Stokes calibration

Stokes calibration involves applying a known viscous drag force to a bead held in the optical tweezer and recording how far it is displaced from the tweezer centre. Application of a triangle wave oscillation of known size and frequency to the specimen chamber with the piezoelectric substage produces a viscous drag force given by Stoke s law 

Brownian movement of the bead held in the optical tweezers serves as a useful probe of the tweezer stiffness. The variance of bead position along one axis, (x), is inversely proportional to the stiffness of the optical tweezers and is directly proportional to absolute temperature. 

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In general, it appears that the Micromerograph, provided that frequent calibration checks are performed, is a good, reproducible instrument for size measurement. The operator time involved is less than with most other methods, and the calcns are not complicated. As in all sedimentation methods, only when the sample particles are spherical does the Stokes diameter that is measured become a measure of absolute particle size. Microscopic examination should be used to check on particle shape and the effect of deagglomeration... 

In the SI system, the theoretical unit of v is m2/s or the commonly used Stoke (St) where 1 St = 0.0001 m2/s = 100 cSt = 100 centiStoke. Similarly, 1 centiStoke = 1 cSt = 0.000001 m2/s = 0.01 Stoke = 0.01 st. The specific gravity of water at 20.2°C (68.4°F) is almost 1. The kinematic viscosity of water at 20.2°C (68.4°F) is for all practical purposes equal to 1 cSt. For a liquid, the kinematic viscosity will decrease with higher temperature. For a gas, the kinematic viscosity will increase with higher temperature. Another commonly used kinematic viscosity unit is Saybolt universal seconds (SUS), which is the efflux time required for 60 mL of petroleum product to flow through the calibrated orifice of a Saybolt universal viscometer, as described by ASTM-D88. Therefore, the relationship between dynamic viscosity and kinematic viscosity can be expressed as... 

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. 

Diffusion coefficients can be related to molecular weight in three ways first by application of the Stokes-Einstein equation, second by combination with sedimentation data, and third by consideration of homologous polymer solutions. In the first method, an equivalent spherical size of the molecules is calculated from Dt, and an approximate molecular weight is found by combining these data with the appropriate density. In the second method, diffusion measurements are coupled with those of sedimentation velocity to give molecular weights, and in the third method, molecular weights may be determined directly from measurements of diffusion coefficients alone once a calibration has been... 

Figure 3. Schematic of turbulent combustor geometry and optical data acquisition system for vibrational Raman-scattering temperature measurements using SAS intensity ratios. Also shown are sketches of the expected Raman contours viewed by each of the photomultiplier detectors, the temperature calibration curve, and several expected pdf s of temperature at different flame radial positions. The actual SAS temperature calibration curve was calculated theoretically to within a constant factor. This constant, which accounted for the optical and electronic system sensitivities, was determined experimentally by means of SAS measurements made on a premixed laminar flame of known temperature. Measurements of Ne concentration were made also with this apparatus, based on the integrated Stokes vibrational Q-branch intensities. These signals were related to gas densities by calibration against ambient air signals.

The accuracy of the temperature pdf data obtained with the Raman Stokes/anti-Stokes technique has been assessed by tests made on a known and well-calibrated laminar premixed flame source, viz., a porous plug burner (20). These data, which were checked by analytical calculations based upon the optical and electronic properties of our detection system, showed a roughly 5-7% standard deviation, which has been considered acceptable for present measurement purposes (2 7). However, additional problem not considered in this type of test, can exist. For example ... 

In order to probe some of these questions - an essential endeavor in forming a clear interpretation of our results - we wish to compare our experimentally-determined data with predictions from a simple model. The experimental data available (See Fig. 3) are instantaneous values of flame temperature from the N2 Stokes/anti-Stokes intensity ratio (plotted as histograms in Fig. 4) and simultaneously-obtained values of Nj density (determined from the absolute value of the N. Stokes intensity calibrated against the value obtained for N2 in ambient air). Accordingly, we have produced "comparison" plots using the following scheme (24) If we calculate flame gas density and temperature as a function of flame stoichiometry (i.e., as a function of the fuel/air equivalence ratio see Fig.7), then we can... 

An Improved disc centrifuge photosedimentometer (DCP) was developed for use in the determination of the particle size and size distribution of latices, pigments and other particulates. Separation is based on Stokes Law for the sedimentation of particles in a centrifugal force field and does not rely on the use of particle size calibrants or standards. The DCP Instrument provides accurate stable particle size analyses over a wide range of conditions while at the same time is rugged enough for heavy use in both a research and quality control environment. A stand-alone data collection, analysis and management system was developed both for routine quality control operation and for research use of the instrument. 

This method may be applied to solid, liquid, or gaseous samples. Considering the fact that the difference in wavenumbers between the Stokes and the anti-Stokes signals is frequently large, the spectral sensitivity of the detector should be taken into account. A calibration curve may be obtained, as proposed by D Orazio and Schrader (1974). A typical example is shown in Fig. 6.8-16 see also Sec. 2.4 and Fig. 2.4-2. 

A comparison of experimental CO2 viscosities obtained over a wide range of temperatures and pressures with that of previously reported viscosites (14) taken over that same range is illustrated in Figure 3. The three different experimental curves shown correspond to a particular calibration fluid, water or CO2, or the constant derived from the Navier-Stokes equation. 

The curve which corresponds to the calibration based on CO2 at 1000 psia was, as expected, the most accurate of the three with an absolute average percent deviation (AAPD) of 3.84. The constant derived from the Navier-Stokes equation was found to be extremely sensitive to the gap size between the aluminum cylinder and tube wall. For example, changing the tube diameter to values within the specified tolerance (- /- 0.0002 inches), changed viscosity calculations by as much as 17.60 percent. 

Kinematic viscosity is measured by timing the flow of a fixed volume of material through a calibrated capillary at a selected temperature (ASTM D-445, IP 71). The unit of kinematic viscosity is the stokes, and kinematic viscosities of waxes are usually reported in centistokes. Saybolt Universal seconds can be derived from centistokes (ASTM D-2161) ... 

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