Lagrangian analysis of consecutive images: Quantification of mixing processes in drops moving in a microchannel

Hyejin Han, Eric M. Furst, Chongyoup Kim

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


A tracking method and statistical analysis is introduced to quantify the mixing of moving droplets in the Lagrangian reference frame. Aqueous microrheology samples are produced as droplets in immiscible oil using a microfluidic T-junction. Samples from initially unmixed streams of the same viscosity-fluids (water/water) or different viscosity-fluids (water/glycerin solution) are dyed with different colors to visualize their internal motions and to quantify the extent of their mixing as a function of the age in the channel. The homogeneity of the material distribution in the drop is quantified by computing skewness of pixel intensity profiles or Shannon entropy index. Such analysis is important to ensure that samples are uniformly mixed for high-throughput rheological measurements using microrheology. Samples with a high viscosity ratio mix more rapidly than those with the same viscosities and the mixing length in traversing drops in the microchannel decays exponentially with traveling displacement until the drop reaches a diffusion limit.

Original languageEnglish
Pages (from-to)489-499
Number of pages11
JournalRheologica Acta
Issue number7
Publication statusPublished - 2014 Jun

Bibliographical note

Funding Information:
This work was partially supported by Mid-career Researcher Program through NRF grant funded by the MEST (Ministry of Education, Science and Technology), Korea (No. 2010-0015186). This work was funded in part by a seed grant from the University of Delaware’s NIH Center of Biomedical Research Excellence, Molecular Design of Advanced Biomaterials (P20-RR017716).


  • Extent of mixing
  • Microchannel
  • Microrheology
  • Shannon entropy
  • Skewness

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


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