Simulation of aggregating colloids in shear flow

Turbulent route to two-dimensional soft crystals

We investigate the effect of a two-dimensional, incompressible, turbulent flow on soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag and short-range interparticle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and noncrystalline phases as a function of the Stokes number. Furthermore, the nature of preferential concentration, characterized by the correlation dimension, is significantly different from that of particle-laden flows in the absence of repulsive potentials.

Viscosity Model for Nanoparticulate Suspensions Based on Surface Interactions

In this paper, a widely mechanistic model was developed to depict the rheological behaviour of nanoparticulate suspensions with solids contents up to 20 wt.%, based on the increase in shear stress caused by surface interaction forces among particles. The rheological behaviour is connected to drag forces arising from an altered particle movement with respect to the surrounding fluid. In order to represent this relationship and to model the viscosity, a hybrid modelling approach was followed, in which mechanistic relationships were paired with heuristic expressions. A genetic algorithm was utilized during model development, by enabling the algorithm to choose among several hard-to-assess model options. By the combination of the newly developed model with existing models for the various physical phenomena affecting viscosity, it can be applied to model the viscosity over a broad range of solids contents, shear rates, temperatures and particle sizes. Due to its mechanistic nature, the model even allows an extrapolation beyond the limits of the data points used for calibration, allowing a prediction of the viscosity in this area. Only two parameters are required for this purpose. Experimental data of an epoxy resin filled with boehmite nanoparticles were used for calibration and comparison with modelled values.

Numerical Simulation of the Rheological Behavior of Nanoparticulate Suspensions

Nanoparticles significantly alter the rheological properties of a polymer or monomeric resin with major effect on the further processing of the materials. In this matter, especially the influence of particle material and disperse properties on the viscosity is not yet understood fully, but can only be modelled to some extent empirically after extensive experimental effort. In this paper, a numerical study on an uncured monomeric epoxy resin, which is filled with boehmite nanoparticles, is presented to elucidate the working principles, which govern the rheological behavior of nanoparticulate suspensions and to simulate the suspension viscosity based on assessable material and system properties. To account for the effect of particle surface forces and hydrodynamic interactions on the rheological behavior, a resolved CFD is coupled with DEM. It can be shown that the particle interactions caused by surface forces induce velocity differences between the particles and their surrounding fluid, which result in increased drag forces and cause the additional energy dissipation during shearing. The paper points out the limits of the used simulation method and presents a correction technique with respect to the Péclet number, which broadens the range of applicability. Valuable information is gained for a future mechanistic modelling of nanoparticulate suspension viscosity by elucidating the interdependency between surface forces, shear rate and resulting drag forces on the particles.

Rheological properties of fresh and reconstituted milk protein concentrates under standard and processing conditions

As the processability of fresh and reconstituted milk protein concentrates crucially depends on their rheological properties, a considerable amount of studies focuses on this topic. By means of a direct comparison, we are the first to clearly show that distinct rheological differences can exist between fresh and reconstituted milk protein concentrates under standard and processing conditions. We show that reconstituted milk protein concentrates made from commercial milk protein powders exhibit higher viscosities than fresh ones. Furthermore, we found that during intense shearing, the reconstituted milk protein concentrates undergo a loss of structure, which manifests itself in a significant viscosity decrease. The inverse effect can be observed for fresh milk protein concentrates. Besides these differences, the reconstituted milk protein concentrates exhibit gel-like properties above a certain protein content. We attribute these observations to protein-protein interactions in the milk protein powder, which are induced by manufacturing and/or storing conditions. Our results demonstrate that rheological properties of fresh and reconstituted milk protein concentrates are quantitatively not invariably interchangeable. Thus, the purpose of this article is to emphasize the necessity for researchers and engineers to take into account the rheological particularities of different milk protein concentrates prior to usage.

Shear-Induced Alignment of Janus Particle Lamellar Structures

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)-the ratio of the viscous shear to the Brownian forces-the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation-lamellae with their normals parallel to the direction of the velocity gradient-for intermediate values of Pe, and (3) perpendicular orientation-lamellae with their normals parallel to the vorticity direction-for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required.

Rich Janus colloid phase behavior under steady shear

We study the assembly of single-patch colloidal Janus particles under steady shear flow via Brownian dynamics simulations. In the absence of flow, by varying the Janus patch size and the range and strength of the anisotropic interaction potential, Janus colloids form different aggregates such as micelles, wormlike clusters, vesicles and lamellae. Under shear flow we observe rearrangement, deformation, and break-up of aggregates. At small and intermediate Péclet (Pe) numbers-the ratio between shear and Brownian forces-the competition between rearrangement, deformation, and break-up favors the growth of micelles and vesicles increasing mean cluster size, which is consistent with a previous numerical study of Janus particles under shear. This initial shear-induced growth causes micelles and vesicles to reach a maximum cluster size at Pe ≈ 1 and Pe ≈ 10, respectively. After this growth micelles dissociate continuously to reach a dilute colloidal "gas phase" at Pe ≈ 10 while vesicles dissociate into micelles with high aspect ratio at Pe ≈ 10 and finally break-up into a gas phase at Pe ≈ 30. Wormlike clusters initially break-up into micelles with high aspect ratio at Pe ≈ 0.1, and proceed to finally reach a gas phase at Pe ≈ 10. Lamellae initially break into smaller lamellae that align with the flow in the velocity-velocity-gradient plane and finally break-up into a gas phase at Pe ≈ 100. The different cluster sizes and morphologies observed as functions of interaction range, Janus patch size, interaction strength, and shear rate, open new actuation routes for reconfigurable materials and applications.

Hydrodynamic forces and critical stresses in low-density aggregates under shear flow

The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.

Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics

The hydrodynamic properties of rigid fractal aggregates have been investigated by considering their motion in shear flow in the Stokesian dynamics approach. Due to the high fluid viscosity and small particle inertia of colloidal systems, the total force and torque applied to the aggregate reach equilibrium values in a short time. Obtaining equilibrating motions for a number of independent samples, one can extract the average hydrodynamic characteristics of the given fractal aggregates. Despite the geometry of these objects being essentially disordered, the average drag-force distributions for aggregates show symmetric patterns. Moreover, these distributions collapse on a single master curve, characteristic of the nature of the aggregates, provided the positions of the particles are rescaled with the geometric radius of gyration. This result can be used to explain the reason why the stress acting on an aggregate and moments of the forces acting on contact points between particles follow power-law behaviors with the aggregate size. Moreover, the values of the exponents can be explained. As a consequence, considering cohesive force typical for colloidal particles, we find that even aggregates smaller than a few dozen particles must experience restructuring when typical shear flow is applied.

Temperature-induced intermicellization of "hairy" and "crew-cut" micelles in an aqueous solution of a thermoresponsive copolymer

Temperature-induced intermicellar structures in aqueous solutions of the thermoresponsive methoxypoly(ethylene glycol)-block-poly(N-isopropylacrylamide) (MPEGn-b-NIPAAM71) copolymer that exhibit a lower critical solution temperature were studied by means of turbidimetry, dynamic light scattering (DLS), shear viscosity, and rheo small-angle light scattering (rheo-SALS) methods. The length of the hydrophilic chains (MPEG) of the copolymer varies from n=0 to n=114. It is shown that this change has a major impact on the temperature-induced association behavior of the polymer in solution. The turbidity results at quiescent conditions revealed a transition peak in the turbidity curve at intermediate temperatures, and this peak as well as the cloud point is shifted toward higher temperatures with increasing length of the hydrophilic chains of the copolymer. The DLS measurements disclosed a fast and a slow relaxation mode, which both are diffusive. From the fast and slow relaxation times the sizes of unimers/micelles and intermicellar clusters, respectively, can be determined. The temperature-induced aggregation is less pronounced in solutions of copolymers with long hydrophilic chains, and the intermicellar structures exhibit an interesting transition at intermediate temperatures. In the shear viscosity measurements large association complexes are formed at high temperatures and at low shear flow for the polymers with short hydrophilic chains, whereas at high shear rates breakup of interaggregate chains was observed. For the copolymer with the highest number of hydrophilic chains (n=114), a novel transition peak was found in the viscosity data. The rheo-SALS results divulged shear-induced structural changes of the association complexes at elevated temperatures. For copolymers with short hydrophilic chains, shear-induced disruption of association complexes was found at higher temperatures, whereas for hairy micelles augmented shear flow promoted the growth of complexes.

Tangential-force model for interactions between bonded colloidal particles

Recently, Pantina and Furst [Phys. Rev. Lett. 94, 138301 (2005)] experimentally demonstrated the existence of tangential forces between bonded colloidal particles and the capability of these bonds to supporting bending moments. We introduce a model to be used in computer simulations that describes these tangential interactions. We show how the model parameters can be determined from experimental data. Simulations using the model are in agreement to the measurement by Pantina and Furst. Application of the model to an aggregate with fractal structure leads to more realistic behavior than using classical approaches only.

Shear effects on crystal nucleation in colloidal suspensions

Extensive two-dimensional Langevin dynamics simulations are used to determine the effect of steady shear flows on the crystal nucleation kinetics of charge stabilized colloids and colloids whose pair potential possess an attractive shallow well of a few k_{B}T 's (attractive colloids). Results show that in both types of systems small amounts of shear speeds up the crystallization process and enhances the quality of the growing crystal significantly. Moderate shear rates, on the other hand, destroy the ordering in the system. The very high shear rate regime where a reentering transition to the ordered state could exist is not considered in this work. In addition to the crystal nucleation phenomena, the analysis of the transport properties and the characterization of the steady state regime under shear are performed.

Anomalous Transition in Aqueous Solutions of a Thermoresponsive Amphiphilic Diblock Copolymer

The influence of shear flow on aggregation and disaggregation in aqueous solutions of the thermoresponsive methoxy-poly(ethylene glycol)-block-poly(N-isopropylacrylamide) (MPEG53-b-PNIPAAM113) copolymer that exhibits a lower critical solution temperature was investigated with the aid of turbidity, shear viscosity, and rheo small angle light scattering (rheo-SALS) methods. The turbidity results at quiescent conditions revealed a novel transition peak in the turbidity curve at intermediate temperatures, which reflects the delicate interplay between temperature-induced aggregation and shrinking of the species. A similar anomalous transition peak (located at the same temperature) was observed in the steady shear viscosity measurements at intermediate temperatures, and the amplitude of the peak was reduced with increasing shear rate as a consequence of breakup of interaggregate chains. At low temperatures (low sticking probability), enhanced shear rate generated interpolymer aggregates; whereas in the high-temperature domain (high sticking probability) association structures were broken up as the shear rate was increased. The rheo-SALS experiments disclosed growth of aggregates at low temperatures and destruction of association complexes at high temperatures. An increase of the cloud point temperature with rising shear rate is reported, which is interpreted as being a disruption of clusters under the influence of shear stresses.

Dependence of fragmentation behavior of colloidal aggregates on their fractal structure

The fragmentation dynamics of aggregate of non-Brownian particles in shear flow is investigated numerically. The breakup behaviors of aggregates having the same connectivity but the different space-filling properties are examined. The Lagrangian particle simulation in a linear flow field is performed. The effect of surrounding fluid on the motion of multiple particles is estimated by Stokesian dynamics approach. The inter-particle force is calculated from the retarded van der Waals potential based on the Lifshitz theory. The results obtained in this work indicate that the fragmentation behavior of colloidal aggregates depends on their fractal structure. However, if the resultant aggregate size is smaller than the critical one, the fragmentation behavior shows the universality regardless of their original structure. Furthermore, the restructuring of aggregate in shear flow and its effect on the fragmentation process are also discussed.

Stress jumps on weakly flocculated dispersions: Steady state and transient results

Weakly flocculated, thixotropic suspensions have been investigated by means of fast stress jump experiments. With a suitable procedure, reliable stress relaxation data could be collected starting 20 ms after cessation of flow. This technique has been used to determine the elastic and hydrodynamic contributions to the shear stress. Steady state as well as transient flows have been studied for suspensions containing either fumed silica or carbon black particles in a Newtonian medium. In both systems, the elastic stress totally dominates the response at low shear rates and consequently also the apparent yield stress. This stress contribution becomes negligibly small at high shear rates. The hydrodynamic contribution to the viscosity has finite limits at both the low and high shear rate ends. The data are relevant for testing rheological models. As an illustration, it is shown that the data agree qualitatively with the model proposed by Potanin et al. (J. Chem. Phys. 102 (14) (1995) 5845-5853).

Interfacial and rheological properties of humic acid/hematite suspensions

This work deals with the effect of humic acid (HA) adsorption on the interfacial properties, the stability, and the rheology of aqueous iron oxide (hematite) suspensions. It is first of all demonstrated that HA effectively adsorbs onto hematite, mainly at acid pH. Since the charge of the HA chains is negative, it will be electrostatically attracted to the hematite surface below the point of zero charge of the particles, when they are positively charged. Electrophoresis measurements of hematite suspensions as a function of pH in the presence and absence of HA clearly demonstrate the adsorption of negatively charged entities on the oxide. Since the HA-covered particles can be thought of as "soft" colloids, Ohshima's theory was used to gain information on the surface potential and the charge density of the HA layer (H. Ohshima, in: A.V. Delgado (Ed.), Interfacial Electrokinetics and Electrophoresis, Dekker, New York, 2002, p. 123). A different procedure was also used to ascertain the degree of modification experienced by the hematite surface when placed in contact with HA solutions. The contact angles of selected liquids on pretreated hematite layers lead to the conclusion that the humic acid molecules impart to the particles a significant electron-donor character, in turn increasing their hydrophilicity. All this amount of information is used in the work for the interpretation of the rheological properties of hematite suspensions; the results are consistent with a stabilizing effect of HA adsorption on the suspensions, mainly as a consequence of the increased electrostatic repulsion between particles.

Kinetic pathways of sheared block copolymer systems derived from Minkowski functionals

We employ Minkowski functionals to analyze the kinetics of pattern formation under an applied external shear flow. The considered pattern formation model describes the dynamics of phase separating block copolymer systems. For our purpose, we have chosen two block copolymer systems (a melt and a solution) that exhibit a hexagonal cylindrical morphology as an equilibrium structure. Our main objective is the determination of efficient choices for the treshold values that are required for the calculation of the Minkowski functionals. We find that a minimal set of two treshold values (one from which should be equal to an average density value and another to a higher density value) is sufficient to unraffle the phase separation kinetics. Given these choices, we focus on the influence of the degree of phase separation, and the instance at which the shear is applied, on the kinetic pathways. We also found a remarkable similarity of the time evolution of Euler characteristic and the segregation parameter for the average density choice.

Anisotropic capillary interactions and jamming of colloidal particles trapped at a liquid-fluid interface

We determine the capillary attraction and equilibrium configurations of particles trapped at a liquid-fluid interface due to the pinning of their contact line. We calculate analytically the asymptotic interaction energy between two particles and, numerically, the multibody energy landscape for up to four contacting particles. Our results are consistent with recent experiments. We show that a system composed of a large number of such particles behaves as a jammed system.

Microstructure and Viscosity of Aggregating Colloids under Strong Shearing Force

Disaggregation under strong shearing force is simulated for an aggregating colloid based on a sticky particle model which can describe the disaggregating and aggregating kinetics, the deformation, and the rupture of clusters with a minimum number of parameters. For a 2-dimensional system, the viscosity and coordination number of the model colloid are calculated at each time step, and the changes of microstructure with shear flow are observed directly by displaying the configuration of particles onto a monitor. The viscosity depends on both area fraction and shear rate, but coordination number depends only on shear rate. Furthermore, the viscosity and coordination number at steady state are independent of the initial state of particles, which indicates that the disaggregation and aggregation are mutually reversible. Copyright 1999 Academic Press.

Two-Dimensional Simulation of the Breakup Process of Aggregates in Shear and Elongational Flows

A modified discrete element method in which the hydrodynamic contribution is taken into account is proposed to simulate the deformation and breakup process of coagulated particles in two-dimensional shear and elongational flows. The simulation was performed for aggregates of various sizes, constitutive particles and fractal dimensions, and the followings were found: (i) the average number of particles in broken fragments <i> is related with the intensity of flow field Gamma by <i> ~ Gamma-P, where the value of P for aggregates of fractal dimension 1.8 is about 0.86 in the shear flow and about 1.0 in the elongational flow, (ii) aggregates are fragmented in the same fashion if their fractal dimension is the same, and a scaling law for fragmentation will hold if their fractal dimension, particle number and ratio of the minimum gap between neighboring particles to the particle size are the same among aggregates, (iii) aggregates in flow fields are broken by splitting into the smaller fragments but not by eroding particles one by one from their surface, and (iv) the elongational flow is more effective to break up aggregates than the shear flow under usual flow conditions. Copyright 1998 Academic Press.

Light Scattering Experiments on Shear Induced Structures of Micellar Solutions

The formation of shear induced structures (SIS) of a mixed micellar solution of tetradecyldimethylaminoxide and sodium dodecylsulfate is studied by light scattering experiments under shear (rheo-optical method). In the shear rate- as well as in the time-dependent measurements we found an aggregation process taking part in the SIS formation. Below the critical shear rate for the occurrence of SIS, the shear rate dependent experiments show an increased scattering intensity, indicating micellar associates. Above the critical shear rate, we found structures oriented in the direction of flow. The time dependent measurements show that the SIS formation can be regarded as a process which can be divided into three stages: induction-aggregation-orientation. After the aggregation, we found a temporal process in which the orientation increases to reach complete orientation in the direction of flow.