Quasi-steady imbibition of physiological liquids in paper-based microfluidic kits: Effect of shear-thinning

Abstract

In the present work, spontaneous imbibition of shear-dependent fluids is numerically investigated in a two-layered, rectangular/fan-shaped, paper-based diagnostic kit using the modified Richards equation. It is shown that the average velocity at the test line of the kit is strongly influenced by the absorbent pad's microstructure with its contact angle playing a predominant role. Assuming that the test fluid is shear-thinning, a generalized version of the Richards equation, valid for power-law fluids, was used to investigate the effect of shear-thinning on the quasi-steady regime. The shear-thinning behavior of the test fluid is predicted to shorten the duration of the constant-velocity regime on the nitrocellulose membrane used as the test cell. By manipulating the contact angle and/or choosing appropriate microstructure for the absorbent pad, it is still possible to establish a constant velocity regime at the test line for nearly five minutes even for such fluids. A comparison between our numerical results and published numerical results obtained using simplistic theories has revealed the key role played by the transition, partially-saturated zone near the advancing front during the liquid imbibition. The general conclusion is that use should preferably be made of robust models such as Richards equation for the design of lateral-flow, paper-based assays.

Viscoelastic Effects on Spontaneous Imbibition in Unsaturated Porous Membranes of Complex Shapes

“…The two-phase form of the modified Darcy’s law, valid for imbibition of viscoelastic fluids, reads as + ∇ p c false( S false) = true( μ eff ( S ) k ( S ) boldq true) true[ 1 + α true∥ boldq true∥ β true] Now, what remains to be done is to properly model μ eff ( S ), k ( S ), and ∇⃗ p c ( S ) in this equation. For μ eff ( S ), we rely on the relationship recently developed by Asadi et al for power-law fluids μ eff ( S ) = m ( 3 n + 1 4 n ) true( 1 2 m true) ( n − 1 ) / n false( false| ∇ p c ( S ) false| false) ( n − 1 ) / n true( 8 κ ( 19 / 18 ) ln ⁡ ε / ln false( 8 / 9 false) S − 0.4 · k false( S false) ε true) ...…”

“…Due to the severe nonlinearity of the VRE model, an analytical solution of the equations in this model (i.e., eqs 12a–12c) is deemed out of sight, and so we look for a numerical solution. In our recent works, , we have shown that the PDE solver of the finite element software package COMSOL can be used with great success for simulating imbibition flows of non-Newtonian fluids obeying the power-law model. For this reason, in the present work, we have decided to rely on the same solver for simulating the imbibition flow of viscoelastic fluids.…”

“…Now, what remains to be done is to properly model μ eff (S), k(S), and ∇ ⃗ p c (S) in this equation. For μ eff (S), we rely on the relationship recently developed by Asadi et al 6 for power-law fluids…”

“…1 But, industrial and physiological fluids are often realized to exhibit non-Newtonian behavior, and for such complex fluids, only recently, we are witnessing the development of theoretical imbibition models. One can particularly mention the recent works by Asadi et al 6,7 for inelastic shear-dependent fluids obeying the power-law model. 8 But, as stands, the effect of viscoelasticity on spontaneous imbibition still remains unexplored.…”

“…They speculated that perhaps the weight of the imbibed liquid was to blame, their theoretical model lacked the gravitational term. Asadi et al 6 included the gravitational term in their generalized Richards equation (developed for predicting imbibition of power-law fluids) and reached to the conclusion that gravity played no significant role simply because the height of the sandstone core sample used in the tests was just 5 cm. So, as stands, the main cause of the discrepancy in the work of Zhu et al 9 remains unexplored.…”