Water ( , ) wicks into a dry cotton fabric whose pores behave as cylindrical…

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

Water (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 into a dry cotton fabric whose pores behave as cylindrical capillaries of radius r=5.0 μmr=5.0\,\mu\mathrm{m}. The water fully wets the fibres, so the contact angle θc≈0\theta_c\approx0. ((a)) Using Washburn's law, L2=γrcos⁡θc t/(2μ)L^2 = \gamma r\cos\theta_c\,t/(2\mu), find the time needed for the wetted front to advance L=3.0 cmL=3.0\,\mathrm{cm}. ((b)) Find how far the front would have advanced after four times that time.

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