scholarly journals Increasing the Prediction Efficiency of Hansen Solubility Parameters in Supercritical Fluids

2019 ◽  
Vol 63 (2) ◽  
pp. 286-293
Author(s):  
Csaba Dezső András ◽  
László Mátyás ◽  
Botond Ráduly ◽  
Rozália Veronika Salamon
Keyword(s):  
Coordinate System ◽  
Physical Meaning ◽  
Three Dimensional ◽  
Predictive Ability ◽  
Solubility Parameters ◽  
Solvent Mixtures ◽  
Cohesion Energy ◽  
Hansen Solubility Parameters ◽  
Cartesian Coordinate ◽  
Hansen Parameters

This work describes a simplified method developed for calculating the Hansen parameters (HSPs) for scCO2-polar modifier solvent mixtures. The method consists in fitting 2nd order equations on the calculated values of HSPs of pure components in function of pressure and temperature. It has been proved that these equations are suitable for the characterization of the above system. The current work also proposes a modified representation method, which eliminates the shortcomings of the original ternary Teas diagram, normally used for the representation of the Hansen parameters. On the one hand, the Teas diagram uses quantities without any physical meaning and, on the other hand, the illustration of the solubility information is distorted because it does not take into account the differences of the Hildebrand parameters of different solvents. The factors we have chosen to represent on the ternary diagram possess physical meaning (cohesion energy density partitions). The distortion was eliminated by extending the Teas diagram to a prismatic three dimensional representation. We proved that the Hansen-ellipsoid from the Cartesian coordinate system (dd = f (δH, dp)) is transformed in an ellipsoid also in the new coordinate system (the transformation is pseudo-isomorphic). Nonetheless, the suggested corrections improve the accuracy of the Hansen method, in some cases the interactions between the solvents and the dissolved materials are still not predicted with sufficient accuracy. Most probably a thermodynamic-based correction of the values of the HSPs of small molecules could lead to a significant improvement of the predictive ability of the newly developed method.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

scholarly journals Using of Parallel Coordinates in Finding Minimum Distance in Time-Space

2019 ◽  
Vol 21 (3) ◽  
pp. 3-7
Author(s):  
Olga Blazekova ◽  
Maria Vojtekova
Keyword(s):  
Coordinate System ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Fourth Dimension ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Parallel Coordinates ◽  
Time Space ◽  
Cartesian Coordinate

Airspace domain may be represented by a time-space consisting of a three-dimensional Cartesian coordinate system and time as the fourth dimension. A coordinate system provides a scheme for locating points given its coordinates and vice versa. The choice of coordinate system is important, as it transforms data to geometric representation. Visualization of the three and more dimensional data on the two-dimensional drawing - computer monitor is usually done by projection, which often can restrict the amount of information presented at a time. Using the parallel coordinate system is one of possibilities to present multidimensional data. The aim of this article is to describe basics of parallel coordinate system and to investigate lines and their characteristics in time-space.

Sorption properties of hydrothermally modified wood and data evaluation based on the concept of Hansen solubility parameter (HSP)

Holzforschung ◽  
2013 ◽  
Vol 67 (5) ◽  
pp. 595-600 ◽  
Author(s):  
Jelena Chirkova ◽  
Ingeborga Andersone ◽  
Juris Grinins ◽  
Bruno Andersons
Keyword(s):  
Hydrogen Bonding ◽  
Sorption Isotherms ◽  
Solubility Parameters ◽  
Dispersion Force ◽  
Sorption Behavior ◽  
Cohesion Energy ◽  
Vapor Sorption ◽  
Hansen Solubility Parameters ◽  
Hansen Solubility ◽  
Modified Wood

Abstract The effect of the hydrothermal modification (HTM) of the deciduous woods birch and aspen on their sorption behavior has been investigated by the vapor sorption method. An analysis of the experimental results was carried out based on the concept of Hansen solubility parameters (HSP), which takes into account the contribution of different forces – dispersion forces, dipole action, and hydrogen bonding – to the total cohesion energy. Sorption isotherms were measured concerning the vapors of water, methanol, and ethanol with unmodified and HTM woods at 160°C and 170°C during 3 and 1 h, respectively. The choice of sorbates was based on the parts of the hydrogen bonding and dispersion force to cohesion energy, in decreasing order of the former and increasing order of the latter. As a criterion of sorption, the value of the monolayer capacity was used, which was derived from the Brunauer-Emmett-Teller equation. Vapor sorption with unmodified and modified wood increased with increasing dispersion force component of the HSP of the sorbate. However, more substantial increase occurred for HTM wood, that is, wood surface became more hydrophobic. The reason for this observation is the change in the decreasing ratio holocellulose/lignin upon HTM. However, the chemical structure of lignin is also changed by HTM.

scholarly journals Viscous Analysis of Three-Dimensional Turbomachinery Flows on Body Conforming Grids Using an Implicit Solver

1991 ◽  
Author(s):  
K. F. Weber ◽  
R. A. Delaney
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Implicit Solver ◽  
Cartesian Coordinate ◽  
Solution Accuracy

A 3-D Navier-Stokes analysis for turbomachinery flows on C- or O-type grids is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Navier-Stokes equations and is derived from an early version of the ARC3D flow code developed at NASA Ames Research Center. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the z-axis, and then mapped to a general body-fitted coordinate system. All viscous terms are calculated and the turbulence effects are modelled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked body-conforming grids. Modifications made to convert ARC3D from external flow to internal turbomachinery flows and to improve solution accuracy are given in detail. The body-conforming grid construction procedure is also presented. Calculations for several rotor flows have been made, and results of code experimental verification studies are presented. Comparisons of the solutions obtained on the C- and O-type grids are also presented, with particular attention to shock resolution.

Advancing Diffusion Model for Diffusion in a Cube of Medium

2012 ◽  
Vol 28 (2) ◽  
pp. 345-354 ◽  
Author(s):  
C.-C. Lin ◽  
C.-L. Tsai ◽  
P.-K. Wu ◽  
H.-J. Lee
Keyword(s):  
Exact Solution ◽  
Coordinate System ◽  
Diffusion Model ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Cartesian Coordinate System ◽  
Cartesian Coordinate ◽  
First Time

AbstractA solution based on an advancing model for the content of diffusion material in a cube of medium is derived. The cube is assumed to be surrounded by diffusion material, and the diffusion material penetrates through all six surfaces and diffuses toward the center of the cube. The model accounts for the interaction between the diffusions in the three principle coordinates of the Cartesian coordinate system. For the first time, an exact solution of the content of the diffusion material based on the advancing model is derived in a clean form for a three-dimensional case.

scholarly journals The system of acquisition and archiving of motion parameters of mobile systems - an overview of measuring sensors

2019 ◽  
Vol 20 (1-2) ◽  
pp. 234-240
Author(s):  
Jakub Grabiński ◽  
Konrad Waluś
Keyword(s):  
Coordinate System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mobile Systems ◽  
Measuring System ◽  
Starting Point ◽  
Macro Scale ◽  
Mems Technology ◽  
Motion Parameters ◽  
Cartesian Coordinate

As part of the work, a measuring system is presented that allows collecting and recording vehicle motion parameters. To build the system, an inertial navigation module was used, consisting of two-axis accelerometers and gyroscopes made in MEMS technology. The tests were carried out and calculation methods were developed to allow the collected data to be referenced, to a point in the three-dimensional space, in order to determine the trajectory of the vehicle's movement. The built-in measuring system uses three types of sensors: accelerometer, gyroscope, magnetometer. Each of these sensors allows the measurement of the physical size in three orthogonal axes of the Cartesian coordinate system. In addition, the work uses a satellite navigation module (GPS), as a reference on the "macro" scale (coordinate system related to the center of the globe with a radius of about 6371 km) for the inertial updating module (INS / IMU), enabling accurate measurement in the "micro" scale (the coordinate system associated with the starting point of the traffic for the route, the length of which does not exceed several hundred meters). The article presents an overview of available measuring sensors with special consideration of the parameters of selected sensors and errors introduced into the measurement system.

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