Advanced Undergraduate Laboratory

Department of Physics

University of Toronto

FVF: Fractal Viscous Fingering

Why do fractal patterns so often appear in nature? Radial viscous fingering is a paradigm case of a very general type of fractal growth which includes the dendritic growth of crystals (like snowflakes), diffusion limited aggregation (DLA), dielectric breakdown, electrodeposition, mocha diffusion patterns on pottery, the branching of propagating cracks and bacterial colonies, among many others. In this experiment, both the initial fingering instability and the emergence of the fractal pattern are studied.

This experiment is related to research carried out in Prof. Stephen Morris's Experimental Nonlinear Physics Group.

Write-Up in PDF Format.

(The experiment is new. Contact Prof. Stephen Morris for help.)

A movie showing fractal viscous fingering:

Additional resources:

• Python codes and other items for data analysis:
  • The latest code can be downloaded and run on the lab computer.
  • The code can also be viewed on the department's GitLab server.
  • Code for making FVF movies from image sequences, using ffmpeg. Here are example movies:[1][2][3]
  • Fractal images for testing box counting code:
    • Sierpinski triangle image, adpated from Wikipedia, with dimension close to the exact value of log(3)/log(2).
    • Large diffusion limited aggregation (DLA) image, adapted from Wikipedia.
    • Radial viscous fingering image, adapted from Sharon et. al..
  • Additional analysis code by undergraduate students:
    • Radius of gyration code for estimating fractal dimension, by George Lu (2018).
    • Area and Radius function for estimating area and radius of gyration, by George Lu (2018).
    • Package of improved analysis codes, by Matthew Gerry (2019).
• Other useful things:
  • Manual for the peristaltic pump
  • Manual for the camera. Model: GS3-U3-32S4M-C.
  • ImageJ, a free, cross platform image analysis package in Java.
  • ffmpeg, a free, cross platform command-line tool for making movies from sequences of images.

A thresholded and flood filled image of an air bubble injected into mineral oil in a a very thin gap at a pressure of 30 psi.
This image uses the reflect_pipe method to remove the inlet pipe that you see in the video above.

Last updated on 5 September 2019