Scaling of the viscoelasticity of weakly attractive particles
Edited by Qichao Hu
November 29th, 2010
Colloidal particle suspensions have a diverse range of rheological properties. By adjusting the interparticle interactions and the particle volume fraction, the rheology can be controlled. This paper presents a model that combines the elasticity of a solid network formed by the particles and the viscosity of the suspending fluid.
The example that they used consisted of carbon black suspended in base stock oil, and the experiments were done both as functions of particle volume fraction and interaction potential. This has applications in the automobile industry where suspensions of carbon black in oil are used as test systems to model the behavior of used motor oils where aggregation of soot leads to undesired viscosity increases.
A double-tailed dispersant, acting as a surfactant, is introduced to control the interparticle interactions. The more polar amine group binds to the surface of the carbon black allowing the two long hydrocarbon tails to stabilize the particles. Increasing dispersant concentration in solution leads to increased surface-adsorbed layer, and reduces the attractive interactions between the particles.
The primary particle size of the carbon black is about 30nm using electron microscopy. However, the carbon black particles tend to cluster and aggregate, and large shear is needed to break up the aggregates, and to measure the volume fraction. Without the dispersant, carbon black particles are strongly attractive to each other.
The mechanical properties of the suspensions are shown in the figure below.
At the highest volume fraction, the suspension is clearly elastic. Also all the data can be scaled onto a single master curve (as shown in figure below). The scaling behavior has never been reported previously. For fluid-like dilute suspension, with Newtonian fluid behavior characteristics, their data cannot be scaled onto the master curve.
The explanation for this model is that the carbon blacks form a solid but tenuous network with a purely elastic, frequency-independent modulus, whose magnitude increases with the volume fraction as the network becomes more robust. Interspersed throughout the tenuous network is the suspending fluid, which as a purely viscous modulus. Thus at low frequency, the elasticity of the network dominates, while at high frequency, the viscosity of the network dominates.
Since there is a sharp difference between the scaling behavior and that of a Newtonian fluid, there must be a critical onset of the elastic solid. This critical onset of the solid-like network is related to both change in volume fraction, and in the interaction energy between particles. There is a boundary between fluid and solid phases in the phase diagram.
Also since the interparticle bonds are not permanent, the strucutre may ultimately flow at very low frequency. The frequency of the breakup will increase as the network becomes weaker.
Overall this work provides a means to summarize a wide range of rheological behavior. Moreover, it is a great tool for determining the effectiveness of a dispersant to disperse soot in motor oil.