Calculation of isentropic compressibility and sound velocity in two-phase fluids

Derivative properties from equations of state (EoS) are well defined for homogeneous fluid systems. However, some of these properties, such as isothermal and isentropic (or adiabatic) compressibilities and sound velocity need to be calculated at conditions for which a homogeneous fluid splits into two (or more) phases, liquid or vapor. The isentropic compressibility and sound velocity of thermodynamically equilibrated fluids exhibit important discontinuities at phase boundaries, as noticed long ago by Landau and Lifschitz in the case of pure fluids. In this work, the two-phase isentropic compressibility (or inverse bulk modulus) is expressed in terms of the two-phase isothermal compressibility, two-phase thermal expansivity and an apparent heat capacity, defined as the partial derivative of total enthalpy with respect to temperature at constant pressure and composition. The proposed method is simple (simpler than previous approaches), easy to implement and versatile; it is not EoS-dependent and it requires only a flash routine and the expression of total enthalpy at given pressure, temperature and composition. Our approach is applied to a variety of fluid systems representative of reservoir applications and geophysical situations, including petroleum fluids (oil and gas condensate) and mixtures of water and gas (methane or CO₂). For low gas content in the two-phase fluid, i.e., near bubble point conditions, we obtain significantly lower bulk moduli and sound velocities than predicted within Wood's conventional approach, in which the liquid and gas phases are considered to be “frozen” at the passage of the acoustic wave.     

一种多光谱高温计无源温区的标定方法研究

目前,高温测量中,多光谱高温计具有高分辨率与高信噪比的优点,但无源温区(大于3 000℃)标定方法的发展却远滞后于多光谱高温计制造水平,并已严重影响高温计的测量精度和应用范围。为突破高温测量领域中无源温区标定方法的瓶颈,文章提出了一种多光谱高温计无源温区的标定方法。此方法利用已知温度点的多光谱高温计的输出电压U建立了一种基于幂函数的温度-电压(T-U)模型。在此基础上应用导数最小二乘法对模型参数求解,实现对无源温区的标定。理论和实测数据都验证了此方法的有效性与精度。在多光谱高温测量应用的光谱范围(0.4～1.1μm)内,对精度优于3‰,1%和3%的无源温区标定范围做出理论上的划分。     

Determination of Ternary Mixtures of Vitamins by Ratio-Spectra Zero-Crossing Derivative Spectrophotometry

Abstract

The ratio-spectra zero-crossing first and third derivative spectrophotometry have been used for determining ternary mixtures of Vitamin 86, Vitamin B1 and Vitamin B12. The procedures are accurate, nondestructive and do not require solving of equations.

In both methods, calibration graphs are linear, with zero-intercept, up to 48 μg/ml of Vitamin B6, 64 μg/ml of Vitamin B1 and 60 μg/ml of Vitamin B12. Correlation coefficients range from 0.9999 to 1.0000.

Working wavelengths, 311, 272.5 and 215.5 nm, respectively, in the 1st-derivative mode and 300.5, 271.5 and 365 nm in the 3rd-derivative mode. Detection limits for each drug at p=0.01 level of significance were calculated to be 0.002, 0.009 and 0.004 μg/ml and 0.002, 0.004 and 0.001 μg/ml, in the first and third-derivative methods, respectively. Both methods apply favourably to either synthetic mixtures or commercial injections for these drugs.

An exhaustive statistical treatment of the experimental findings was performed to confirm the validity of the methods.     

Simultaneous Determination of Two Synthetic Dyes Erytrosine and Sunset Yellow in a Pharmaceutical Syrup By First Derivative Visible Spectrophotometry

ABSTRACT.

A rapid first derivative spectrophotometric method for simultaneous determination of two synthetic dyes, erytrosine (E 127) and sunset yellow (E 110), in a mixture is proposed. The procedure does not require any separation step. The method was applied for determining the two compounds in a pharmaceutical syrup. Good linearity, accuracy, precision and selectivity were found, and the method is proposed for routine quality control purposes.     

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

The derivative nonlinear Schrödinger (DNLS) equation, which governs the propagation of the femtosecond optical pulse in a monomodal optical fiber, is analytically studied in this Letter. Breather and double-pole solutions are derived from the two-soliton solution with the choice of parameters. It is found that the parameters in the DNLS equation cannot only control the phase and propagation direction of the breather and double pole, but also influence the interaction period of the breather. Elastic collisions between a breather and a dark/anti-dark soliton are studied by the qualitative analysis and graphical illustration. The stability of the breather and double-pole solutions is also analyzed.     

A New Efficient Transform Mechanism with Convergence Analysis of the Space-Fractional Telegraph Equations

This article"s goal is to investigate the space-fractional telegraph equation using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). Using the Banach fixed point theorem, we explore proofs for the existence and uniqueness theorems applying it to a nonlinear differential equation. Using our method, exact solutions of the space-fractional telegraph equation and time-fractional diffusion problems have been obtained. To demonstrate the effectiveness of the suggested scheme, four examples are provided.