Modelling of solid particle aggregation dynamics in non-wetting liquid medium

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Abstract

The aim of this work is to re-examine and, if need be, to discuss or modify several of the elements of the classical aggregation dynamics models and to adapt them to the case of aggregation in non-wetting media and particularly alumina inclusions aggregation in a turbulent flow of liquid steel. As proved by several experiments and models, solid particles in contact in non-wetting media are linked by gaseous bridges which may pre-exist prior to the aggregate formation. In this paper, the role of these gaseous cavities in the aggregation process is considered. In particular, a complete calculation of the interaction force between hydrophobic surfaces (Bjerkness–Ruckenstein model) is performed. Main aspects of the aggregation dynamics are envisaged in the particular conditions which result from non-wetting. Hydrodynamic interactions between particles are modified by non-wetting, thus the collision efficiency coefficient and the aggregation kernel. The fragmentation kernel of the aggregates, however, is modified to a larger extent and is equal to zero in most cases. Numerical applications are presented in the reference case (alumina particles in liquid steel). A general procedure of use of this model in other non-wetting situations is given too.

Introduction

Aggregation of hydrophilic particles in stirred liquid media can be considered as a relatively well-understood process in spite of the variety and complexity of its aspects. Good models exist in particular for representing the physicochemical interactions between aggregates and for predicting the collision rates and their efficiency [1], [2], [3], [4], [5], [6], [7], [8], [9]. The procedure proposed by Kusters et al. [8] has revealed so far particularly efficient to take into account the porous character of the aggregates in a comprehensive dynamical model.

Aggregation of solid particles in non-wetting media is less known, at least on certain aspects. A large number of experimental works indeed have definitely proved the existence of strong long range (20–200 nm) attractive forces between hydrophobic surfaces in water [10], [11], [12], [13]. Their most likely explanation focuses upon the bridging of nanobubbles which pre-exist on the hydrophobic surface. The existence of these bubbles has been first deduced from force measurements and then confirmed by direct observations [14], [15], [16], [17], [18]. Concerning the aggregation process itself, these bubbles play a major role, in bridging the particles which have entered in contact. Hydrodynamic aspects are also relatively well known: drag force on hydrophobic particle, repulsive hydrodynamic force between hydrophobic particles in motion.

In recent works, we investigated two experimental situations of solid aggregation in non-wetting conditions. The first one concerns “clean” steel production [19]. Steel-making processes include a de-oxidation step in which a reducing agent, aluminium, for instance, is added to the liquid steel. Consequence is the formation in the bath of metal oxide particles, typically, 3–10 μm alumina inclusions. Observations show that these inclusions tend to gather and to form ramified clusters of 50–300 μm which keep a strong cohesion in spite of the highly turbulent conditions created by the melt flow in certain parts of the reactor. These clusters are responsible for defects which may seriously alter the steel mechanical properties. The conditions of formation and the characteristics of these aggregates have given rise to several works for many years [20], [21], [22]. Assumption of gas bridges between particles was put forward in this case too to explain the high cohesion and size of the observed agglomerates. We re-visited recently this problem [19]. Because of the lack for results due to the difficult experimental conditions (temperature 2000 K), we developed the analogy with aggregation of hydrophobic silica particles in water–ethanol solution [23]. In particular, we clearly proved that the unusual optical properties of the aggregates could be explained by the invasion of their structure by gas pockets.

For practical reasons of product quality, process control, equipment sizing and design, comprehensive models of aggregation dynamics in non-wetting media are becoming necessary. To our knowledge, however, no quantitative predictive model – we mean comparable to Kusters approach [8] – is presently available to analyse and interpret aggregation in non-wetting media.

From a general point of view, aggregation models should take into account the following aspects [7], [8], [9]: (i) nature and intensity of physicochemical interactions between separate solid particles at rest; (ii) collision frequency; (iii) collision efficiency; (iv) link creation between particles; (v) fragmentation; (vi) aggregate morphology.

The aim of this work is to re-examine and, if need be, to discuss or modify several of the elements of the classical aggregation models and to adapt them to the case of aggregation in non-wetting media and particularly alumina inclusions aggregation in a turbulent flow of liquid steel.

A simplified version of this model has been applied to the case of hydrophobic silica aggregation [23] in aqueous media; however its complete development has never been published extensively yet.

Section snippets

Three-phase systems in case of non wetting

For the reference system, alumina (S), liquid steel (L) and gas (G), respective interfacial tensions at the operating temperature of 2000 K are: γSG = 0.65 J m−2, γLG = 1.70 J m−2, γSL = 1.96 J m−2. Equilibrium of the contact line between the three phases gas–liquid–solid (when it exists) imposes the Young relation:γSGγSL=γLGcosθIn the present case, θ = 140° (2.44 rad). Contact angle is greater than 90°, as expected in case of non-wetting.

The presence of bubbles at the surface of hydrophobic surfaces in

Dynamical aspects of aggregation in non-wetting media

In this section, we will successively examine the effect of non-wetting and connected phenomena on the aggregation and fragmentation kernels.

Conclusion

In this paper we propose a set of theoretical considerations in the aim of building a model of aggregation of a solid in a non-wetting liquid. From thermodynamic considerations we prove that gas pockets can spontaneously form in the underlying cavities of the solid–liquid surface. These cavities play an essential part in the formation of gas bridges between particles in contact. The role of this interfacial gas layer is examined in three steps of the aggregation mechanism:

  • (i)

    the possible

References (55)

  • E. Ruckenstein

    The instability of the solid–liquid interface and the hydrophobic force

    J. Colloid Interf. Sci.

    (1997)
  • K. Hotta et al.

    The capillary binding force of a liquid bridge

    Powder Technol.

    (1974)
  • G. Lian et al.

    A theoretical study of the liquid bridge forces between two rigid spherical bodies

    J. Colloid Interf. Sci.

    (1993)
  • E. Ruckenstein et al.

    On the no-slip boundary condition of hydrodynamics

    J. Colloid Interf. Sci.

    (1983)
  • O.I. Vinogradova

    Coagulation of hydrophobic and hydrophilic solids under dynamic conditions

    J. Colloid Interf. Sci.

    (1995)
  • O.I. Vinogradova

    Slippage of water over hydrophobic surface

    Int. J. Miner. Process

    (1999)
  • V. Oles

    Shear-induced aggregation and breakup of polystyrene latex particles

    J. Colloid Interf. Sci.

    (1992)
  • R. David et al.

    Crystallization and precipitation engineering—a discrete formulation of the agglomeration rate of crystals in a crystallization process

    Chem. Eng. Sci.

    (1991)
  • H.S. Mumtaz et al.

    Orthokinetic aggregation during precipitation: a computational model for calcium oxalate monohydrate

    Trans. Inst. Chem. Eng.

    (1997)
  • R.C. Sonntag et al.

    Structure and breakup of flocs subjected to fluid stresses. II. Theory

    J. Colloid Interf. Sci.

    (1987)
  • P. Ayazi Shamlou et al.

    Growth-independent breakage frequency of protein precipitates in turbulently agitated bioreactors

    Chem. Eng. Sci.

    (1994)
  • S.P. Tha et al.

    Interaction forces between red cells agglutinated by antibody

    Biophys. J.

    (1986)
  • M.Z. Smoluchowski

    Drei vorträge über diffusion, brownsche molekular-bewegung und koagulation von kolloidteilchen

    Z. Phys. Chem.

    (1916)
  • H.R. Kruyt
    (1952)
  • P.G. Saffman et al.

    On the collision of drops in turbulent clouds

    J. Fluid Mech.

    (1956)
  • T.G. Van de Ven et al.

    The microrheology of colloidal dispersions. VII. Orthokinetic doublet formation of spheres

    Colloid Polym. Sci.

    (1977)
  • K. Higashitani et al.

    Kinetic theory of shear coagulation for particles in a viscous fluid

    J. Chem. Eng. Jpn.

    (1982)
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