Newton vs Stokes

The dynamics of small granular particles is governed mainly by their interaction with the surrounding air (the Stokesian regime). In contrast, for larger particles, the dynamics is dominated by the direct contact forces and gravity (Newtonian regime). 

In this project we have studied experimentally and numerically the transition from one regime to the other, by means of two well-chosen systems in which the Stokesian and Newtonian forces act in opposite directions:

Faraday heaping

The formation of Faraday heaps on a vibrating plate is caused by a subtle interplay between the Stokesian forces (drag, air pressure) and the Newtonian forces (from collisions and gravity). The former drive the particles toward the center of the heap while the latter drive the particles outward. The slope angle of a stable heap is determined by the balance between the opposite particle fluxes from the Stokesian and Newtonian forces. Also the coarsening of a landscape of many small heaps into one large heap was shown to be a result of these two types of forces.

Figure 1: Numerically simulated Faraday heaping in a vibrated granular bed after 0, 30, 55 and 240 driving cycles. After a few cycles, some slight surface ripples start to grow into small heaps, which coarsen into larger heaps until a steady state with a single Faraday heap is reached.

Chladni patterning

When particles are sprinkled on a resonating plate, the Newtonian forces will drive relatively large particles to the nodal lines, giving rise to the famous Chladni patterns, whereas very fine particles are driven to the anti-nodes by the Stokesian forces. We have made a detailed study of the air currents that drive these fine particles. We also found a novel phenomenon: When the acceleration of the resonating plate is below g, particles will always move to the anti-nodes, irrespective of their size or weight, since in this case both the Stokesian and the Newtonian forces are directed toward the anti-nodes.

Figure 2: (a) Top view of a flexible plate resonating in its 2 × 2 mode on which heavy particles have been sprinkled. After a few seconds most particles have collected at the nodal lines, forming a classic Chladni pattern. (b) The same plate with very light particles. Due to the presence of air, the particles now migrate to the anti-nodes and after 4 seconds an inverse Chladni pattern has formed.

We will further use our numerical code to elucidate other granular systems, where the role of air plays a crucial role.

Info: Devaraj van der Meer

Researchers: Henk Jan van Gerner, Detlef Lohse, Devaraj van der Meer.
Collaborators: Ko van der Weele (University of Patras), Martin van der Hoef, Hans Kuipers (Fundamentals of Chemical Reaction Engineering, U Twente) 
Embedding: JMBC
Sponsors: FOM


Coarsening of Faraday Heaps: Experiment Simulation, and Theory ,
H.J. van Gerner, G. Caballero Robledo, D. van der Meer, J.P. van der Weele, and M. van der Hoef
Phys. Rev. Lett. 103, 028001 (2009)BibTeΧ
Interplay of air and sand: Faraday heaping unravelled
H.J. van Gerner, M. van der Hoef, D. van der Meer, and J.P. van der Weele
Phys. Rev. E 76, 051305 (2007)BibTeΧ

Max Planck Gesellschaft