In this study, we investigated the behavior of Discontinuously Rate Thickening Suspensions (DRTS) in capillary breakup, where a thin suspension filament breaks up under the action of surface tension forces.We performed experiments with 55% by weight suspension of cornstarch in glycerol. To minimize the effect of gravity on the experiments, we developed a new experimental method, where the filament is supported in a horizontal position at the surface of an immiscible oil bath by the interfacial tension of the oil-air interface. It was found that after a brief transition period, the radius of the filament decreases at an exponentially decaying rate, which is half the deformation rate at which the apparent viscosity of DRTS appreciably increases beyond it's low-deformation rate value. Late in the filament's evolution, a bead forms in its center, leading to formation of morphologically complex, high aspect ratio structures. It was found that the formation of these structures is caused by the viscous drag exerted on the filament by the oil bath.The behavior of DRTS filaments in capillary breakup was modeled with 1-dimensional approximations to momentum and mass balance equations, which are valid in the limit of slender geometry of the filament. The rheology of the suspension was modeled with a simple function diverging at the deformation rate at which the increase in viscosity becomes appreciable. The governing nonlinear coupled partial differential equations were solved numerically with a finite volume scheme using the Newton's method. It was found that this simple model reproduces the observed behavior well.It was found that in contrast to Newtonian filaments, the viscous stress in the DRTS filaments reaches a plateau and does not increase indefinitely. This is a result of a coupling between the nonlinear rheology of the suspension and the nonlinearity associated with evolving shape of the filament. It was found that the evolution of DRTS filaments with no external viscous drag depends on the value of a single parameter, i/Wi, which is a function of the Weissenberg number Wi associated with the flow, and the aspect ratio of the filament . When i/Wi < 1/3, the viscous stress at the center of the filament scales as (-, and when i/Wi > 1/3, the viscous stress scales as Wi-1 . These findings are supported by analytical arguments based on the governing equations in the regime where i/Wi < 1/3.The formation of the beaded structures was investigated, focusing on the appearance of the first bead at the center of the filament. It was found that the viscous drag from the environment plays a central role in formation of the beads. Numerical solutions, theoretical arguments and experiments were found to be in agreement.
We use nonlinear behavior of thin-walled structures — an approach inspired by biological systems (the human airway, for example) — to address one of the most important problems facing subsistence farmers in developing countries: lack of access to inexpensive, water-efficient irrigation systems. An effective way of delivering water to crops is through a network of emitters, with up to 85% of the water delivered being absorbed by plants. However, of the 140 million hectares of cropped land in India alone, only 61 million are irrigated and just 5 million through drip irrigation. This is, in part, due to the relatively high cost of drip irrigation. The main cost comes from the requirement to pump the water at relatively high pressure (>1bar), to minimize the effect of uneven terrain and viscous losses in the network, and to ensure that each plant receives the same amount of water. Using a prototype, we demonstrate that the pressure required to drive the system can be reduced significantly by using thin-walled structures to design emitters with completely passive self-regulation that activates at approximately 0.1bar. This reduction in driving pressure could help bring the price of drip irrigation systems from several thousand dollars to approximately $300, which is within reach of small-scale farmers. Using order-of-magnitude calculations, we show that due to increased sensitivity of the proposed design to the applied pressure differential, a pressure compensating valve for drip irrigation could be built without using costly silicone membranes.
We investigate the effect of localized leakage on the storage of buoyant fluids in inclined porous reservoirs, with application to the geological storage of CO2. We find that once the current has propagated some distance beyond the point of leakage, its profile becomes steady in time, save for the nose, which advances at a constant speed. Crucially, this steady state implies that the efficiency of storage (defined as the instantaneous proportion of the injected fluid that does not leak) tends to a finite value. This contrasts with previous studies of localized leakage in horizontal reservoirs, which found that the efficiency of storage tends to zero at late times. We analyse the steady-state efficiency and the time scales of evolution for a leakage point located either upslope or downslope of the injection point using analytical and numerical methods. These findings are verified by model laboratory experiments. Finally, we consider the implications of our results for the geological storage of CO2 under sloping cap rocks compromised by a fracture or fissure.
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