A mathematical theory of microscale hydrodynamic cloaking and shielding by electro-osmosis

In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being annulus or confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the condition that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding

Enhanced Microscale Hydrodynamic Near-cloaking using Electro-osmosis

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the cloaking conditions and relationship of shapes are quantified more accurately. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking

tert-Butyl 2-borono-1H-pyrrole-1-carboxyl­ate

In the crystal structure of the title compound, C9H14BNO4, the boronic acid group and carbamate groups are nearly co-planar with the pyrrole ring, making dihedral angles of 0.1 (2) and 2.2 (2)°, respectively. Intra­molecular and inter­molecular O—H⋯O hydrogen bonds help to stabilize the structure, the latter interaction leading to inversion dimers.

Improving Methane Production During the Anaerobic Digestion of Waste Activated Sludge: Cao-ultrasonic Pretreatment and Using Different Seed Sludges

AbstractThree individual seed sludges, which domesticated by filter paper (SS1), food waste (SS2) and grease (SS3), respectively, were used for enhancing the methane production of waste activated sludge (WAS). Also CaO-ultrasonic pretreatment was performed on WAS to evaluate the effectiveness on improving efficient anaerobic digestion (AD). The results showed that WAS being acidated for 24h after CaO-ultrasonic pretreatment was an effective method for increasing initial methane production rate. The daily concentration of volatile fatty acids (VFAs) during the AD course showed that the propionic was easier to be reduced after adding seed sludge. The optimum seed sludge for improving methane production and biodegradability of WAS was SS3, which led to an increase in the methane production of 68.92% and VS reduction of 69.20% higher than the control. This pretreatment combined with adding optimum seed sludge can greatly improve clean energy generation from WAS

1-Butyl-3-(1-naphthyl­meth­yl)benzimidazolium hemi{di-μ-iodido-bis­[diiodidomercurate(II)]} dimethyl sulfoxide monosolvate

In the title compound, (C22H23N2)[Hg2I6]0.5·(CH3)2SO, the 1-butyl-3-(1-naphthyl­meth­yl)benzimidazolium anion lies across a centre of inversion. The dihedral angle between the benzimidazolium and naphthalene ring systems is 81.9 (3)°. In the crystal structure, π–π stacking inter­actions are observed between the imidazolium ring and the unsubstituted benzene ring of the naphthalene ring system, with a centroid–centroid separation of 3.510 (5) Å. In the centrosymmetric anion, the Hg(II) atoms are in a distorted tetrahedral coordination. The dimethyl sulfoxide solvent mol­ecule is disordered over two sites with occupancies of 0.615 (9) and 0.385 (9)