We present experimental measurements of the normal stresses in sheared Stokesian suspensions. Though the suspending fluid is Newtonian, dispersing rigid non-Brownian particles in it yields a suspension that is non-Newtonian, as it exhibits normal stress differences and an excess isotropic pressure in viscometric flows. At small to moderate concentrations, the normal stresses are very small in magnitude, and hence difficult to measure. This difficulty is compounded by the presence of noise due to unavoidable experimental artifacts. Owing to these limitations, most measurements reported earlier were carried out at relatively high particle concentrations, and some at shear rates large enough that the effects of particle and fluid inertia may have been significant. In our study, we have used a novel technique to measure the small stress levels. This was achieved by applying a sinusoidally varying shear rate with a fixed (low) frequency superimposed on a constant shear rate, and using a lock-in amplifier to measure the Fourier component of the same frequency in the stress signal. We have measured normal stresses in cylindrical-Couette and parallel-plate geometries, and combined these measurements to determine the two normal stress differences for particle volume fractions in the range 0.3–0.45. While the normal stresses are very small at low concentrations, they rise rapidly with increasing concentration. The normal stresses vary linearly with the magnitude of the shear rate, and are independent of its sign. In contrast to polymeric solutions, both normal stress differences are negative, and the first normal stress difference is significantly smaller in magnitude. We compare our data with the results of earlier studies, and observe good agreement.

We report the normal stresses in a non-Brownian suspension in plane Couette flow determined from Stokesian Dynamics simulations. The presence of normal stresses that are linear in the shear rate in a viscometric flow indicates a non-Newtonian character of the suspension, which is otherwise Newtonian. While in itself of interest, this phenomenon is also important because it is believed that normal stresses determine the migration of particles in flows with inhomogeneous shear fields. We simulate plane Couette flow by placing a layer of clear fluid adjacent to one wall in the master cell, which is then replicated periodically. From a combination of the traceless hydrodynamic stresslet on the suspended particles, the stresslet due to (non-hydrodynamic) inter-particle forces, and the total normal force on the walls, we determine the hydrodynamic and inter-particle force contributions to the isotropic ‘particle pressure’ and the first normal stress difference. We determine the stresses for a range of the particle concentration and the Couette gap. The particle pressure and the first normal stress difference exhibit a monotonic increase with the mean particle volume fraction ϕ. The ratio of normal to shear stresses on the walls also increases with ϕ, substantiating the result of Nott & Brady (1994) that this condition is required for stability to concentration fluctuations. We also study the microstructure by extracting the pair distribution function from our simulations; our results are in agreement with previous studies showing anisotropy in the pair distribution, which is the cause of normal stresses.

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We report an analysis, using the tools of nonlinear dynamics and chaos theory, of the fluctuations in the stress determined from simulations of shear flow of Stokesian suspensions. The simulations are for shear between plane parallel walls of a suspension of rigid identical spheres in a Newtonian fluid, over a range of particle concentration. By analyzing the time series of the stress, we find that the dynamics underlying these fluctuations is deterministic, low-dimensional, and chaotic. We use the dynamic and metric invariants of the underlying dynamics as a means of characterizing suspension behavior. The dimension of the chaotic attractor increases with particle concentration, indicating the increasing influence of multiple-body interactions on the rheology of the suspension with rise in particle concentration. We use our analysis to make accurate predictions of the short-term evolution of a stress component from its preceding time series, and predict the evolution of one component of the stress using the time series of another. We comment on the physical origin of the chaotic stress fluctuations, and on the implications of our results on the relation between the microstructure and the stress.

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Experiments and numerical simulations were carried out for an evaporating sessile droplet. The droplet was confined in the narrow gap between two glass plates, making it a "Hele-Shaw" droplet and particle image velocimetry technique was used. In case of the evaporating droplet with pinned contact line and exposed to ambient condition, two symmetric but counterrotating convection cells were observed. After complete evaporation, the particles deposited on the substrate near the contact line. The direction of the flow was reversed for a droplet placed on uniformly heated substrate, and the final deposition pattern was a large spot at the center with a thin line at the periphery. For asymmetrically heated substrate a single convection cell appeared, and the final deposition was also asymmetric. When the liquid was subjected to localized heating, the contact line no longer remains pinned and a relatively uniform deposition was obtained after complete drying.

Evaporation-induced particle deposition patterns like coffee rings provide easy visual identification that is beneficial for developing inexpensive and simple diagnostic devices for detecting pathogens. In this study, the effect of chemotaxis on such pattern formation has been realized experimentally in drying droplets of bacterial suspensions. We have investigated the velocity field, concentration profile, and deposition pattern in the evaporating droplet of Escherichia coli suspension in the presence and absence of nutrients. Flow visualization experiments using particle image velocimetry (PIV) were carried out with E. coli bacteria as biological tracer particles. Experiments were conducted for suspensions of motile (live) as well as nonmotile (dead) bacteria. In the absence of any nutrient gradient like sugar on the substrate, both types of bacterial suspension showed two symmetric convection cells and a ring like deposition of particles after complete evaporation. Interestingly, the droplet containing live bacterial suspension showed a different velocity field when the sugar was placed at the base of the droplet. This can be attributed to the chemoattractant nature of the sugar, which induced chemotaxis among live bacteria targeted toward the nutrient site. Deposition of the suspended bacteria was also displaced toward the nutrient site as the evaporation proceeded. Our experiments demonstrate that both velocity fields and concentration patterns can be altered by chemotaxis to modify the pattern formation in evaporating droplet containing live bacteria. These results highlight the role of bacterial chemotaxis in modifying coffee ring patterns.