Microrheology: A review

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:

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.

Contraction flows allow 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.

• To estimate the local rheological response, the motion of nano-scale particles can be studied [26]. Systems can be “passively driven” where the motion 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].