A decorator's primer paint is modelled as a Bingham plastic with yield stress and density
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids
Bending, Ringing, Breaking and Flowing, Ch Non-Newtonian and viscoelastic fluids
Problem
A decorator's primer paint is modelled as a Bingham plastic with yield stress τy=6.0Pa and density ρ=1150kgm−3. It is applied to a vertical wall as a wet film of thickness h=0.35mm. The ridges a brush leaves are levelled by surface tension: with γ≈0.03Nm−1 and a ridge radius of curvature of about 0.1mm, their Laplace pressure γ/r is about 300Pa, far above τy, so the paint in the ridges yields. Once yielded, it flows and levels as a Maxwell fluid with relaxation time τM=3.0s, until the film stiffens as its solvent leaves. Take g=9.8ms−2.
((a)) Using the Bingham model for a layer on a vertical surface, find the greatest thickness of wet film this paint could support without sliding under its own weight, and confirm that the applied film of thickness h is stable.
((b)) The standard formulation is touch-dry (effectively solidified) after tdry=45minutes. Using the Deborah number De=τM/tdry, with the drying time as the observation time, decide whether the film has time to flow and erase the brush ridges before it sets, or whether it dries with the ridges frozen in.
((c)) A fast-curing variant of the same paint, intended for stencilling, sets touch-dry in tdry=0.50s. Repeat the Deborah-number judgement for this variant and state which of the two paints will show visible brush or spray-pattern marks once dry.