Original Research Paper
Development of a method for determining the maximum van der Waals force to analyze dispersion and aggregation of particles in a suspension

https://doi.org/10.1016/j.apt.2020.03.021Get rights and content

Highlights

  • We propose a method for determining a maximum value of the van der Waals force, Fv,max.

  • The proposed method can estimate the representative value of maximum van der Waals force.

  • The simulated aggregate size distributions (ASDs) agreed with the measured ASDs qualitatively.

Abstract

A new method for determining the maximum value of the van der Waals force, Fv,max, has been developed to analyze the dispersion and aggregation behavior of primary particles in a suspension. The simulation method considered the van der Waals force, the electrical double-layer force and the lubrication force as remote inter-primary-particle interaction forces. Distinct Element Method (DEM) was applied to tracking the motion of primary particles, and DEM was coupled with Computational Fluid Dynamics (CFD) by DEM-CFD coupling model to represent the motion in liquid. Aggregate size distributions (ASDs) were measured and simulated at different pHs and shear rates in order to determine the Fv,max and to validate the proposed method. The simulated ASDs qualitatively agreed with the experimental values in general. The result, therefore, indicates that the dispersion and aggregation behavior of primary particles could be analyzed by using the Fv,max determined by the proposed method.

Introduction

Controlling dispersion and aggregation of fine particles is important in a number of industries such as waste water treatment, mineral processing and ceramic powder processing [1], [2], [3], [4], [5] because it is related to process efficiencies and quality of the products. For instance, the size of aggregates is important to improve efficiency and quality due to its effect on the physical properties of the suspensions such as viscoelasticity and particle settling rate. Dispersion and aggregation have often been changed by adding surface modifiers (such as surfactants and flocculants) and by applying shear forces. In particular, the influence of shear forces needs to be understood, because shear forces can be applied via a range of different ways in order to control the dispersion and aggregation, and because many processes operations inherently result in shear forces being applied to suspensions.

Increasing shear rate increases the probability of collisions between primary particles [6], which is a necessary prerequisite for aggregation. Prolonged shear during or after formation of aggregates can both break them down or restructure and densify them. The details of these transformations depend on the rate and time of shear [7], [8], [9], [10], [11], [12], [13]. Thus, it is important first to understand the aggregation and dispersion behavior of primary particles under a shear flow.

Time-resolved aggregation behavior is difficult to observe directly by any experimental methods because the aggregation occurs in the microscopic field over quite short time scales and the aggregates show complex behavior such as collisions, breakage and re-aggregation. Simulation techniques offer an advantage here, enabling observation and analysis of phenomena such as aggregation behavior in suspension without interfering.

There are several reports that the behavior of aggregates in fluid flow has been analyzed by using a simulation [8], [14], [15], [16]. The van der Waals force Fv was used in their reports to consider the attractive force causing the aggregation, and is often represented by the following:Fv=-AHdp24D2nijwhere AH denotes the Hamaker constant, dp primary particle diameter. nij and D represent normal direction vector and the surface distance between two primary particles, respectively. The van der Waals force diverges to infinity when the primary particles are in contact with each other (surface distance D = 0), so that the maximum value of the van der Waals force, Fv,max, needs to be determined by some assumptions of the finite equilibrium separation distance.

When the behavior of primary particles is simulated, Fv,max is generally given as the value where the Born repulsive force is stronger than the van der Waals force (that is the surface distance D is from 0.1 to 0.4 nm [17], [18], [19], [20]). However, the assumption could be unsuitable for analyzing the behavior of primary particles because there are reports that Fv,max is generally assumed to be much larger than a real attractive force due to surface roughness or conditions of primary particles [21], [22], and Fv,max strongly affects the behavior of primary particles in the simulation [16]. The typical roughness of colloidal particle surfaces is about 9 nm [23].

The experiments for measuring the inter-primary-particle interaction forces including the van der Waals force have been conducted by using an Atomic Force Microscope (AFM) [24]. However, a number of measurements are required to obtain the representative value of Fv,max because the AFM measures the interaction between two primary particles. On the other hand, Fv,max could be estimated by measuring an Aggregate Size Distribution (ASD) in a suspension because it was known that Fv,max affects the size of aggregates in a suspension [17].

Thus, in this paper, a new method for determining the representative value of Fv,max by measuring a ASD is developed to analyze the dispersion and aggregation behavior of primary particles in a suspension. Furthermore, the simulation method is validated with experimental results of the other ASDs at different pHs and shear rates.

Section snippets

Simulation method

First of all, the proposed method for determining the Fv,max is introduced in Section 2.1. In addition, the following phenomena must be considered simultaneously to simulate the dispersion and aggregation behavior of primary particles in liquid:

  • (a)

    Motion of primary particles

  • (b)

    Inter-primary-particle interaction

  • (c)

    Motion of fluid

  • (d)

    Primary-particle-fluid interaction

Section 2.2 presents the Distinct Element Method (DEM) [25] considering the inter-primary-particle interaction forces, which addresses the

Materials and methods

The effects of a shear force and particle interaction forces (magnitude of attraction or repulsion) on the ASDs were measured for three suspensions with different pH in order to determine the Fv,max in the simulation and to validate the proposed method for determining the Fv,max.

Experimental results of ASDs and ζ-potentials at each pH

The ASDs were measured at each shear rate as shown in Fig. 2. The D10, D50 and D90 denote aggregate diameters where the cumulative volume of undersize particles is 10%, 50% and 90%, respectively, of the total volume of particles. It was found that the D10 and D50 at pH 4 and pH 7 were nearly independent of the shear rate, although D90 at pH 7 slightly increased with increasing shear rate. In addition, the D50 at pH 4 was similar to the primary particle diameter (D50 = 0.59 μm [39]). On the

Conclusion

A new method for determining the maximum value of the van der Waals force, Fv,max, has been developed to analyze the dispersion and aggregation behavior of primary particles in a suspension. The method was that the Fv,max was determined by comparing the simulated ASD with the measured ASD. The simulation considered the van der Waals force, the electrical double-layer force and the lubrication force as the inter-particle-interaction forces. The simulation using the obtained Fv,max for the ASDs

Acknowledgements

Thanks to Dr. Michelle DaSilva for support in facilitating the visit of Kizuku Kushimoto to the University of Melbourne. Thanks to Raul Cavalida for help with rheology.

A part of this research was supported by Japan Science and Technology Agency (JST), Adaptable and Seamless Technology transfer Program through Target-driven R&D (A-STEP) Industrial needs response type High Performance of Ceramics and Manufacturing Process [Grant number: JPMJTS1615].

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