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Role of diffusion in mixing inkjet printed droplets

Yatin Darbar*

Ahmed Said Ismail

Thomas C. Sykes

David Harbottle

Harvey M. Thompson and Mark C. T. Wilson†

  • Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, LS2 9JT, United Kingdom

  • School of Chemical and Process Engineering, University of Leeds, Leeds, LS2 9JT, United Kingdom

  • *Contact author: yatin_darbar@hotmail.co.uk
  • †Contact author: M.Wilson@leeds.ac.uk
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Phys. Rev. Fluids 11, 073603 – Published 21 July, 2026

DOI: https://doi.org/10.1103/q4tr-jknx

Abstract

The mixing dynamics of a coalescing sessile and impacting liquid droplet on a solid surface is studied numerically. The numerical simulations utilize the volume of fluid method coupled with an advection-diffusion equation to assess diffusive mixing within the droplets. The simulation methods are extensively validated against analytical and experimental results confirming their ability to capture diffusion in droplet systems. Using dimensions and properties relevant to inkjet printing systems, the timescale for droplet mixing in printing and other microfluidic applications that concern the impact and coalescence of droplets is determined. Results show little mixing occurs during the impact and relaxation of the printed droplets, with complete homogenization driven mainly by molecular diffusion over a much longer timescale than the impact. The effects of key printing parameters, including droplet size, printing separation and substrate wettability are explored to quantify their impact on droplet mixing times. Understanding the effect of these parameters on the timescale for droplet mixing gives potential avenues to enhance or suppress droplet mixing before the mechanisms of evaporation or curing become relevant.

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Phys. Rev. Fluids 11, 073603– Published 21 July, 2026
  • Received 18 December 2025
  • Accepted 29 June 2026
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