Particle clusters in concentrated suspensions. 2. Information theory and particle clusters

Abstract

We reconstruct the probability distributions of cluster sizes of uniform spheres in concentrated suspensions subjected to homogeneous shear flow by combining partial experimental information with techniques derived from the Maximum Entropy Principle (MEP) and Information theory. Observations of the clusters of a small fraction of labeled particles are used as constraints in a statistical inference procedure based on the MEP to predict the shape of the cluster size distributions for all spheres. The breadth of the cluster size distributions is inferred by applying a technique derived from information theory to the experimental observations. We find that the average cluster size increases rapidly and nonlinearly as the volume concentration increases. Over the range of our data, the average cluster size decreases slightly and the distributions of cluster sizes become more random as the rate of shear increases.

Development of a predictive power law relationship for polymer composites based on newtonial carrier concentrated slurries

“…What follows is the theory development that was initiated at Clarkson University and found in Zak [2] and Radhakrishnan [3]. In sufficiently concentrated suspensions, it has been shown by several investigators, Segr e and Silberberg [4], Karnis et al [5], Karnis et al [6], Cox and Mason [7], Gauthier et al [8], Park et al [9], Hoffman [10], Graham and Bird [11], Graham and Steele [12], GardalaMaria and Acrivos [13], Husband and Gadala-Maria [14], Parse and Gadala-Maria [15], Ackerson [16], Petit and Noetinger [17], Bossis and Brady [18], Brady and Bossis [19], Bossis and Brady [20], Phillips et al [21], and Durlofsky and Brady [22] that macroscopic structures were present as the suspension was deformed. These macroscopic clusters of agglomerated particles had a significant effect on the behavior of the suspension.…”

Characterizing the flow of slurries using percolation theory‐based functions

“…A preliminary description relating to filled polymers can be found in . In sufficiently concentrated suspensions, it has been shown that macroscopic structures were present as the suspension was deformed. These macroscopic clusters of agglomerated particles had a significant effect on the behavior of the suspension.…”