Theoretical treatment of the spectrophotometric titration of bivalent cations with complexon-iii and metal-specific indicators

It was derived theoretically that a sharp end-point of this spectrophotometrical titration is defined, in order of importance, by: 1. *K_C ? *K_I (numerically speaking, log$\text{*K}{}_{\mathrm{C}}\text{*K}{}_{\mathrm{I}}$ should be at least 4); 2. *K_I being large (numerically e.g. 10⁴-10⁵); this is already reached by choosing a high pH; 3. it being low; 4. m_t being as high as possible.     

A three-parameter model describing the experimental relation between shear stress and shear rate for laminar flow of aqueous polymer solutions

Summary A three-parameter model is introduced to describe the shear rate — shear stress relation for dilute aqueous solutions of polyacrylamide (Separan AP-30) or polyethylenoxide (Polyox WSR-301) in the concentration range 50 wppm – 10,000 wppm. Solutions of both polymers show for a similar rheological behaviour. This behaviour can be described by an equation having three parameters i.e. zero-shear viscosity ₀, infinite-shear viscosity , and yield stress ₀, each depending on the polymer concentration. A good agreement is found between the values calculated with this three-parameter model and the experimental results obtained with a cone-and-plate rheogoniometer and those determined with a capillary-tube rheometer.

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Zusammenfassung Der Zusammenhang zwischen Schubspannung und Schergeschwindigkeit von strukturviskosen Flüssigkeiten wird durch ein Modell mit drei Parametern beschrieben. Mit verdünnten wäßrigen Polyacrylamid-(Separan AP-30) sowie Polyäthylenoxidlösungen (Polyox WSR-301) wird das Modell experimentell geprüft. Beide Polymerlösungen zeigen im untersuchten Schergeschwindigkeitsbereich von ein ähnliches rheologisches Verhalten. Dieses Verhalten kann mit drei konzentrationsabhängigen Größen, nämlich einer Null-Viskosität ₀, einer Grenz-Viskosität und einer Fließgrenze ₀ beschrieben werden. Die Ergebnisse von Experimenten mit einem Kegel-Platte-Rheogoniometer sowie einem Kapillarviskosimeter sind in guter Übereinstimmung mit den Werten, die mit dem Drei-Parameter-Modell berechnet worden sind.

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a Pa^–1 physical quantity defined by:a = {1 – ( / ₀)}/ ₀ - c l concentration (wppm) - D m capillary diameter - L m length of capillary tube - P Pa pressure drop - R m radius of capillary tube - u m s^–1 average velocity - v _r m s^–1 local axial velocity at a distancer from the axis of the tube - shear rate (–dv _r /dr) - local shear rate in capillary flow - s^–1 wall shear rate in capillary flow - Pa s dynamic viscosity - _a Pa s apparent viscosity defined by eq. [2] - ( _a ) Pa s apparent viscosity in capillary tube at a distanceR from the axis - ₀ Pa s zero-shear viscosity defined by eq. [4] - Pa s infinite-shear viscosity defined by eq. [5] - l ratior/R - kg m^– density - Pa shear stress - ₀ Pa yield stress - _r Pa local shear stress in capillary flow - _R Pa wall shear stress in capillary flow _R = (PR/2L) - _v m³ s^–1 volume rate of flow With 8 figures and 1 table     

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ε_L and the pressure gradient ΔP_TP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ε_L < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ε_L and ΔP_TPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ε_L < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ε_L < 0.06. Further, it has been shown that in the domain 38 < < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.     

On the theory of structural modulation of Na2CO3

A theory is proposed for the explanation of the structural modulation of the ground state of Na₂CO₃. The modulation phase is seen as a generalisation of the concept of (anti) ferroelectric and ferroelastic phases out of the centre of the Brillouinzone. The instability of the structure is caused by the dipolar interactions, and is driven by the linear polarizability. It is shown that the nonlinearity in the polarizability alone, via the harmonic forces, stabilizes the system, and the Landau-free energy of the well-known form is derived.     

Method for determination of the equivalence point in potentiometric titrations

A method is developed for calculating the end-point and the ionization constant in a potentiometric titration. The influence of dilution is studied. The method is compared with the procedure of KOLTHOFF and that of HAHN.     

Expected demand for service parts when failure times have a Weibull distribution

The expected demand for service parts is easy to calculate, as long as their failure rate is constant. Certain service parts, however, have a failure rate that is time-dependent. If their failure times have a Weibull distribution, the simple calculation methods brake down and much computational effort is required to determine the expected demand exactly. This paper presents a simple approximation of the expected demand that compares well with exact answers.     

Elasticity and its limits: Yielding and melting in (modulated) ionic crystals

A microscopic foundation of the theory of static isothermal homogeneous deformation is given for classical (ionic) crystals which may have atomic electric dipoles and which may be in a structurally modulated (slightly distorted) phase. Special effects due to the dipoles and the modulations are mentioned and a comparison is made with the dynamic elasticity as measured via acoustic waves. An attempt is made to predict the limits of the elastic regime i.e. yielding under stresses and melting under heating.     

Viscous heating and heat transfer in cone-and-plate rheogoniometry

Summary At higher shear rates the relation between shear stress and shear rate appears to deviate from the for Newtonian fluids expected linear behaviour. In cone-and-plate rheogoniometry one of the most important causes of that is the effect of viscous heating. Accurate measurements carried out with a 10 cm diameter cone and plate lead to a semi-logarithmic, linear relationship between temperature increase and time for a Newtonian oil which dynamic viscosity varies approximately linearly with time. A simple model based on a heat balance describes this behaviour quantitatively.

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Zusammenfassung Bei newtonschen Flüssigkeiten weisen die Experimente eine Abweichung vom linearen Zusammenhang zwischen Schubspannung und Schergeschwindigkeit auf. Im Kegel-Platte-Meßsystem ist die Wärmeproduktion durch innere Reibung die wichtigste Ursache der Abweichung. Bei newtonschen Flüssigkeiten, deren dynamische Viskosität sich ungefähr linear mit der Temperatur verändert, ergeben sorgfältig ausgeführte Messungen mit einem Kegel von 10 cm Durchmesser einen linearen Zusammenhang zwischen der Zeit und dem Logarithmus der Temperaturzunahme. Ein aus der Wärmebilanz abgeleitetes Modell vermag dieses Verhalten quantitativ zu beschreiben.

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Symbols A platen surface (m²) - B viscosity constant from eq. [1] (Pa s K^–1) - S _B standard deviation ofB (Pa s K^–1) - S _t0 standard deviation oft ₀ (s) - S _t0 standard deviation oft ₀ (s) - S ₀ standard deviation of ₀ (Pa s) - t time (s) - t ₀ time def. by eq. [5] (s) - t ₀ time def. by eq. [11] (s) - T temperature (°C) - T ₀ temperature of the surrounding air (°C) - T highest experimental temperature (°C) - V volume of the fluid between the platen (m³) - W heat capacity of the system (J K^–1) - heat transfer coefficient (W m^–2 K^–1) - shear rate (s^–1) - dynamic viscosity (Pa s) - ₀ dynamic viscosity atT ₀ (Pa s) - dimensionless temperature def. by eq. [4a] (–) - dimensionless time def. by eq. [4b] (–) - dimensionless time def. by eq. [10] (–) With 4 figures and 2 tables