Fluid dynamics of dilatant fluids

Abstract

Dense mixture of granules and liquid often shows a sever shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of dispersed particles. With simple assumptions for an equation of the state variable, we demonstrate that the model can describe basic features of the dilatant fluid such as the stress-shear rate curve that represents discontinuous severe shear thickening, hysteresis upon changing shear rate, instantaneous hardening upon external impact. Analysis of the model reveals that the shear thickening fluid shows an instability in a shear flow for some regime and exhibits the shear thickening oscillation, i.e. the oscillatory shear flow alternating between the thickened and the relaxed states. Results of numerical simulations are presented for one and two-dimensional systems.

Experimental observation of shear thickening oscillation

“…The observed frequency of the oscillation is about 20 Hz, which is roughly in the range expected by the model for the flow width of several centimeters. These features are consistent with those of the shear thickening oscillation predicted by the phenomenological model [22].…”

“…Se=1.0kPa at S e = 0.1 kPa, thus the transition is consistent with a Hopf bifurcation as has been expected for the phenomenological model [21,22]. In the case of the thinner fluid of the 41 wt% concentration, a slower oscillation around 5 Hz remains at S e = 0.1 kPa (Fig.3(a)).…”

“…Originally, the order-disorder transition of the dispersed particles was proposed [1,[10][11][12], but later the hydrodynamics cluster formation by the lubrication force is considered to be more consistent with experimental observations and numerical simulations [13][14][15][16]. More recently, the shear thickening transition is discussed in connection with the jamming and/or the compaction of granules [17][18][19][20].Recently, the present authors constructed a phenomenological model that describes macroscopic flowing properties of a shear thickening fluid [21,22]. By analyzing the model, they pointed out that the discontinuous thickening upon increasing the shear rate signifies that the shear thickening fluid is actually shear stress thickening, not shear rate thickening because only the shear stress thickening can produce the S-shaped flow curve with an unstable…”

“…Recently, the present authors constructed a phenomenological model that describes macroscopic flowing properties of a shear thickening fluid [21,22]. By analyzing the model, they pointed out that the discontinuous thickening upon increasing the shear rate signifies that the shear thickening fluid is actually shear stress thickening, not shear rate thickening because only the shear stress thickening can produce the S-shaped flow curve with an unstable branch shear stress unstable shear rate branch, that causes the discontinuous transition experimentally observed (Fig.1).…”

“…the shear thickening oscillation, when the applied external shear stress is in the unstable region. It was predicted using the phenomenological model [21,22], and its basic mechanism can be understood as follows; A uniform shear flow in the unstable branch can be destabilized by an infinitesimal disturbance toward the thickened p-1 state. Once the thickening starts, the flow is decelerated, which imposes the inertia stress.…”