Traditional rheometry provides many methods for learning about the bulk physical properties of the sample, but the data does not show how the sample flows in the cross-section of the measuring system. Knowing such information would provide insights into how the individual parts of the sample respond to various conditions in pipe flow. Understanding the three common flow instabilities – shear banding, wall slip, and plug flow – helps engineers know what to expect from pipe flow and aides in testing ways to prevent or enhance them in processing and application.
Extended use and development of various particle tracking rheometry methods will produce new correlations between sensory qualities and flow properties for food and consumer products. (1, 2) Emulsions, micelles, gels, colloidal dispersions and even sewage wastes have been studied with these techniques. (1)
Wall slip occurs when the sample at the rotating wall of the measuring system does not move at the same velocity as the wall. Slippage at the wall may be triggered by various surface chemistries and lubrication forces that reduce the friction between sample and measuring system. A greater effective shear rate results instead of the intended applied shear rate. The most rudimentary manner to visually observe wall slip is to draw a line along the sample loaded in a parallel plate and after applying a strain (small deformation) see if the line forms a fairly straight line or if it is crooked near either wall. (1) A slopping line with discontinuities is a qualitative representation of the velocity gradient in the sample (Figure 1).
Additionally, wall slip can induce layered bands. Shear banding is the occurrence of two or more flowing layers of fluid that maintain different flow velocities despite being under the same applied shear rate (Figure 2). The actual shear rate is different for the two layers, typically with a band in the middle not touching the wall and another that is close to the wall. One study measured the actual shear rate of one band to be around 5 1/s, while the other band near the wall maintained an effective shear rate of 70 1/s. (3)
Shear bands and wall lubrication can be triggered by inter-particle interactions generated by the chemical and physical properties of the specimen. Steric depletion, (4) particle migration, and hydrophobicity are just a few mechanisms that can directly contribute to flow instabilities. (1) Lubrication layers at the walls often play a role in forming shear bands by expelling particles, (1, 5) and shear band formation in foams has been attributed to the presence of impurities (small solid particulates). (6)
When shear bands persist over time, some bands may slow down to a point where they do not move at all. Plug flow is often evident in dense suspensions and paste-like samples that have flow bands of non-moving fluid among channels of flowing sample. The “plug” may result from a variety of chemical and physical phenomena that prevent the entire sample from flowing under the applied shear rate. Materials that experience plug flow typically also display wall slip and shear banding that over time contribute to the development of the plug.
Substances that display flow instabilities may be transported more easily than materials that move with the applied velocity gradient. (1) The process of eating and digesting food relies on wall slip to move the consumed substances through the digestive track. (1, 7) Another example from the body is that red blood cells have been observed to slip along the walls of tiny arteries in order to be propelled forward. (1, 8) Additionally, plug flow control in 3D printing nozzles has been shown to produce successful waste-reduction. (1, 9) Furthermore, food processing and enhanced oil recovery involve wall slip of emulsions and foams. (6) Dense colloidal suspensions used for building materials were shown to display wall slip, shear banding, and plug flow in varying degrees based on the usage of adsorbed and non-adsorbed polymer additives. (4)
Recording local sample flow behavior inside the rheometer’s gap has been undertaken for decades with ever advancing methods that track the velocity of the layers within the sample. Visual methods use confocal microscopy aligned with a rheometer to see fluorescent markers in the sample, visually revealing the velocity gradient in the flow field. (1) However, most materials cannot be viewed in such a manner, and thus more complex techniques are typically undertaken to track local flow. Laser doppler velocimetry gives data on velocity of particles in the sample that scatter the laser light while particle image velocimetry (PIV) casts a laser sheet into the sample perpendicular to the flow plane. (1) Particles reflect the laser light and their displacement over time may be recorded based on the reflected intensity in captured images via particle tracking velocimetry (PTV). (1) For samples that are too opaque to transmit the laser, ultrasonic speckle velocimetry (USV) can be utilized to send and receive ultrasound echoes from tracer particles in the sample. Magnetic resonance imaging (MRI) rheometry achieves a similar result while offering a 3D rendering of the flow field but it is best used for long-term measurements instead of short time data capturing capable with USV.
Expanding rheology studies to include probing of localized flow has aided the research and development of several soft materials.
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(1) Cloitre, M., and Bonnecaze, R., “A review on wall slip in high solid dispersions”, Rheologica Acta, 2017, 56, 283.
(2) Ozkan, S., “Characterization of yield stress and slip behaviour of skin/hair care gels using steady flow and LAOS measurements and their correlation with sensorial attributes”, International Journal of Cosmetic Science, 2012, 34.
(3) Lopez-Gonzalez, M., Holmes, W., and Callaghan, P., “Rheo-NMR phenomena of wormlike micelles”, Soft Matter, 2006, 2, 855.
(4) Murray, L., et al., “Influence of adsorbed and nonadsorbed polymer additives on the viscosity of magnesium oxide suspensions”, Journal of Applied Polymer Science, 2018, 135, 3, 45696.
(5) Gibbs et al., “Rheometry and detection of apparent wall slip for Poiseuille flow of polymer solutions and particulate dispersions by nuclear magnetic resonance velocimetry”, Journal of Rheology, 1996, 40, 425.
(6) Cohen-Addad, S., and Höhler, R., “Rheology of foams and highly concentrated emulsions”, Current Opinion in Colloid & Interface Science, 2014, 19, 536.
(7) Stokes, J., Boehm, M., and Baier, S., ”Oral processing, texture and mouthfeel: from rheology to tribology and beyond”, Current Opinion in Colloid & Interface Science, 2013, 18, 349.
(8) Roman, S. et al., “Going beyond 20μm-sized channels for studying red blood cell phase separation in microfluidic bifurcations”, Biomicrofluidics, 2016, 10, 034103.
(9) Smay, J., Cesarano, J., and Lewis, J., “Colloidal inks for directed assembly of 3-D periodic structures”, Langmuir, 2002, 18, 5429.
Thanks are given to Jason Bice for fruitful discussion.