Instrument constant

Wagner and DUlont have described a low-shear viscometer in which the inside diameter of the outer, stationary cylinder is 30 mm and the outside diameter of the inner, rotating cylinder is 28 mm the rotor is driven by an electromagnet. The device operates at 135°C and was found to be free of wobble and turbulence for shear rates between 3 and 8 sec V The conversion of Eq. (2.7) to Eq. (2.9) shows that F/A = (i7)(dv/dr) (instrument constant) for these instruments Evaluate the instrument constant for this viscometer. 

Direct Indicating Viscometer. This is a rotational type instrument powered by an electric motor or by a hand crank. Mud is contained in the annular space between two cylinders. The outer cylinder or rotor sleeve is driven at a constant rotational velocity its rotation in the mud produces a torque on the inner cylinder or bob. A torsion spring restrains the movement. A dial attached to the bob indicates its displacement. Instrument constants have been so adjusted that plastic viscosity, apparent viscosity, and yield point are obtained by using readings from rotor sleeve speeds of 300 and 600 rpm. 

The quantity k3 may be considered as an instrumental constant to be determined in a blank experiment—that is, without added solute. In this case, the current is given by I(t)/I(0) = (1 - vt/d) exp( - k3 t), from which k can be determined. With the solute added, the current initially decays exponentially (fast decay) from which is determined h + k2 + k3, while the ratio of the initial plateau to the initial current gives k2/(k] + k2 + k ). The detachment rate k2 is now obtained from the last two numbers, and then the attachment rate fe, is also obtained since k3 is already predetermined. In short, both attachment (kj and detachment (k2) rates are obtainable from the time dependence of the cell current following a brief pulse of ionizing radiation. 

The instrument constant B can be determined by measuring the t in two fluids of known density. Air and water are used by most workers (22). In our laboratory we used seawater of known conductivity and pure water to calibrate our vibrating flow systems (53). The system gives accurate densities in dilute solutions, however, care must be taken when using the system in concentrated solutions or in solutions with large viscosities. The development of commercial flow densimeters has caused a rapid increase in the output of density measurements of solutions. Desnoyers, Jolicoeur and coworkers (54-69) have used this system to measure the densities of numerous electrolyte solutions. We have used the system to study the densities of electrolyte mixtures and natural waters (53,70-81). We routinely take our system to sea on oceanographic cruises (79) and find the system to perform very well on a rocking ship. 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

A constant is often determined from measurements with a Newtonian oil, particulady when the calibrations are supplied by the manufacturer. This constant is valid only for Newtonian specimens if used with non-Newtonian fluids, it gives a viscosity based on an inaccurate shear rate. However, for relative measurements this value can be useful. Employment of an instrument constant can save a great deal of time and effort and increase accuracy because end and edge effects, slippage, turbulent interferences, etc, are included. 

The relationship between viscosity, angular velocity, and torque for a Newtonian fluid in a concentric cylinder viscometer is given by the Maigules equation (eq. 26) (21,146), where M is the torque on the inner cylinder, h the length of the inner cylinder, Q the relative angular velocity of the cylinder in radians per second, R the radius of the inner cylinder wall, Rr the radius of the outer cylinder wall, and k an instrument constant. 

Other Rotational Viscometers. Some rotational viscometers employ a disk as the inner member or bob, eg, the Brookfield and Mooney viscometers others use paddles (a geometry of the Stormer). These nonstandard geometries are difficult to analyze, particularly for an infinite bath, as is usually employed with the Brookfield and the Stormer. The Brookfield disk has been analyzed for Newtonian and non-Newtonian fluids and shear rate corrections have been developed (22). Other nonstandard geometries are best handled by determining instrument constants by calibration with standard fluids. 

The speed at which a sphere rolls down a cylindrical tube filled with a fluid or down an angled plate covered with a film of the fluid also gives a measure of viscosity. For the cylindrical tube geometry, equation 35, a generalized form of the Stokes equation is used for any given instrument, where v is the translational velocity of the rolling sphere and k is the instrument constant determined by calibration with standard fluids. 

Assume that the enzyme is roughly spherical and that the instrument constant in the Siegert relation is unity and determine the hydrodynamic radius RH of the enzyme. Given that the partial molar volume V of the enzyme is 0.74 10 3 m3/kg and the molecular weight M is 4.78 102 kg/mol, determine the dry radius Rs for the enzyme and obtain the ratio RH/RS). Can the difference between RH and Rs be attributed to the bound water on the enzyme The viscosity ij of water at 293K may be taken as 0.001 kg/m s. 

The magnitude of the intercept implies that the instrumental constant is roughly 0.95.)... 

Experimental. Viscosities. The absolute viscosities in centipoises (cp.) for several amide-water systems at 25 °C. were obtained using calibrated Ubbelohde viscometers and calculated from -q = p[Kt — L/t where p is density of mixture, and K and L are instrument constants. The results, plotted against the mole fraction of water, are shown in Figures 1 and 8. 

Under these conditions of complete saturation the fluorescence signal becomes independent of laser power and the species number density N-T can be theoretically evaluated with only the knowledge1of the spectroscopic and instrumental constants. 

In these equations, B is an instrumental constant <)> is the probability that an absorbed photon leads to fluorescence and A (X) and A (X) are, respectively, the absorbance of the fluorophore only, and the total absorbance under left circularly polarized excitation at wavelength X. Note that we have assumed that < > is independent of excitation polarization and wavelength. The form of eqs. (26) and (27) display one of the problems in simple interpretation of FDCD results in terms of ordinary CD spectroscopy. On the front surface of the sample cell the intensity of the alternating circular polarizations will be equal, but if Ar does not equal A then the intensities will change due to differential absorption. Just as in CPL measurements, one is concerned in this case with measurement of the differential signal and the total fluorescence intensity, F(X)... 

Re F stands for the real part of the function F. The function fcs(r) models a slowly varying background, which is usually present in all of the measurements. The constant background term B is measured by the autocorrelator using special time bins with extra delay. / () is the intensity of the local oscillator (may represent scattering due to the interface itself) the term 2/S0// 0 indicates the relative amount of particle-scattered light and reference scattered photons and should not exceed 0.1 for heterodyne detection. The quantity / is an instrumental constant, a value around 0.5 indicating a reasonably optimized system for homodyne detection. 

Some of the factors in the foregoing equation are instrument constants and are determined independently of the actual light scattering measurement. These include no (refractive index of pure solvent at the experimental temperature and wavelength) L (Avogadro s constant) X, which is set by the experimenter and r, an instrument constant. 

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