A Review of Microfluidic Devices for Rheological Characterisation

Abstract

The rheological characterisation of liquids finds application in several fields ranging from industrial production to the medical practice. Conventional rheometers are the gold standard for the rheological characterisation; however, they are affected by several limitations, including high costs, large volumes required and difficult integration to other systems. By contrast, microfluidic devices emerged as inexpensive platforms, requiring a little sample to operate and fashioning a very easy integration into other systems. Such advantages have prompted the development of microfluidic devices to measure rheological properties such as viscosity and longest relaxation time, using a finger-prick of volumes. This review highlights some of the microfluidic platforms introduced so far, describing their advantages and limitations, while also offering some prospective for future works.

Keywords: microfluidics; rheometry; viscoelasticity.

Figure 1

(a) Fluid between two parallel plates in stationary conditions. (b) A force is applied to the upper plate, leading to a shear flow along the y-direction. (c) Examples of Newtonian liquids with viscosity independent of the shear rate (solid red line), shear-thinning liquids having viscosity that decreases when increasing the shear rate (dashed blue line) and shear-thickening liquids having viscosity that increases when increasing the shear rate (dot-dashed black line). (d) Fluid between two parallel plates arranged horizontally in stationary conditions. (e) A force is applied to the plate on the left, thus leading to an extensional flow along the x-direction. (f) Schematic of the flow in a cylindrical channel, encountered in capillary rheometry.

Figure 2

Examples of Micro-Electro-Mechanical Systems (MEMS) employed in microfluidic rheometry. (a,b) Schematic of the microfluidic rheometer made of PDMS with pressure sensors also made of flexible PDMS containing silver and black carbon conductive particles. (c) Good agreement between conventional and microfluidic rheometry data using the apparatus in (a,b). Reprinted with permission from Springer Nature: Rheologica Acta, Pan and Arratia, Copyright (2013) [17]. (d,e) Schematic of the microfluidic device with an electrofluidic circuit employed as pressure sensor. (f) Good agreement was observed between bulk and microfluidic viscosity data for whole blood samples. The inset is a real-time image of blood cells in the microfluidic channel. Reprinted with permission from Lee et al., Analytical chemistry, 90, 2317–2325 [18]. Copyright 2018, American Chemical Society. (g) Schematic of the hand-held, automatic capillary viscometer. (h) Good agreement was observed between bulk and microfluidic viscosity data for xanthan gum 1.0 wt% solutions. Reprinted from Sensor and Actuators:B, 313, 112176, Lee et al., hand-held, automatic capillary viscometer for analysis of Newtonian and non-Newtonian fluids [19], Copyright (2020), with permission from Elsevier. (i) Schematic of a microfluidic viscometer using magnetically actuated micro post arrays. (j) Good agreement was observed between bulk and microfluidic viscosity data for sucrose and Karo solutions. Reprinted from Judith et al. [20].

Figure 3

Examples of microfluidic rheometers based on interfacial phenomena. (a) The interface between a reference Newtonian liquid and a sample is studied to obtain the viscosity of the sample liquid. (b) Measurements carried out using the device in (a) on PEO solutions at 2 and 4 wt%. Reprinted with permission from Springer Nature, Microfluidics and Nanofluidics, Guillot and Colin, Copyright (2014) [27]. (c) Serpentine microfluidic device for the measurement of longest relaxation time in curved microfluidic devices. (d) Measurement of longest relaxation time for several PEO solutions in the dilute regime. Reprinted from Zilz et al. [28]. (e) Schematic of the 3D printed capillary circuit microfluidic rheometer. (f) Good agreement was found between the 3D printed capillary circuit data and those obtained using another microfluidic rheometer. Reprinted from Oh et al. [29]. (g) Schematic of the iCapillary device based on monitoring the sample air interface using a smartphone. (h) Good agreement was found between iCapillary data and conventional rheology data for PEO solutions. Reprinted with permission from Springer Nature, Rheologica Acta, Solomon et al., Copyright (2016) [30]. (i) Microfluidic rheometer based on the droplet formation mechanisms in flow-focusing geometry. Reprinted with permission from Li et al., Analytical Chemistry, 89, 3996–4006 [31]. Copyright 2017, American Chemical Society.

Figure 4

Examples of microfluidic rheometers based on particle tracking. (a) Schematic of a microfluidic device for creep measurements, aimed at deriving the longest relaxation time $\lambda$. (b) Measurements of $\lambda$ as a function of the polymer molecular weight for several polyacrylamide solutions, using the microfluidic rheometer in (a). Reprinted from Reference [56], with permission of The Royal Society of Chemistry. (c) Schematic of the microfluidic rheometer based on digital holography microscopy. (d) Good agreement between microfluidic and conventional rheometry data for several PEO solutions. Reprinted with permission from Gupta and Vanapalli [58], with the permission of AIP publishing. (e) Schematic of the $\mu$-Rheometer microfluidic rheometer, based on the transversal migration of rigid particles flowing in microchannels. (f) Good agreement between the $\mu$-rheometer and the OSCER [69] was found for polystyrene solution in dioctyl phthalate. Reprinted from Del Giudice et al. [64]. (g) Schematic of the $\mu$-rheometer for the simultaneous measurement of zero-shear viscosity and longest relaxation time. (h) Good agreement was observed between microfluidic and bulk zero-shear viscosity data for several PEO solutions. (i) Good agreement was observed between microfluidic and bulk longest relaxation time data for several PEO solutions. Reprinted from Del Giudice [68].

Figure 5

Examples of extensional microfluidic rheometers. (a) Schematic of the cross-slot microfluidic device, with two inlets and two outlets. (b) Flow birefringence measurements of polystyrene in dioctyl phthalate solutions. Different flow conditions are represented. Reprinted with permission from Reference [69], with permission of The Royal Society of Chemistry. (c) Schematic of the hyperbolic-contraction extensional rheometer. Reprinted with permission from Springer Nature, Rheologica Acta, Ober et al., Copyright (2013) [91]. (d) Schematic of the differential pressure extensional rheometer. The experimental snapshots represent different types of hyperbolic contractions channel compared to the straight reference channel. Reprinted with permission from Kim et al., Copyright (2018), The Society of Rheology [92]. (e) Schematic of the miniature capillary breakup extensional rheometer, where the liquid bridge is generated using electrowetting-on-dielectric actuation. (f) Experimental snapshots of the loading step for the device in (e). Reprinted with permission from Reference [93], with permission of The Royal Society of Chemistry.

Figure 6

Examples of microfluidic rheometers integrated to Small Angle Neutron Scattering (SANS) and Small Angle X-ray Scattering (SAXS). (a) Schematic of SANS integrated to a microfluidic device. Reprinted from Reference [103]. (b) Schematic of SANS experiments performed on a four-mill microfluidic device. Reprinted from Reference [110]. (c) Schematic of a SAXS apparatus integrated to a microfluidic device. Reprinted with permission from Reference [111], with permission of The Royal Society of Chemistry.