Viscosity Controls Rapid Infiltration and Drainage, Not the Macropores

The paper argues that universal approaches to infiltration and drainage in permeable media pivoting around capillarity and leading to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has to account for relatively fast infiltration and drainage based on Newton’s viscous shear flow, while the other one draws from capillarity and is responsible for storage and relatively slow redistribution of soil water. Already in the second half of the 19th Century were two separate processes postulated, however, Buckingham’s and Richards’ apparent universal capillarity-based approaches to the flow and storage of water in soils dominated. The paper introduces the basics of Newton’s shear flow in permeable media. It then presents experimental applications, and explores the relationships of Newton’s shear flow with Darcy’s law, Forchheimer’s and Richards’ equations, and finally extends to the transport of solutes and particles.

Motion of a non-axisymmetric particle in viscous shear flow

We examine the motion in a shear flow at zero Reynolds number of particles with two planes of symmetry. We show that in most cases the rotational motion is qualitatively similar to that of a non-axisymmetric ellipsoid, and characterised by a combination of chaotic and quasiperiodic orbits. We use Kolmogorov–Arnold–Moser (KAM) theory and related ideas in dynamical systems to elucidate the underlying mathematical structure of the motion and thence to explain why such a large class of particles all rotate in essentially the same manner. Numerical simulations are presented for curved spheroids of varying centreline curvature, which are found to drift persistently across the streamlines of the flow for certain initial orientations. We explain the origin of this migration as the result of a lack of symmetries of the particle’s orientation orbit.

Floquet stability analysis of capsules in viscous shear flow

Observations in experiments and simulations show that the kinematic behaviour of an elastic capsule, suspended and rotating in shear flow, depends upon the flow strength, the capsule membrane material properties and its at-rest shape. We develop a linear stability description of the periodically rotating base state of this coupled system, as represented by a boundary integral flow formulation with spherical harmonic basis functions describing the elastic capsule geometry. This yields Floquet multipliers that classify the stability of the capsule motion for elastic capillary numbers $Ca$ ranging from $Ca=0.01$ to 5. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon $Ca$, over many periods of the rotation. The transitions in this stability behaviour correspond to the different classes of rotating motion observed in previous studies.