Study of Slip Flow in Unconventional Shale Rocks Using Lattice Boltzmann Method: Effects of Boundary Conditions and TMAC

Steady, laminar, fully developed flows of a Newtonian fluid driven by a constant pressure gradient in (1) a curvilinear constant cross section triangle bounded by two straight no-slip segments and a circular meniscus and (2) a wedge bounded by two rays and an adjacent film bulging near the corner are studied analytically by the theory of holomorphic functions and numerically by finite elements. The analytical solution of the first problem is obtained by reducing the Poisson equation for the longitudinal flow velocity to the Laplace equation, conformal mapping of the corresponding transformed physical domain onto an auxiliary half-plane and solving there the Signorini mixed boundary value problem (BVP). The numerical solution is obtained by meshing the circular sector and solving a system of linear equations ensuing from the Poisson equation. Comparisons are made with known solutions for flows in a rectangular conduit, circular annulus and Philip’s circular duct with a no-shear sector. Problem (2) is treated by the Saint-Venant semi-inverse method: the free surface (quasi-meniscus) is reconstructed by a one-parametric family, which specifies a holomorphic function of the first derivative of the physical coordinate with respect to an auxiliary variable. The latter maps the flow domain onto a quarter of a unit disc where a mixed BVP for a characteristic function is solved by the Zhukovsky–Chaplygin method. Velocity distributions in a cross section perpendicular to the flow direction are obtained. It is shown that the change of the type of the boundary condition from no slip to perfect slip (along the meniscus) causes a dramatic increase of the total flow rate (conductance). For example, the classical Saint-Venant formulae for a sector, with all three boundaries being no-slip segments, predict up to four times smaller rate as compared to a free surface meniscus. Mathematically equivalent problems of unconfined flows in aquifers recharged by a constant-intensity infiltration are also addressed.     

Raft mediated surface grafting of t‐butyl acrylate onto an ethylene–propylene copolymer initiated by gamma radiation

RAFT mediated grafting of poly(t‐butyl acrylate) onto the surface of a commercial poly(ethylene‐co‐propylene), Elpro, has been carried out using initiation by ⁶⁰Co γ‐radiation at 298 and 273 K. The polymerizations were in bulk monomer and using the RAFT agent 1‐phenylethyl phenyldithioacetate. The rates of homopolymerization and grafting were found to decrease with increasing RAFT agent concentration, indicating that both polymerization processes involve participation of the RAFT agent. There was good agreement between the predicted and experimental molecular weights of the homopolymer that had a narrow polydispersity. The poly(t‐butyl acrylate) grafts were hydrolyzed by trifluoroacetic acid to form poly(acrylic acid) grafts, which could either be further functionalized or used to control the surface polarity of the Elpro. ATR‐FTIR spectroscopy was used to characterize the grafts and Raman spectroscopy was used to assess the depth of the grafts. The water contact angle for the Elpro surface grafted with poly(acrylic acid) was found to be linearly dependent on the amount of the graft present. The living nature of the grafted chains was demonstrated by the addition of a second block of polystyrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1074–1083, 2007     

Heat transfer analysis of energy and exergy improvement in water-tube boiler in steam generation process

Journal of Thermal Analysis and Calorimetry - Steam generation is an essential process in steel production. Saturated steam is used in the cold-rolling mills of sample steel company to raise the...     

6-alkoxy-3,4-dihydro-2h-pyrans from substituted α,β-unsaturated esters

Cycloaddition reactions of substituted α,β-unsaturated esters with various electronich olefins lead to 6-alkoxy-3,4-dihydro-2H-pyrans.     

Separating maps on weighted function algebras on topological groups

Let G ₁ and G ₂ be locally compact groups and let ω ₁ and ω ₂ be weight functions on G ₁ and G ₂, respectively. For i = 1, 2, let also C ₀(G _i , 1/ω _i ) be the algebra of all continuous complex-valued functions f on G _i such that f/ω _i vanish at infinity, and let H: C ₀(G ₁, 1/ω ₁) → C ₀(G ₂, 1/ω ₂) be a separating map; that is, a linear map such that H(f)H(g) = 0 for all f, g ∈ C ₀(G ₁, 1/ω ₁) with fg = 0. In this paper, we study conditions under which H can be represented as a weighted composition map; i.e., H(f) = φ(f ℴ h) for all f ∈ C ₀(G ₁, 1/ω ₁), where φ: G ₂ → ℂ is a non-vanishing continuous function and h: G ₂ → G ₁ is a topological isomorphism. Finally, we offer a statement equivalent to that h is also a group homomorphism.     

The M/M/1 queue with inventory, lost sale, and general lead times

We consider an M/M/1 queueing system with inventory under the $(r,Q)$ policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random variables and can take various distributions. The derived stationary distributions are used to formulate long-run average performance measures and cost functions in some numerical examples.     

A study of a simulated low Earth environment on the degradation of FEP polymer

Spacecraft flying in a low Earth orbit environment require thermal blankets to provide protection from direct solar heat from the sun. Fluorinated ethylene propylene copolymer is one of the major components of these thermal blankets. In this study, the effect of a simulated low Earth orbit environment on FEP was investigated. UV and VUV degradation of fluorinated ethylene propylene (FEP) copolymer was studied using ESR and XPS. The ESR study revealed the formation of a terminal polymer chain radical. The stability of this radical has been investigated under different environments. An XPS study of FEP film exposed to VUV and atomic oxygen showed that oxidation takes place on the polymer surface. The study revealed also that the percentage of CF₂ in the polymer surface decreased with exposure time and the percentage of CF, CF₃ and carbon attached to oxygen increased. SEM micrographs of FEP film exposed to VUV and atomic oxygen produced a rough surface with regular undulations similar to sand dunes. © 1998 John Wiley & Sons, Ltd.     

Geometry, charge distribution, and surface speciation of phosphate on goethite

The surface speciation of phosphate has been evaluated with surface complexation modeling using an interfacial charge distribution (CD) approach based on ion adsorption and ordering of interfacial water. In the CD model, the charge of adsorbed ions is distributed over two electrostatic potentials in the double-layer profile. The CD is related to the structure of the surface complex. A new approach is followed in which the CD values of the various surface complexes have been calculated theoretically from the geometries of the surface complexes. Molecular orbital calculations based on density functional theory (MO/DFT) have been used to optimize the structure of a series of hydrated surface complexes of phosphate. These theoretical CD values are corrected for dipole orientation effects. Data analysis of the PO4 adsorption, applying the independently derived CD coefficients, resolves the presence of two dominant surface species. A nonprotonated bidentate (B) complex is dominant over a broad range of pH values at low loading (< or =1.5 micromol/m(2)). For low pH and high loading, a strong contribution of a singly protonated monodentate (MH or MH-Na) complex is found, which differs from earlier interpretations. For the conditions studied, the doubly protonated bidentate (BH2) and monodentate (MH2) surface complexes and the nonprotonated monodentate (M) complex are not significant contributors. These findings are discussed qualitatively and quantitatively in relation to published experimental in-situ CIR-FTIR data and theoretical MO/DFT-IR information. The relative variation in the peak intensities as a function of pH and loading approximately agrees with the surface speciation calculated with the CD model. The model correctly predicts the proton co-adsorption of phosphate binding on goethite and the shift of the IEP at low phosphate loading (< or =1.5 micromol/m(2)). At higher loading, it deviates.