Imaging Forces in Flowing Sand

Sand is an example of a “granular media”:  a collection of discrete solid particles that we encounter on a daily basis: besides sand, coffee beans, rice and even Lego bricks belong to this interesting class of materials. Despite their everyday relevance, the way these materials flow or, say, resist your weight when you stand on them at the beach, remains poorly understood.

To better understand granular materials, we want to see the interparticle forces, and how these forces collectively generate their flow behavior. To visualize interparticle forces, in this project we focus on a particular class of granular materials called suspensions, which are particles dispersed in a fluid. Suspensions have interesting and sometimes complicated flow behavior, as you can also notice on the shoreline. One aspect of suspensions is however very intuitive: they become more viscous when you have more particles per unit volume of suspension.. Many decades ago, Krieger and Dougherty were one of the first to establish an empirical law for this “volume fraction” dependent behavior. They found empirically that

Formula.png




With ηs the effective viscosity of the suspension, ηf the viscosity of the carrier fluid, φ the volume fraction of the solid and φO a critical volume fraction at which the viscosity practically diverges. Many different empirical laws to describe this divergence have been proposed.

Although the phenomenology has been captured by others, the origin of the divergence remains largely obscure. What is the role of flow structure and the microscopic force structure in this emergent rigidity?

To answer this question, we focus on visualizing stress distributions in sheared suspensions, which requires photoelastic particles (particles that have an optical response when they are exposed to external forces). Such methods have already proven to be successful in two-dimensional packings (Figure 1)[1,2]. We are extending this method to three dimensions. In order to do so, we need stable, highly photoelastic millimeter-sized particles.

In this project you will work on the research question in our lab at PCC. Depending on your interest and the timeframe, activities include:

  • Synthesis of (photoelastic) particles
  • Measuring mechanical properties of individual particles
  • Visualizing stress distributions while simultaneously probing the flow behavior of suspensions

The equipment you will use are e.g. rheometers and a Dynamic Mechanical Analyzer (DMA). However, for many of these activities you might need to design and fabricate custom equipment or tools. To help you in this, we have a 3D-printer and many optical and mechanical components available.

We are looking for a motivated BSc or MSc student with a hands-on mentality and an interest in soft matter physics. Want to know more? Contact Marcel Workamp or Joshua Dijksman.

[1] Behringer, R. P., Howell, D., Kondic, L., Tennakoon, S., & Veje, C. (1999). Predictability and granular materials. Physica D: Nonlinear Phenomena, 133(1), 1-17.

[2] Ren, J., Dijksman, J. A., & Behringer, R. P. (2011). Linear shear in a model granular system. Chaos-Woodbury, 21(4), 041105.