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

Richards equation is a robust mathematical model for predicting spontaneous imbibition in unsaturated porous materials, whether granular or fibrous. The main restriction of this imbibition model is that it is valid only for Newtonian fluids. In the present work, we extend the classic Richards equation to viscoelastic fluids using a modified version of the single-phase Darcy's law reported in the literature for several polymer solutions. In two-dimensional flows, the viscoelastic Richards model obtained this way turns out to be in the form of a system of three highly nonlinear coupled partial differential equations for the moisture content and the velocity field. The model is numerically validated against published experimental data for a shear-thinning polymer solution imbibed in a tight sandstone core sample extracted from a typical oil reservoir. The viscoelastic Richards model is then used to investigate the effect of a fluid's elasticity on the quasi-stationary regime in a two-dimensional porous membrane of complex shape typically used in diagnostic kits. The obtained numerical results suggest that elasticity has a retarding effect on spontaneous imbibition in capillary-driven, paper-based kits. Based on this new imbibition model, it is predicted that viscoelasticity of the displacing liquid can extend the duration of the quasi-stationary regime on the test line of diagnostic kits. The conclusion is that, for extending the quasi-steady regime in capillary-driven kits, it might prove useful to enhance the degree of elasticity of the test fluids using appropriate rheology modifiers.

Capillary imbibition and flow of wetting liquid in irregular capillaries: A 100-year review

Capillary imbibition, such as plant roots taking up water, reservoir rocks absorbing brine and a tissue paper wiping stains, is pervasive occurred in nature, engineering and industrial fields, as well as in our daily life. This phenomenon is earliest modeled through the process that wetting liquid is spontaneously propelled by capillary pressure into regular geometry models. Recent studies have attracted more attention on capillary-driven flow models within more complex geometries of the channel, since a detailed understanding of capillary imbibition dynamics within irregular geometry models necessitates the fundamentals to fluid transport mechanisms in porous media with complex pore topologies. Herein, the fundamentals and concepts of different capillary imbibition models in terms of geometries over the past 100 years are reviewed critically, such as circular and non-circular capillaries, open and closed capillaries with triangular/rectangular cross-sections, and heterogeneous geometries with axial variations. The applications of these models with appropriate conditions are discussed in depth accordingly, with a particular emphasize on the capillary flow pattern as a consequence of capillary geometry. In addition, a universal model is proposed based on the dynamic wetting condition and equivalent cylindrical geometry to describe the capillary imbibition process in terms of various solid topologies. Finally, future research is suggested to focus on analyzing the dynamics during corner flow, the snap-off of wetting fluid, the capillary rise of non-Newtonian fluids and applying accurate physical simulation methods on capillary-driven flow processes. Generally, this review provides a comprehensive understanding of the capillary-driven flow models inside various capillary geometries and affords an overview of potential advanced developments to enhance the current understanding of fluid transport mechanisms in porous media.

Quantitative model for predicting the imbibition dynamics of viscoelastic fluids in nonuniform microfluidic assays

We develop a mathematical model to quantitatively describe the imbibition dynamics of an elastic non-Newtonian fluid in a conical (nonuniform cross section) microfluidic assay. We consider the simplified Phan-Thien-Tanner viscoelastic model to represent the rheology of the elastic non-Newtonian fluid. Our model accounts for the geometrical features of the fluidic assay, the key parameters affecting the rheological behavior of the fluid, and predicts the imbibition dynamics effectively. By demonstrating the temporal advancement of the filling length in the conical capillary graphically, obtained for pertinent parametric values belonging to their physically permissible range, we report an underlying balance between capillary and viscous forces during imbibition resulting in three distinct regimes of filling. Nonuniformity in the capillary cross section gives rise to an alteration in the viscous force being applied at the contact line (manifested through the alteration in shear rate) during the imbibition process, which upon maintaining a balance with the dominant capillary force results in three different regimes of filling. We believe that the present analysis has a twofold significance. First, this work will enhance the understanding of underlying imbibition dynamics of viscoelastic fluids (most of the biofluids exhibit viscoelastic rheology) in nonuniform fluidic pathways. Second, the developed model is of significant practical relevance for the optimum design of microfluidic assays, primarily used for sample diagnostics in biochemical and biomedical applications.