Electrodispersion of a liquid of finite elcetrical conductivity in an immiscible dielectric liquid

Order-of-magnitude estimates and numerical computations are used to analyze an electrospray operating in the cone-jet mode in a bath of an immiscible dielectric liquid. In agreement with experimental results in the literature, the analysis predicts that the electric current carried by the jet increases as the square root of the flow rate of dispersed liquid in a wide range of conditions of the flow. The characteristics of the current transfer region determining the electric current are estimated taking into account the viscous drag of the dielectric liquid that surrounds the jet. The electric current is predicted to depart from the square root law for small flow rates, when charge relaxation effects become important in the current transfer region, and also when the flow rate increases to values of the order of QM = ϵ0γ2a/μ22K, where ϵ0 and μ2 are the permittivity and viscosity of the dielectric liquid, K is the electrical conductivity of the dispersed liquid, a is the radius of the capillary needle through which this liquid is injected, and γ is the interfacial tension of the liquid pair. When the flow rate becomes of order QM, the meniscus at the tip of the capillary ceases to resemble a Taylor cone, the current transfer region ceases to be short compared to the size of the meniscus, the electric current levels to a constant value, and the stationary jet cannot extend very far downstream of the meniscus

Numerical computation of the domain of operation of an electrospray of a very viscous liquid

A numerical study is carried out of the injection of a very viscous liquid of small electrical conductivity at a constant flow rate through an orifice in a metallic plate under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet emanating from its tip are investigated by computing the flow, the electric field and the transport of electric charge in the meniscus and a leading region of the jet. A stationary solution is found only for values of the flow rate above a certain minimum. At moderate values of the applied field, this minimum flow rate decreases when the applied field or the conductivity of the liquid increase. The electric shear stress acting on the surface of the liquid is not able to drive the liquid into the jet at flow rates smaller than the minimum while, for any flow rate higher than the minimum, the transfer of electric current to the surface may occur in a slender region of the jet where charge relaxation effects are small and the field induced by the electric charge of the jet is important. At high values of the applied field, the flow rate must be higher than another minimum, which increases with the applied field, in order for the viscous stress to balance the strong electric stress acting on the meniscus. The two conditions taken together determine lower and upper bounds for the applied field at a given flow rate, but the value of the applied field at which a stationary jet is first established when this parameter is gradually increased is higher than the lower bound, leading to hysteresis. When the liquid is electrosprayed in a surrounding dielectric fluid, the viscous shear stress that this fluid exerts on the surface of the jet eventually balances the electric shear stress and stops the continuous stretching of the jet. A fraction of the conduction current is left in the jet when the effect of the outer liquid comes into play in the region where this current is transferred to the surface, and no stationary solution is found above a maximum flow rate that decreases when the viscosity of the outer liquid increases or the applied field decreases. Order of magnitude estimates of the electric current and the conditions in the current transfer region are worked out

Effects of fresh gas velocity and thermal expansion on the structure of a Bunsen flame tip

Numerical computations and order-of-magnitude estimates are used to describe the tip region of a Bunsen flame where the flame departs from a planar flame at an angle to the incoming fresh gas flow. A single irreversible Arrhenius reaction with high activation energy is assumed. The well-known linear relation between flame velocity and curvature is recovered in the thermodiffusive limit, when the thermal expansion of the gas is left out, for velocities of the fresh gas (U0) only slightly larger than the velocity of a planar flame (UL), provided this flame is stable. For large values of the velocity ratio U0/UL, the tip region becomes slender and the curvature of the reaction sheet at the tip increases proportionally to U0/UL. The thermal expansion of the gas across the flame reduces the aspect ratio of the tip region. A qualitative analysis of the structure of the tip region for very exothermic reactions shows that this region ceases to be slender when the burnt-to-fresh gas temperature ratio becomes of the order of the velocity ratio U0/UL. For even larger values of the temperature ratio, the tip region becomes a cap of characteristic size not very different from the thickness of a planar flam

Domestic violence on undocumented Latina women in Texas

textDomestic violence is a steadily growing problem and a source of major concern all over the country. Texas is not the exception, and, not surprisingly, different organizations have advocated for the adoption of resolutions declaring freedom from domestic violence as a human right. The City of Austin Council and Travis County adopted resolutions of this kind in 2014. Even though the topic has captured the attention of authorities, the situation is more complicated when it comes to undocumented Latina women, since they are forced to face other obstacles alongside being in an abusive situation. Such obstacles are the difficulties of accessing the legal system because of their lack of knowledge, or because of language barriers -- all circumstances occurring in a context of fear and threats by the perpetrator of the violence. In some cases, women and children are abused by United States citizens or legal permanent residents, who take advantage of their legal status and protection that the women and children lack. This report tells the stories of some women in Texas and tries to raise awareness of this matter within the community. The report also explains different legal remedies the women can use, such as the Violence Against Women Act (VAWA), through which they may obtain lawful permanent residency.Journalis

On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain

Lattice Boltzmann versus Molecular Dynamics simulation of nano-hydrodynamic flows

A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by Molecular Dynamics (MD) computer simulation and compared to results of Lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed.Comment: 4 pages, 4 figure

Stock Return Predictability and Oil Prices

This paper shows that oil price changes, measured as short-term futures returns, are a strong predictor of excess stock returns at short horizons. Ours is a leading variable for the business cycle and exhibits low persistence which avoids the ctitious long-horizon predictability associated to other predictors used in the literature. We compare our variable with the most popular predictors in a sample period that includes the recent nancial crisis. Our results suggest that oil price changes are the only variable with forecasting power for stock returns. This signi cant predictive ability is robust against the inclusion of other variables and out-of-sample tests. We also study the cross-section of expected stock returns in a conditional CAPM framework based on oil price shocks. Our model displays high statistical signi cance and a better t than all the conditional and unconditional models considered including the Fama French three-factor model. From a practical perspective, ours is a high-frequency, observable variable that has the advantage of being readily available to market-timing investors.Return predictability, business cycle, crude oil, futures prices, asset pricing, conditional CAPM