A lateral-flow diagnostic test strip is modelled as a bundle of straight

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Stokes flow, lubrication and viscous wetting

Problem

A lateral-flow diagnostic test strip is modelled as a bundle of straight, open capillaries of radius r=2.0 μmr = 2.0\,\mu\mathrm{m}, into which an aqueous sample (γ=0.0728 N m−1\gamma = 0.0728\,\mathrm{N\,m^{-1}}, μ=1.00×10−3 Pa s\mu = 1.00\times10^{-3}\,\mathrm{Pa\,s}) wicks with contact angle θc=0\theta_c = 0 (fully wetting). Gravity is negligible compared with the capillary suction. ((a)) By balancing the Laplace suction at the advancing meniscus against the Poiseuille resistance of the column of liquid already drawn into a capillary of length L(t)L(t), derive Washburn's law relating LL and tt. ((b)) Use the result to predict the time needed for the sample to travel the strip's full length of L=25 mmL = 25\,\mathrm{mm}.

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