# Prosiectau Ffiseg ar gyfer myfyrwyr bl.3 a bl.4

### Two-dimensional flow in granular media

#### (supervisor: Rudi Winter)

Nature of project: experimental, data analysis

Available to students on full-time physics degree schemes or joint students.

#### Project description and methodology

When a collection of particles passes through a channel which is narrow enough to limit the flow but large compared to the individual particles, the channel can become clogged up by particles coming to rest against each other, diverting the onward force to the sides of the channel. This is often observed when aggregate, grain or powder is transferred through a funnel or hopper. Try pouring a bag of flour into a narrow-necked storage vessel through a funnel!

The flow behaviour of granular flows in small-angle funnels depends on the geometry of the funnel. Different flow regimes have been identified depending on the sloping angle of a two-dimensional funnel. Under certain conditions, the flow is intermittent consisting of quasi-periodic kinematic shock waves that propagate against the flow.

In this project, the different flow regimes will be studied, using a funnel apparatus similar in design to that used in [1]. The different flow regimes will be established as a function of the sloping angle. The number density fluctuations and the power spectrum of these flow regimes will be established using video capture and numerical techniques. The system will comprise 3-4mm balls which may be single size or polydisperse. The funnel can be of any material but will require a transparent lid to allow video capture of the flow regimes.

This project will involve the design and construction of the funnel system and the video capture of different flow regimes with subsequent processing of the images. Once data have been taken, there will be the need to analyse and interpret them, which necessitates both image and numerical analysis.

A successful project will develop beyond the above in one/some of the following directions:
(1) Study the effect of polydispersity (different sizes amongst the spheres).

(2) Investigate the effect of shaking on the flow regime to study the onset of a critical acceleration in which the intermittent flow becomes fluidised.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

This project is only available as a Y3 project.

Please speak to Rudi Winter (ruw) if you consider doing this project.

Initial literature for students:

1. S. Hørlück et al.; Phys Rev E 67 (2003) 021304
2. B Andreotti, Y Forterre, O Pouliquen; Granular Media: Between Fluid and Solid; Cambridge University Press (2013)
3. JC Tsai et al.; Phys Rev E 65 (2001) 011306

#### Novelty, degree of difficulty and amount of assistance required

The project has components of experiment design, image processing and numerical and statistical analysis. While all of these aspects are required for a successful project, the focus of the project can be tailored to the specific interests of the students taking this project.

#### Project milestones and deliverables (including timescale)

milestoneto be completed by
Design of funnel system and breakdown of project into numerical and experimental componentsChristmas
Construction of funnel and identification of criteria for different flow regimesend of October
Video capture and image processing of different flow regimesmid-March
Numerical and statistical analysis of different flow regimesEaster

Students taking this project will have to submit a full risk assessment form