHORS

Written by Wilfried Sire.

[1-6]“Microrheology: A Review of the Method and Applications, PietroCicuta et Al.”

[7]Pipe and McKinley, “Microfluidic Rheometry.”

[8]“Rheology: Principles, Measurements and Applications, C. W. Macosko et Al.”

[9]“Nanoliter Viscometer for Analyzing Blood Plasma and Other Liquid Samples. N. Srivastava et Al.”

[10]“Micro-Viscometer Based on Electrowetting on Dielectric. Electrochim, Y.-Y Lin et Al.”

[11]“Rheology of Complex Fluids by Particle Image Velocimetry in Microchannels, G. Degré et Al.”; “Initiation À La Rhéologie”; “Nonlocal Effects in Flows of Wormlike Micellar Solutions, C. Masselon et Al.”

[12]“A PDMS Viscometer for Microliter Newtonian Fluid, Z. Han et Al.”

[13]“Rheology of Complex Fluids by Particle Image Velocimetry in Microchannels, G. Degré et Al.”; “Viscosimeter on a Microfluidic Chip, P. Guillot et Al.”; “Nonlocal Effects in Flows of Wormlike Micellar Solutions, C. Masselon et Al.”

[14]“Nanoliter Viscometer for Analyzing Blood Plasma and Other Liquid Samples. N. Srivastava et Al.”; “Viscosimeter on a Microfluidic Chip, P. Guillot et Al.”; “Micro-Viscometer Based on Electrowetting on Dielectric. Electrochim, Y.-Y Lin et Al.”; “A PDMS Viscometer for Microliter Newtonian Fluid, Z. Han et Al.”

[15]“High Shear Microfluidics and Its Application in Rheological Measurement, K. Kang et Al.”

[16]“High Shear Rate Viscometry, C. J. Pipe et Al.”

[17]“Polymer Cha& Extension Produced by Imping&g Jets and Its Effect on Polyethylene Solution, F. C. Frank et Al.”; “Flow Birefringence of Dilute Polymer Solutions in Two-Dimensional Flows, G. G. Fuller et Al.”; “Extensional Viscosity Measurements for Low-Viscosity Fluids, G. G. Fuller et Al.”; “A 3D Numerical/Experimental Study on a Stagnation Flow of a Polyisobutylene Solution, Jeroen F.M. Schoonen et Al.”

[18]“Optical Rheometry, G. G. Fuller .”

[19]“Microfluidic Analog of the Four-Roll Mill, S. D. Hudson et Al.”; “Microfluidic Four-Roll Mill for All Flow Types, J. S. Lee et Al.”

[20]“Rheo-Optics of Equilibrium Polymer Solutions: Wormlike Micelles in Elongational Flow in a Microfluidic Cross-Slot, J. A. Pathak et Al.”; “Elastic Instabilities of Polymer Solutions in Cross-Channel Flow, P. E. Arratia et Al.”; “Polymeric Filament Thinning and Breakup in Microchannels, P. E. Arratia et Al.”

[21]“Microfluidic Analog of the Four-Roll Mill, S. D. Hudson et Al.”; “Microfluidic Four-Roll Mill for All Flow Types, J. S. Lee et Al.”

[22]“Converging Flow of Polymer Melts in Extrusion Dies, F. N. Cogswell”; “On the Planar Extensional Viscosity of Mobile Liquids, P. R. Williams et Al.”; “An Approximate Analysis for Contraction and Converging Flows, D. M. Binding”; “A Converging Channel Rheometer for the Measurement of Extensional Viscosity, D. F. James et Al.”

[23]“The Extensional Flow Capillary as a New Method for Extensional Viscosity Measurement, A. Everage et Al.”

[24]Pipe and McKinley, “Microfluidic Rheometry.”

[25]“Converging Flow of Polymer Melts in Extrusion Dies, F. N. Cogswell”; “An Approximate Analysis for Contraction and Converging Flows, D. M. Binding.”

[26]“Microrheology of Complex Fluids, T. A. Waigh et Al.”; “Going with the Flow, R. G. Larson et Al.”

[27]“Diffusing-Wave Spectroscopy: The Technique and Some Applications, D. A. Weitz et Al.”; “One- and Two-Point Micro-Rheology of Viscoelastic Media, L Starrs et Al.”

[28]“Femtonewton Force Spectroscopy of Single Extended DNA Molecules, J-C Meiners et Al.”; “Passive and Active Microrheology with Optical Tweezers, R. R. Brau et Al.”

[29]“Local Measurements of Viscoelastic Parameters of Adherent Cell Surfaces by Magnetic Bead Microrheometry, A. R. Bausch et Al.”

[30]“Single Polymer Dynamics in an Elongational Flow, T. T. Perkins et Al.”; “Single-Polymer Dynamics in Steady Shear Flow, D. E. Smith et Al.”; “Dynamics of Dilute and Semidilute DNA Solutions in the Start-up of Shear Flow, J. S. Hur et Al.”

[31]“Dynamic Pattern Formation in a Vesicle-Generating Microfluidic Device, T. Thorsen et Al.”; “Formation of Dispersions Using ‘“flow Focusing”’ in Microchannels, S. L. Anna et Al.”; “Geometrically Mediated Breakup of Drops in Microfluidic Devices, D. R. Link et Al.”

[32]Choi et al., “Ordered Patterns of Liquid Crystal Toroidal Defects by Microchannel Confinement”; Shojaei-Zadeh and Anna, “Role of Surface Anchoring and Geometric Confinement on Focal Conic Textures in Smectic-A Liquid Crystals.”