Thomas Gillespie

An extension of Goodeve's impulse theory of viscosity to pseudoplastic systems

Abstract An attempt has been made to derive a theory of pseudoplasticity which may be used as a guide in combined studies of rheology and flocculation kinetics. Goodeves impulse theory of viscosity was used as a starting point. The shear stress-shear rate relation obtained is a more general form of the well-known Williamson empirical equation for pseudoplasticity. The behavior of a given system may be traced in terms of link formation and link rupture rate constants which are related to flocculation and deflocculation rate constants which are susceptible to experimental investigation. Some preliminary data obtained with thickened pseudoplastic latex systems are used to illustrate the application of the theory.

The effect of capillary liquid on the force of adhesion between spherical solid particles

Abstract The force of adhesion between two identical wetted spheres has been calculated from the equations of Radushkevich and Melrose for the capillary pressure. The iterative procedure which was used was facilitated by a new approximate closed expression for the capillary pressure. Calculated data are presented relating the force of adhesion to the amount of liquid, the particle radii, the surface tension, and the contact angle. Experimental data obtained with glass spheres held together by water or mineral oil were found to be in agreement with the results predicted by capillary theory.

The effect of aggregation and particle size distribution on the viscosity of newtonian suspensions

Abstract It is shown that the effective solids volume fraction, φeff, of a suspension is given by the equation φeff = αφ + κα2φ2 when the particle volume fraction is φ. The parameter α is a function of the number of particles in aggregates, aggregate shape, and the packing factor of the particles in aggregates. The parameter k is equal to 0.9 for a suspension of unidisperse and unisize solid particles but increases with an increase in the axial ratio of aggregates and decreases if the flow units in a suspension are of different sizes. The relative viscosity of a suspension is given by ƞ r = 1 + φ eff/2 (1 - φ eff ) 2 which is a simple extension of the equation which results from Einsteins famous analysis after making the correction indicated by Einstein in a subsequent published note.

The capillary rise of a liquid in a vertical strip of filter paper

Abstract A theory previously developed by the author to describe the horizontal spreading of liquids in paper has been applied to the case of a liquid rising by capillary action in a vertical strip of filter paper. The phenomenon is complicated by a surface roughness effect which had to be taken into account. The theory leads to simple expressions for the rate of rise and the distribution of liquid which are in agreement with experiment. When gravity can be neglected, the height of rise is proportional to the square root of the time. When gravity is important, the height of rise is a more complex function of time than the simple square root dependence. In addition, the liquid approaches a limiting height.

The effect of aggregation and liquid penetration on the viscosity of dilute suspensions of spherical particles

Abstract Using Brinkmans method of extending Einsteins relation for the viscosity of very dilute suspensions an equation has been derived which takes into account permanent aggregates and liquid penetration effects. Experiments with uniform particle size latex indicated that appropriate ultrasonic irradiation decreases the viscosity, and this is reflected in a change in the degree of aggregation as measured with a highpower optical microscope. An analysis of literature data indicated that permanent aggregates are present in most if not all experiments and they interfere with the detection of any possible particle size or size distribution effects in dilute suspensions.

The limited flocculation of colloidal systems

Abstract The flocculation of a styrene-butadiene latex by methylcellulose has been examined in detail by direct measurement of the particle concentration as a function of time. The apparent particle concentration decreased in all cases to a steady value corresponding to limited or partial flocculation. The present data and similar literature data on the flocculation of gold sols by salt are in agreement with an equation due to Goodeve which assumes a competition between flocculation and deflocculation processes. The experimental rate constants were compatible with those calculated from established colloid theory using particle diffusion coefficients and the coated particle radius determined from Brownian movement measurements. The present results indicate that the well-known sensitization-stabilization effect of hydrophilic colloid on a hydrophobic colloid is, in the system examined, due to changes in the balance of the flocculation and deflocculation processes.

The effect of size distribution on the rate constants for collisions in disperse systems

Abstract Simple expressions for the rate constants for collisions due to Brownian movement and to relative motion in a laminar current are given for systems containing a distribution of particle sizes. Polydispersity increases the rate constant for diffusion-controlled collisions, but it reduces the rate constant for shear-induced collisions.

Application of the hydrodynamic-structural theory of non-Newtonian flow to suspensions which exhibit moderate shear thickening with particular reference to “dilatant” vinyl plastisols

Abstract A general equation, derived in previous work, fits flow data for moderately shear thickening dispersions of polyvinyl chloride particles in an oil. The theory on which the equation is based predicts that the number of structural links in a disperse system can increase with increasing shear rate without shear thickening, provided n∞/n0 2 the viscosity increases with increasing shear rate to a maximum value and then the viscosity decreases with further increase in shear rate. This effect is explained as a competition between the increase in the number of links with increasing shear rate and the decrease in link lifetime with increasing shear rate. The aging of vinyl plastisols is examined and found to involve changes in both the hydrodynamic and structural viscosity which can be explained by absorption of oil into the porous polyvinyl chloride particles.

Analysis of the flow of shear thinning colloidal and polymeric systems which exhibit elastic recovery or rigidity

Abstract The hydrodynamic-structural theory of viscosity is extended to take into account the possibility of a distribution of relaxation times. A new equation is presented which is easily applied to experimental data. The effect of a distribution of lifetimes is to extend the range of shear rate over which shear thinning occurs. When the ratio of the largest relaxation time to the smallest relaxation time is greater than 1 but less than 10 the new equation gives results in agreement with the Williamson equation. When this ratio of maximum relaxation time to minimum relaxation time is 300 ± 100 the new equation agrees with an equation recently suggested by Cross. The utility of the new equation is discussed and is illustrated by using it to determine the relaxation time spectra in polystyrene melts.

A heuristic analysis of the non-Newtonian flow of a model latex

The method of analyzing the non-Newtonian flow of suspensions based on the unabridged Einstein equation which has been previously described has been applied to Wangs data for a model latex (J. Colloid Interface Sci. 32, 633 (1970)). Changes in the state of aggregation with shear rate quantitatively describe the changes in viscosity. In particular, the high, shear-dependent intrinsic viscosities are explained by the effects of shear on aggregation. At high solids concentration and low ionic strength, the anomalous behavior which has been observed is attributed to a crowding effect which increases the packing factor of the aggregates.