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Shear Thickening Mechanism: History

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Subjects: Mechanics

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Huixin Zhu

Shear thickening fluid (STF) is a dense colloidal suspension of nanoparticles in a carrier fluid in which the viscosity increases dramatically with a rise in shear rate. Due to the excellent energy absorption and energy dissipation of STF, there is a desire to employ STFs in a variety of impact applications.

shear thickening fluids
viscosity
particles

1. Introduction

Shear thickening fluid (STF) is a non-Newtonian fluid that exhibits an abrupt increase in viscosity by a few orders of magnitude with increasing shear rate [1,2,3]. STF behaves as a solid-like material under applied stress due to increasing viscosity, and when the loading is removed from the medium, the STF turns to the initial liquid state. Due to the excellent energy absorption and energy dissipation characteristics of STF, it has been widely used in the Li-ion batteries [4], wearable devices [5], triboelectric nanogenerator (TENG) [6], protective structures [7,8] and some novel applications [9,10,11].

STF consists of a carrier liquid and colloidal particles [12,13]. The particles are generally selected from a number of groups of particles which include silica, polymethyl methacrylate, calcium carbonate, cornstarch, synthetically and naturally occurring minerals, polymers or a mixture of them. Many carrier fluids such as water, ethylene glycol (EG) and poly ethylene glycol (PEG) have been investigated [14]. The common particles and carrier fluids of STFs are summarized in Table 1.

Table 1. The compositions of STFs.

Particles	Carrier Fluids	Additives	Reference
Polystyrene-ethylacrylate (PSt-EA)	EG	—	[2]
Polymethyl methacrylate (PMMA)	Glycerine–water	—	[22]
Polymethyl methacrylate (PMMA)	PEG	—	[23]
Silica nanoparticles	PEG	—	[24]
	Ethyl alcohol and PPG	—	[25]
	PEG	Polyvinyl alcohol	[26]
	Water	—	[27]
	Ionic liquids	—	[28]
	EG	PEG	[29]
	PEG	Graphene	[30]
	Ethanol and PEG	Silane coupling agent	[31]
Fumed silica	PEG	SiC	[32]
		SiC nanowires	[33]
		Carbon nanotubes	[34]
	EG	—	[35]
	PEG	Clay nanoparticles	[29]
Cornstarch	Water	—	[36]
Cornstarch	CsCl in demineralized water	—	[36]
Styrene/acrylate	EG	—	[37]
(Poly)Styrene-acrylonitrile (PSAN)	EG	—	[38]
Polyvinyl chloride (PVC)	Dioctyl phthalate	—	[38]
Precipitated calcium carbonate	PEG	—	[39]
ZrO₂	Mineral oil	—	[40]
Soda-lime glass spheres	Water	—	[40]
Glass spheres	Mineral oil	—	[40]
Polystyrene (PS)	PEG	—	[41]
Nano-silica and calcium	PEG and ethanol	—	[42]
Kaolin clay particles	Glycerol	—	[43]

According to the rheological properties of STF, they can be divided into two categories: continuous shear thickening (CST) and discontinuous shear thickening (DST). CST is observed below threshold value, $\emptyset_{c}$ , and becomes weaker with decreasing volume fraction. DST is an abrupt increase by orders of magnitude in viscosity above a critical value of the applied shear rate [44]. Fernandez et al. [45] proposed a model to identify the nature of the Shear thickening transition which was controlled by the volume fraction and boundary lubrication friction coefficient through the simulations and experiments. Brown et al. [46] gave a good overview on phenomenology and mechanisms of shear thickening and discussed the relations to jamming systems. They proposed different mechanisms and models to explain the common physical properties and a phase diagram for shear thickening behavior. The rheological properties of STF are affected by many factors, including particle volume fraction, particle aspect ratio, particle–particle interactions, hardness, roughness, particle size, size distribution of particle, modification of particle, liquid medium, pH value, temperature and additives of STF, as reviewed by Gürgen [47] and Subramaniam [48]. More recently, Yusuf Salim [49] has reviewed the factors and damage mechanism of the stab and spike resistance performance of STF-impregnated. To improve the impact resistance of textile, different STFs were prepared for the high performance fabric composites [50]. Some approaches to improve the ballistic performance including surface treatments and modifications of fabrics in STF-based soft body armor were elucidated [11,51]. The applications of various STF impregnated fabric composites and the STFs’ contribution on improving the impact, ballistic and stab resistance performance were investigated by many researchers [21,52]. Mechanistic problems due to sudden change in viscosity and recent developments of simulations of the effect of contact forces were discussed in the STF [53].

Over the past few decades, the shear thickening mechanism has been studied by many researchers and extensive studies have been reported in the literature, including the order–disorder transition, hydro-clustering, dilation, jamming and friction contact theory.

2. Order–Disorder Transition Theory

Hoffman [38] first proposed the order–disorder transition theory that the shear thickening phenomenon was concurrent with the transition from order to less ordered flow of particles. Different diffraction patterns were found before and after shear thickening, as shown in Figure 1a. Subsequently, he found that the nanoparticles in the STF are layered order below the critical shear rate and the transition from order to disorder caused a drastic increase in suspension viscosity by experiment [60]. At a certain critical shear rate, particle doublets would form, which moved out of their layers and disrupted the flow, resulting in an increase in the suspension viscosity [61]. Moreover, Laun et al. [62] studied shear-induced particle structures of STF with styrene-ethylacrylate-copolymer spheres in glycol or water by small angle neutron scattering in a wide range of shear rates and found that the particle structures which stopped flowing depended on the shear rate. In an effort to better understand the shear thickening mechanism, computer simulations presented a path forward. Catherall et al. [63] used Stokesian dynamics to investigate the rheology and microstructure of STF under the shear thickening regime; they controlled the interparticle gaps to evaluate the thickening behavior, reporting that at higher hard core volume fractions, larger jumps in viscosity were observed with the transition from order to disorder and the strong thickening behavior was only observed with the enhanced lubricating force.

Figure 1. (a) Different diffraction patterns before (a₁) and after (a₂) shear thickening [38], (b) instantaneous real-space configuration of hydro-clusters [64], (c) the visible effect of dilation for shear thickening fluid of cornstarch in water ((c₁) before shear, the surface of the suspension looked wet and shiny, (c₂) when the shear rate was above the critical shear rate, the nearby suspension appeared rough) [28], (d) the shear-jammed regime explicitly caused by dropping small steel spheres onto the shear thickening fluid [65] and (e) contact networks along the suspension with particle loading of 56% [44].

3. Hydro-Clustering Theory

Brady et al. [66] and Butera et al. [67] found that the order–disorder transition did not always occur during all shear thickening phenomena, suggesting that the order–disorder transition was dispensable for shear thickening. Moreover, Bossis et al. [39] also found that shear thickening behavior was dependent on the formation of large clusters rather than the order–disorder transition. The hydro-clustering mechanism proposed that the particles of STF were driven together into clusters under shear, as a result of short-range hydro-dynamic lubrication forces overcoming the repulsive forces among adjacent particles. The hydro-clustering mechanism has been widely accepted for explaining the shear thickening behavior by many researchers [68,69]. For example, Cheng et al. [64] visualized and identified the hydro-clusters as the onset of thickening in the STF of silica spheres in a water-glycerin mixture using the fast confocal microscopy with simultaneous force measurements. Figure 1b depicts the instantaneous real-space configuration of hydro-clusters and different colors indicate different clusters. Next, Maranzano and colleagues [70] demonstrated the extreme sensitivity of high-shear rheology to the surface properties of suspended particles, which was consistent with the formation of hydro-clusters and the dominance of short-range lubrication forces in the shear thickening state. Later, Chellamuthu et al. [71] measured the extensional properties of fumed silica nanoparticles in polypropylene glycol as a function of concentration and extension rate and found that the dynamic rheological behavior of STF was caused by the formation of large hydro-dynamic clusters. Brady et al. [72] used the Stokesian dynamics to calculate the particle trajectories to find that molecular-dynamics-like method could accurately represent the suspension hydrodynamics.

4. Dilation Theory

Brown et al. suggested that the hydro-clustering theory, which had been successful for clarifying CST, had failed to explain the orders of magnitude increase in viscosity during DST [28,36]. In this mechanism, the shear stress overcomes the onset stresses of the shear thickening, and they begin to shear relative to each other, which causes the grain packing to dilate. Dilation of granular shear flows causes particles to penetrate the liquid-air interface for STF, generating restorative forces transmitted through the suspensions produce a confining shear stress which is proportional to normal stress, resulting in DST [28]. Figure 1c depicts the visible effect of dilation on STF of cornstarch in water [28]. Shear thickening was described as dilatancy, which refers to the expansion of a system due to the change in packing arrangement [73,74]. A dense mixture of granules and liquid is called a dilatant fluid which often exhibits shear thickening behavior with the increase in shear rate. Nakanishi et al. [75] constructed a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of nanoparticles, and the results of model showed that the STF exhibited an instability in a shear flow and shear thickening oscillation.

5. Jamming Theory

In recent years, studies revealed that the explanation of the DST was closely connected to jamming [76,77]. They believed that the nanoparticles of STF would spontaneously aggregate under shear, forming local blockages. The dispersed phase particles diffuse under the action of shearing, and the suspension cannot flow at all, showing the exponential growth of shear stress and the explosive increase in apparent viscosity. Next, a new added mass model was introduced to clarify the dynamic solidification process that the large normal stresses formed using a rapidly growing jammed solid region, which is pushed through the surrounding STF by the impactor [78]. Then, Marc-Andre Brassard et al. [79] reported a new model, in which the viscous-like forces control the impact response of STFs to supplement the add-mass theory. Peters et al. [65] explored the solid behavior in the shear-jammed regime experimentally by dropping small steel spheres (diameter 5.0 mm) onto the STF. The dynamic shear jamming behavior was observed directly, as shown in Figure 1d. Moreover, Seto et al. [80] adopted a numerical method which included hydrodynamics interactions and granular contacts, and observed that contact friction was essential for discontinuous shear thickening. A low viscosity occurred in a contactless (hence, frictionless) state, and a high viscosity exhibited a frictional shear-jammed state. Next, the elongation and breakage of a filament of STF under tensile loading was closely related to the jamming transition seen in its shear rheology as presented by Smith et al. [81]. The jamming theory can well explain the solid–liquid transition in STF, it provides a reasonable explanation for the relationship between shear stress, shear rate and apparent viscosity. However, jamming is just a general term for describing the phenomenon and does not really reveal the nature of the shear thickening phenomenon.

6. Friction Contact Theory

The friction contact theory was adopted to explain the relationship between the CST and DST. Under low shear, the normal contact force between particles is small, and the fluid lubricating force plays a more important role in the impact process. When the normal contact force between particles is large, the fluid film between particles is destroyed, and particle-to-particle contact force and friction force play a leading role. As the shear rate increases, there are more frictional contacts, and the system forms a frictional contact network [45]. Mari et al. [44] numerically obtained that as the shear rate increased, the shear increased as shown in Figure 1e. The uncontacted particles with gray colored line, which connects the centers of two related particles, are drawn, while the red line indicates the particles that will come into contact during the thickening process. Clearly, the contacting particles form an extended contact network in the STF. All the aforementioned studies show that the mutual frictional contact of dispersed phase particles plays an important role in the shear thickening process of STF. In summary, the friction contact model is a theoretical model accepted widely by scholars. It can not only explain the CST behavior and the DST behavior at the same time, but also can be verified through inverse shear rheological experiments and numerical simulations.

This entry is adapted from the peer-reviewed paper 10.3390/polym15102238

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