Valmor F. de Almeida

Transient polymeric drop extension and retraction in uniaxial extensional flows

Abstract We present results from modeling the deformation of a viscoelastic drop suspended in another viscoelastic fluid subjected to uniaxial extensional flow using the DEVSSG-FEM. Viscoelasticity is implemented using the Oldroyd-B constitutive relation for both the drop and surrounding matrix fluids. To allow efficient solution of the discretized problem, we employ an implicit temporal integration scheme with an accelerated quasi-Newton method. Important viscoelastic effects for both drop deformation during extensional flow and drop retraction following cessation of flow are elucidated. Viscoelastic drops in a Newtonian matrix lengthen less at steady state extension than Newtonian drops because of the accommodation of stress by elasticity. However, the stored elastic effects cause rapid tip retraction during the recovery of polymeric drops. Drops stretched in a viscoelastic exterior flow are enhanced in length compared to those in a Newtonian matrix because of first normal stresses from the matrix. During recovery, drops in a viscoelastic matrix can exhibit significant lengthening upon cessation of extensional flows, causing additional strain before retraction. This behavior is strongly dependent on the details of the exterior flow.

Influence of Nitric Acid on Uranyl Nitrate Association in Aqueous Solutions: A Molecular Dynamics Simulation Study

Uranyl ion complexation with water and nitrate is a key aspect of the uranium/plutonium extraction process. We have carried out a molecular dynamics simulation study to investigate this complexation process, including the molecular composition of the various complex species, the corresponding structure, and the equilibrium distribution of the complexes. The observed structures of the complexes suggest that in aqueous solution, uranyls are generally hydrated by 5 water molecules in the equatorial plane. When associating with nitrate ions, a water molecule is replaced by a nitrate ion, preserving the five‐fold coordination and planar symmetry. Analysis of the pair correlation function between uranyl and nitrate suggests that nitrates bind to uranyl in aqueous solution mainly in a monodentate mode, although a small portion of bidentates occur. Dynamic association and dissociation between uranyls and nitrates take place in aqueous solution with a substantial amount of fluctuation in the number of various uranyl nitrate species. The average number of the uranyl mono‐nitrate complexes shows a dependence on acid concentration consistent with equilibrium‐constant analysis, namely, the concentration of [UO2NO3]+ increases with nitric acid concentration.

Molecular Dynamics Simulation of Tri-n-butyl-Phosphate Liquid: A Force Field Comparative Study

Molecular dynamics (MD) simulations were conducted to compare the performance of four force fields in predicting thermophysical properties of tri-n-butyl-phosphate (TBP) in the liquid phase. The intramolecular force parameters used were from the Assisted Model Building with Energy Refinement (AMBER) force field model. The van der Waals parameters were based on either the AMBER or the Optimized Potential for Liquid Simulation (OPLS) force fields. The atomic partial charges were either assigned by performing quantum chemistry calculations or utilized previously published data, and were scaled to approximate the average experimental value of the electric dipole moment. Canonical ensemble computations based on the aforementioned parameters were performed near atmospheric pressure and temperature to obtain the electric dipole moment, mass density, and self-diffusion coefficient. In addition, the microscopic structure of the liquid was characterized via pair correlation functions between selected atoms. It has been demonstrated that the electric dipole moment can be approximated within 1% of the average experimental value by virtue of scaled atomic partial charges. The liquid mass density can be predicted within 0.5-1% of its experimentally determined value when using the corresponding charge scaling. However, in all cases, the predicted self-diffusion coefficient is significantly smaller than a commonly quoted experimental measurement; this result is qualified by the fact that the uncertainty of the experimental value was not available.

Uranyl nitrate complex extraction into TBP/dodecane organic solutions: a molecular dynamics study

Liquid-liquid extraction of uranyl is studied by conducting atomistic molecular dynamics simulation using quantum chemistry calibrated force fields via restrained electrostatic potential fitting of atomic forces. The simulations depict the migration of uranyl nitrate complexes from the aqueous-organic interface into the tri-n-butyl phosphate (TBP)/dodecane organic phase, in the form of UO(2)(NO(3))(2)·H(2)O·2TBP and UO(2)(NO(3))(2)·3TBP. The migration process is characterized by the gradual breaking of all the hydrogen bonds between the complex and the water molecules at the interface. Moreover, our simulation results suggest that the experimentally observed complex UO(2)(NO(3))(2)·2TBP is formed after the migration of the aforementioned complexes into the organic phase by means of a reorganization of the nitrate binding mode from mono to bidentate which removes the excess oxygen atoms bound to uranyl.

Interfacial complex formation in uranyl extraction by tributyl phosphate in dodecane diluent: a molecular dynamics study.

Atomistic simulations have been carried out in a multicomponent two-phase system (aqueous and organic phases in direct contact) to investigate the interfacial molecular mechanisms leading to uranyl extraction from the aqueous to organic phase. The aqueous phase consists of the dissolved ions UO2(2+) and nitrate NO3-, with or without H3O+, in water to describe acidic or neutral condition; the organic phase consists of tributyl phosphate, the extractant, in dodecane as the diluent. We find that the interface facilitates the formation of various uranyl complexes, with a general formula UO2(2+)(NO3-)n *mTBP*kH2O, with n+m+k=5, suggesting a 5-fold coordination. The coordination for all three molecular entities has the common feature that they all bind to the uranyl at the uranium atom with an oxygen atom in the equatorial plane perpendicular to the molecular axis of the uranyl, forming a 5-fold symmetry plane. Nitric acid has a strong effect in enhancing the formation of extractable species, which is consistent with experimental findings.

Domain Deformation Mapping: Application to Variational Mesh Generation

The purposes of this article are, first, to expose the mathematical similarities between variational mesh generation and hyperelasticity theory and, second, to show how elements and tools of hyperelasticity theory can be employed for analysis and practical construction of domain deformation mappings utilized in variational mesh generation.

Molecular dynamics simulations of tri-n-butyl-phosphate/n-dodecane mixture: thermophysical properties and molecular structure.

Molecular dynamics simulations of tri-n-butyl-phosphate (TBP)/n-dodecane mixture in the liquid phase have been carried out using two recently developed TBP force field models (J. Phys. Chem. B 2012, 116, 305) in combination with the all-atom optimized potentials for liquid simulations (OPLS-AA) force field model for n-dodecane. Specifically, the electric dipole moment of TBP, mass density of the mixture, and the excess volume of mixing were computed with TBP mole fraction ranging from 0 to 1. It is found that the aforementioned force field models accurately predict the mass density of the mixture in the entire mole fraction range. Commensurate with experimental measurements, the electric dipole moment of the TBP was found to slightly increase with the mole fraction of TBP in the mixture. Also, in accord with experimental data, the excess volume of mixing is positive in the entire mole fraction range, peaking at TBP mole fraction range 0.3-0.5. Finally, a close examination of the spatial pair correlation functions between TBP molecules, and between TBP and n-dodecane molecules, revealed formation of TBP dimers through self-association at close distance, a phenomenon with ample experimental evidence.

Molecular simulation of water extraction into a tri-n-butylphosphate/n-dodecane solution.

Molecular dynamics simulations were performed to investigate water extraction into a solution of 30 vol % tri-n-butylphosphate (TBP) in n-dodecane. Our computational results indicate that the TBP electric dipole moment has a significant effect on the predicted water solubility. A larger TBP dipole moment decreases the aqueous-organic interfacial tension, leading to increased roughness of the aqueous-organic interface. Interfacial roughness disrupts the interfacial water hydrogen bonding structure, resulting in a presence of dangling water molecules at the interface. The increased interfacial roughness enhances the probability of water molecules breaking away from the aqueous phase and migrating into the organic bulk phase. By varying the atomic partial charges of the TBP molecules to reproduce a dipole moment close to the experimentally measured value, we were able to predict water solubility in close agreement with experimental measurements. In addition, our simulation results reveal the detailed molecular mechanism of the water extraction process, and the various structural forms of water molecules both at the interface and in the bulk organic phase.

Construction of Solution Curves for Large Two-Dimensional Problems of Steady-State Flows of Incompressible Fluids

This work represents a step toward advancing classical methods of bifurcation analysis in conjunction with very large-scale scientific computing needed to model realistically processes which involve laminar and steady flows of incompressible fluids. A robust method of analysis based on pseudoarclength continuation, Newtons method, and direct solution of linear systems is proposed and applied to the analysis of a representative system of fluid mechanics, namely the tilted lid driven cavity. Accurate solution curves, possessing simple singular points, were computed for Reynolds numbers varying from 0 to 10,000 and for different angles of tilt. The results demonstrate that two-dimensional models with up to 1,000,000 algebraic equations can be studied feasibly using the methods described here with state-of-the-art vector supercomputers.

On Equilibration and Sparse Factorization of Matrices Arising in Finite Element Solutions of Partial Differential Equations

Investigations of scaling and equilibration of general matrices have been traditionally aimed at the effects on the stability and accuracy of LU factorizations—the so-called scaling problem. Notably, Skeel (1979) concludes that no systematic scaling procedure can be concocted for general matrices exempt from the danger of disastrous effects. Other researchers suggest that scaling procedures are not beneficial and should be abandoned altogether. Stability and accuracy issues notwithstanding, we show that this unglamorous technique has a profound impact on the sparsity of the resulting LU factors. In the modern era of fast computing, equilibration can play a key role in constructing incomplete sparse factorizations to solve a problem unstably, but quickly and iteratively. This article presents practical evidence, on the basis of sparsity, that scaling is an indispensable companion for sparse factorization algorithms when applied to realistic problems of industrial interest. In light of our findings, we conclude that equilibration with the ∞-norm is superior than equilibration with the 2-norm.