Y. Leong Yeow

A new method of processing the time-concentration data of reaction kinetics

Experimental data of reaction kinetics are usually in the form of concentration versus time. For kinetics investigation it is more convenient to have the data in the form of reaction rate versus concentration. Converting time-concentration data into concentration-reaction rate data is an ill-posed problem in the sense that if inappropriate methods are used the noise in the original data will be amplified leading to unreliable results. This paper describes a conversion procedure, independent of reaction rate model or mechanism, that manages to keep noise amplification under control. The performance of this procedure is demonstrated by applying it to several sets of published kinetic data. Since these data are accompanied by their rate equations, the computed rates are used to obtain the unknown parameters in these equations. Comparison of these parameters with published figures and the ease with which they are obtained highlights the advantages of the new procedure.

Model‐Independent Relationships between Hematocrit, Blood Viscosity, and Yield Stress Derived from Couette Viscometry Data

This paper describes a procedure, based on Tikhonov regularization, for obtaining the shear rate function or equivalently the viscosity function of blood from Couette viscometry data. For data sets that include points where the sample in the annulus is partially sheared the yield stress of blood will also be obtained. For data sets that do not contain partially sheared points, provided the shear stress is sufficiently low, a different method of estimating the yield stress is proposed. Both the shear rate function and yield stress obtained in this investigation are independent of any rheological model of blood. This procedure is applied to a large set of Couette viscometer data taken from the literature. Results in the form of shear rate and viscosity functions and yield stress are presented for a wide range of hematocrits and are compared against those reported by the originators of the data and against independently measured shear properties of blood.

Evaluating the third and fourth derivatives of spectral data

The problem of differentiating spectral data to yield the third and fourth derivatives is converted into one of solving an integral equation of the first kind. This equation is solved by Tikhonov regularization. The method of General Cross Validation is used to guide the choice of the regularization parameter that keeps noise amplification under control. The performance of this route to third and fourth derivative spectra is demonstrated by applying it to a number of published spectra. A computational problem associated with General Cross Validation has been identified.

A general computational method for converting normal spectra into derivative spectra.

The mathematical problem of converting a normal spectrum into the corresponding first- and second-derivative spectra is formulated as an integral equation of the first kind. Tikhonov regularization is then applied to solve the spectral conversion problem. The end result is a set of linear algebraic equations that takes in as input the original spectrum and produces as output the second-derivative spectrum, which is then integrated to yield the first-derivative spectrum. Noise amplification is kept under control by adjusting the regularization parameter (guided by generalized cross-validation) in the algebraic equations. The performance of this procedure is demonstrated by applying it to different types of spectral data taken from the literature.

Applications of maximum entropy method in capillary viscometry

Maximum entropy method (MEM) is presented as a technique for processing data obtained from capillary viscometers. The performance of MEM is assessed by comparing the viscosity versus shear rate curves generated by MEM against that obtained by the standard method based on the “Weissenberg-Rabinowitsch-Mooney equation”. In all the cases in vestigated, MEM proved to be a reliable technique in coping with the experimental noise in the capillary data.

Slow Steady Viscous Flow of Newtonian Fluids in Parallel-Disk Viscometer With Wall Slip

The parallel-disk viscometer is a widely used instrument for measuring the rheological properties of Newtonian and non-Newtonian fluids. The torque-rotational speed data from the viscometer are converted into viscosity and other rheological properties of the fluid under test. The classical no-slip boundary condition is usually assumed at the disk-fluid interface. This leads to a simple azimuthal flow in the disk gap with the azimuthal velocity linearly varying in the radial and normal directions of the disk surfaces. For some complex fluids, the no-slip boundary condition may not be valid. The present investigation considers the flow field when the fluid under test exhibits wall slip. The equation for slow steady azimuthal flow of Newtonian fluids in parallel-disk viscometer in the presence of wall slip is solved by the method of separation of variables. Both linear and nonlinear slip functions are considered. The solution takes the form of a Bessel series. It shows that, in general, as a result of wall slip the azimuthal velocity no longer linearly varies in the radial direction. However, under conditions pertinent to paralleldisk viscometry, it approximately remains linear in the normal direction. The implications of these observations on the processing of parallel-disk viscometry data are discussed. They indicate that the method of Yoshimura and Prud’homme (1988, “Wall Slip Corrections for Couette and Parallel-Disk Viscometers,” J. Rheol., 32(1), pp. 53‐67) for the determination of the wall slip function remains valid but the simple and popular procedure for converting the measured torque into rim shear stress is likely to incur significant error as a result of the nonlinearity in the radial direction. DOI: 10.1115/1.2910901

Obtaining the Shear Stress versus Shear Rate Relationship and Yield Stress of Blood from Capillary Viscometry Data by Tikhonov Regularization

This paper describes a procedure, based on Tikhonov regularization, for extracting the shear stress versus shear rate relationship and yield stress of blood from capillary viscometry data. The relevant equations and the mathematical nature of the problem are briefly described. The procedure is then applied to three sets of capillary viscometry data of blood taken from the literature. From each data set the procedure computes the complete shear stress versus shear rate relationship and the yield stress. Since the procedure does not rely on any assumed constitutive equation, the computed rheological properties are therefore model‐independent. These properties are compared against one another and against independent measurements. They are found to be in good agreement for shear stress greater than 0.1 Pa but show significant deviations for shear stress below this level. A possible way of improving this situation is discussed.

New Development in Processing Pendant Droplet Tensiometry Data

A database linking the dimensionless volume of pendant droplets Vpen and the dimensionless volume of the spherical caps at the apex of the droplets Vcap has been constructed from the governing equations of pendant droplet tensiometry. The Bond number Bo that relates surface tension to gravitational body force appears as an independent parameter in this database. Computing Vpen and Vcap from the measured profile of a droplet and making use of the database allow the prevailing Bo to be determined and surface tension to be calculated. This new way of converting measured profiles into surface tension has a number of advantages, such as reliability and simplicity, compared to existing methods. These are demonstrated by applying the new method to a number of measured profile data taken from the literature.