On the capillary self-focusing in a microfluidic system

A computational framework is developed to address capillary self-focusing in Step Emulsification. The microfluidic system consists of a single shallow and wide microchannel that merges into a deep reservoir. A continuum approach coupled with a volume of fluid method is used to model the capillary self-focusing effect. The original governing equations are reduced using the Hele-Shaw approximation. We show that the interface between the two fluids takes the shape of a neck narrowing in the flow direction just before entering the reservoir, in agreement with our experimental observations. Our computational model relies on the assumption that the pressure at the boundary, where the fluid exits into the reservoir, is the uniform pressure in the reservoir. We investigate this hypothesis by comparing the numerical results with experimental data. We conjecture that the pressure boundary condition becomes important when the width of the neck is comparable to the depth of the microchannel. A correction to the exit pressure boundary condition is then proposed, which is determined by comparison with experimental data. We also present the experimental observations and the numerical results of the transitions of breakup regimes.Comment: To appear in: Fluid Dynamics Researc

The wayward money supply: a post-mortem of 1982

Money supply

The shift in money demand: what really happened?

Demand for money

Evidence on the temporal stability of the demand for money relationship in the United States

Demand for money

Monetary policy and short-term real rates of interest

Monetary policy ; Interest rates

The local impacts of climate change in the Ferlo, Western Sahel

Recent increases in the accuracy of climate models have enhanced the possibilities for analyzing the impacts of climate change on society. This paper explores how the local, economic impacts of climate change can be modeled for a specific eco-region, the Western Sahel. The people in the Sahel are highly dependent on their natural resource base, and these resources are highly vulnerable to climate change, in particular to changes in rainfall. Climate models project substantial changes in rainfall in the Sahel in the coming 50 years, with most models predicting a reduction in rainfall. To connect climate change to changes in ecosystem productivity and local income, we construct an ecological¿economic model that incorporates rangeland dynamics, grazing and livestock prices. The model shows that decreased rainfall in the Sahel will considerably reduce local incomes, in particular if combined with increases in rainfall variability. Adaptation to these climate change projections is possible if reductions in rainfall are followed by destocking to reach efficient grazing levels. However, while such a strategy is optimal from the perspective of society, the stocking rate is determined by individual pastoralists that face few incentives to destoc

Capillary focusing close to a topographic step: Shape and instability of confined liquid filaments

Step-emulsification is a microfluidic technique for droplet generation which relies on the abrupt decrease of confinement of a liquid filament surrounded by a continuous phase. A striking feature of this geometry is the transition between two distinct droplet breakup regimes, the "step-regime" and "jet-regime", at a critical capillary number. In the step-regime, small and monodisperse droplets break off from the filament directly at a topographic step, while in the jet-regime a jet protrudes into the larger channel region and large plug-like droplets are produced. We characterize the breakup behavior as a function of the filament geometry and the capillary number and present experimental results on the shape and evolution of the filament for a wide range of capillary numbers in the jet-regime. We compare the experimental results with numerical simulations. Assumptions based on the smallness of the depth of the microfluidic channel allow to reduce the governing equations to the Hele-Shaw problem with surface tension. The full nonlinear equations are then solved numerically using a volume-of-fluid based algorithm. The computational framework also captures the transition between both regimes, offering a deeper understanding of the underlying breakup mechanism

The dynamics and estimation of short-run money demand

Demand for money

Irreversibility line and low-field grain-boundary pinning in electron-doped superconducting thin films

AC magnetic susceptibilities of electron-doped Pr_{1.85}Ce_{0.15}CuO_4 (PCCO) and Sm_{1.85}Ce_{0.15}CuO_4 (SCCO) granular thin films have been measured as a function of temperature and magnetic-field strength. Depending on the level of homogeneity of our films, two different types of the irreversibility line (IL) defined as the intergrain-loss peak temperature in the imaginary part of susceptibility have been found. The obtained results are described via the critical-state model taking into account the low-field grain-boundary pinning. The extracted pinning-force densities in more granular SCCO films turn out to be four times larger than their counterparts in less granular PCCO films