Inertial burst and pinning in segmented capillary geometries

Résumé fourni par la source

Passive microfluidic valves based on capillary burst at geometric expansions enable autonomous flow control without external actuation, yet existing quasi-steady models do not address whether a dynamically advancing meniscus in spontaneous capillary-driven flow possesses sufficient kinetic energy to overcome Laplace pressure barriers. Here, we extend piecewise capillary flow theory to the inertial–viscous (Bosanquet) regime and derive a dynamic burst criterion from momentum and energy balances across multi-segment cylindrical geometries. Burst or pinning at an abrupt expansion is controlled by the Ohnesorge number, the expansion ratio, and the dimensionless upstream length. Numerical phase diagrams and perturbative analysis yield a critical Ohnesorge number scaling confirmed by collapse onto an approximate master curve. Energy budgets show that the Ohnesorge number governs kinetic energy delivery to the junction: at low Oh, capillary work partitions predominantly into kinetic storage and inflow energy, with minimal viscous dissipation, whereas at high Oh, dissipation accounts for the dominant fraction of capillary work. Threshold behavior requires discrete curvature discontinuities; smooth geometric tapers modulate velocity continuously but produce no pressure barrier, reducing the system to a distributed flow resistor. The resulting framework provides quantitative design bounds for inertial burst valves in autonomous microfluidic systems.

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