Motion of miscible magnetic fluids in a vertical capillary tube

Ching-Yao Chen*, H. C. Lin, W. K. Tsai, C. H. Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


An experimental study of miscible magnetic fluid motion in a vertical capillary tube is presented. Transporting ferrofluids is dominated by a dimensionless magnetic number Ma, which characterizes the ratio of upward magnetic force to the downward gravity. Two distinct stages of motion, referred to as the sub-critical mode of finite lift and the effective transportation, are identified. These two modes are determined by the values of the sub-critical magnetic number Masub and critical magnetic number Macr respectively. For the cases of sub-critical mode (Masub < Ma < Macr), the ferrofluids are lifted to quasiequilibrium heights, which are nearly proportional to the magnetic number Ma. As for the situations of effective transportation (Ma > Macr), a penetrating finger of ferrofluids is formed similar to the conventional miscible displacements. A dimensionless proportionality of fingertip velocity v, magnetic number Ma and field distribution profile fz is obtained as v ∼ Ma1/2 fz by scaling arguments. This proportional correlation shows a good agreement with the experiments.

Original languageEnglish
Pages (from-to)311-317
Number of pages7
JournalJournal of Mechanics
Issue number4
StatePublished - 1 Jan 2008


  • Capillary tube
  • Miscible ferrofluid

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