Physics of Two-Phase Capillary Flow at Microscale
Below 200 µm channel width, capillary pressure dominates over gravitational forces (Bond number Bo < 0.01). The Washburn equation governs fill rate: L = √(Rγcosθ·t/2η) where R is the hydraulic radius, γ is surface tension (0.072 N/m for plasma/air), θ is the contact angle (38° for plasma on COC), and η is dynamic viscosity (1.2 mPa·s). At 50 µm width, predicted fill velocity is 2.8 mm/s with a contact angle hysteresis correction of +4.2% due to surface roughness Ra 0.3 µm from CNC milling.
COMSOL Model Setup & Mesh Strategy
The Level Set method (LSM) was selected for interface tracking over Volume-of-Fluid (VOF) due to superior mass conservation at the capillary scale. A physics-controlled swept mesh with 3 µm maximum element size at channel walls was applied — 1.2M elements total. Surface tension was implemented as a continuum surface force (CSF). Blood plasma was modelled as a Newtonian fluid (validated for Hct < 45% in channels < 1mm). Solver: PARDISO direct solver, adaptive time-stepping 0.001–0.05s. Compute time: 4.3 hours per geometry variant on 32-core workstation.
Parametric Optimisation Findings
A 72-variant parametric sweep (channel width 30–100 µm, corner radius 0–25 µm, vent hole diameter 0.1–0.4 mm) revealed that corner radius is the dominant variable: sharp 90° corners create air entrapment vortices that increase fill time by 31%. Rounded corners (r = 15 µm) eliminated entrapment in 96% of simulated cases. Vent hole sizing follows a critical threshold: below 0.15 mm, back-pressure build-up stalls flow; above 0.30 mm, evaporation rate exceeds acceptable limits (>5 µL/h at 37°C).
Experimental Validation Protocol
Physical validation used high-speed microscopy (Photron FASTCAM Nova, 1000 fps) to track the fluid front through fluorescent-dyed plasma. 30 cartridge replicates per geometry variant were tested at 25°C. Fill time, meniscus shape, and air inclusion events were compared to COMSOL predictions. The 94.8% concordance was achieved for the final optimised geometry; early variants showed only 71% concordance, prompting the addition of fluid-structure interaction (FSI) coupling for deformable PDMS sections.