The mechanical response of solid particles dispersed in a Newtonian fluid exhibits a wide range of nonlinear phenomena including a dramatic increase in the viscosity with increasing stress, a phenomenon knows a shear thickening.  This effect has important implications for a variety of industrial applications and natural processes.

We recently developed a new way to directly measure the stresses at the boundaries of sheared dense suspensions, Boundary Stress Microscopy.  The approach adapts traction force microscopy to rheological experiments. Traction force microscopy (TFM) involves coating a rigid substrate with a uniform elastic layer of known stiffness and incorporating markers to observe and quantify displacements of the layer produced by surface forces, and employing mathematical inversion techniques to deduce the magnitude and direction of those forces. The experimental setup, sketched in the figure below, sandwiches the suspesnions between a glass slide coated with a thin, uniform transparent rubbery material of known stiffness and a rotational rheometer for applying controlled stress (by rotating under a controlled torque).

In a typical measurement, a constant stress is and we record the instantaneous shear rate and local stress as determined by BSM. The figure below shows the typical flow curves (average viscosity at fixed applied stress) recorded by the rheometer for suspensions of different concentrations.

At concentrations or stresses below the shear thickening regime, the shear rate is constant in time, and the observed surface displacements and resulting calculated boundary stresses are uniform and equal to the applied stress.   In the shear thickening regime, however, we found localized surface displacements that are much higher than the average displacement. The figure below shows an example of the spatial map of the component of the boundary stress in the velocity (flow) direction calculated from the measured displacement fields.

The regions of high stress at the boundary appear with increasing frequency as the applied stress is increased, as can be clearly seen in a time series of the average stress in each image (Figure below). At the start of the shear thickening region (top curve), most images do not exhibit high stress regions, and thus have a small average stress. High stress fluctuations are clearly separated from the smooth background and appear intermittently separated by large quiescent periods. As the applied stress is increased (successive curves offset vertically), the high stress events do not get substantially larger (in terms of total stress), but occur much more frequently. Thus these high-stress regions represent a larger fraction of the total surface area, and quantitative analysis showed that this increase accounts for the observed shear thickening [1].

Based on a quantitative analysis of the spatiotemporal dynamics of the boundary stresses, we proposed that  high boundary stresses reflect high viscosity fluid phases that span the gap of the rheometer, sheared equally from above and below and at rest in a frame co-moving with the center of mass of the suspension [1], as summarized in the sketch below:

 

[1]  Localized stress fluctuations drive shear thickening in dense suspensions, V. Rathee, D. L. Blair, J. S. Urbach, Proceedings of the National Academy of Sciences, 114:8740-8745 (2017).