A general condition for spontaneous capillary flow in uniform cross-section microchannels


Spontaneous capillary flow (SCF) is a powerful method for moving fluids at the microscale. In modern biotechnology, composite channels—sometimes open—are increasingly used. The ability to predict the occurrence of a SCF is a necessity. In this work, using the Gibbs free energy, we derive a general condition for the establishment of SCF in any composite microchannel of constant cross section, i.e., a microchannel comprising different wall materials and even open parts. It is shown that SCF occurs when the Cassie angle is smaller than π/2 (θ* < π/2). For a homogeneous confined channel, this relation collapses to the well-known hydrophilic contact angle θ < π/2.

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Correspondence to Jean Berthier.

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Berthier, J., Brakke, K.A. & Berthier, E. A general condition for spontaneous capillary flow in uniform cross-section microchannels. Microfluid Nanofluid 16, 779–785 (2014). https://doi.org/10.1007/s10404-013-1270-1

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  • SCF (spontaneous capillary flow)
  • Gibbs thermodynamic equation
  • Cassie law