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1. Laboratory Measurements of Capillary-gravity Wave Scattering from Barriers with Contact Line Effects

   Wang, Zhengwu; Liu, Guoqin; Zhang, Likun (November 2023, 76th Annual Meeting of the Division of Fluid Dynamics)

   Contact lines at a three-phase boundary (solid, liquid and air) play an essential role in the dynamics of the free surface of liquids in surface-tension-dominated fluids. While previous studies on the contact line effect have mainly focused on frequency and damping of standing wave modes in capillary dynamics, our study focuses on the contact line effect on capillary-gravity wave scattering from barriers. Models have predicted the contact line effects on capillary-gravity wave scattering from a barrier in ideal fluid configurations, but the lack of experimental data has hindered the progress. This research presents an experimental study that utilizes an acoustic approach to measure variations of the scattering with the barrier depth, barrier width, and surface wave frequency. Our study provides both evidence and quantitative measurements of the contact line effect on capillary-gravity wave scattering in realistic fluid configurations. 

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2. Near-contact approach of two permeable spheres

   https://doi.org/10.1017/jfm.2021.588  

   Reboucas, Rodrigo B; Loewenberg, Michael (October 2021, Journal of Fluid Mechanics)

   An analysis is presented for the axisymmetric lubrication resistance between permeable spherical particles. Darcy's law is used to describe the flow in the permeable medium and a slip boundary condition is applied at the interface. The pressure in the near-contact region is governed by a non-local integral equation. The asymptotic limit$$K=k/a^{2} \ll 1$$is considered, where$$k$$is the arithmetic mean permeability, and$$a^{-1}=a^{-1}_{1}+a^{-1}_{2}$$is the reduced radius, and$$a_1$$and$$a_2$$are the particle radii. The formulation allows for particles with distinct particle radii, permeabilities and slip coefficients, including permeable and impermeable particles and spherical drops. Non-zero particle permeability qualitatively affects the axisymmetric near-contact motion, removing the classical lubrication singularity for impermeable particles, resulting in finite contact times under the action of a constant force. The lubrication resistance becomes independent of gap and attains a maximum value at contact$$F=6{\rm \pi} \mu a W K^{-2/5}\tilde {f}_c$$, where$$\mu$$is the fluid viscosity,$$W$$is the relative velocity and$$\tilde {f}_c$$depends on slip coefficients and weakly on permeabilities; for two permeable particles with no-slip boundary conditions,$$\tilde {f}_c=0.7507$$; for a permeable particle in near contact with a spherical drop,$$\tilde {f}_c$$is reduced by a factor of$$2^{-6/5}$$. 

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3. Experimental Study of Wetting effect on Capillary-gravity Wave Scattering from a Barrie

   Wang, Zhengwu; Liu, Guoqin; Zhang, Likun (November 2024, 77th Annual Meeting of the Division of Fluid Dynamics)

   The wetting phenomenon at three-phase boundaries (solid, liquid, and gas) affects capillary-gravity wave scattering from barriers, but there is a lack of experimental data and comparison with simulations. The scattering is affected by surface tension and the contact lines at the three-phase boundary. When the solid surface conditions vary, the contact angle and the shape of the meniscus generated by the wetting effect change accordingly. It is possible to measure the influence of the wetting effect on the scattering by coating the barrier surface to be hydrophobic or hydrophilic. Our previous work focused on how the scattering is affected by the portion of the barrier immersed under the water surface with a pinned contact line. In this study, we will coat the barrier surface to experimentally measure how the wetting with different coatings affect the scattering. A comparison of the experimental measurements with numerical simulations of potential flow of the waves will be potentially included. 

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4. Asymptotic solutions for self-similarly expanding fault slip induced by fluid injection at constant rate

   https://doi.org/10.1017/jfm.2025.10593  

   Viesca, Robert C (September 2025, Journal of Fluid Mechanics)

   We examine the circular, self-similar expansion of frictional rupture due to fluid injected at a constant rate. Fluid migrates within a thin permeable layer parallel to and containing the fault plane. When the Poisson ratio$$\nu =0$$, self-similarity of the fluid pressure implies fault slip also evolves in an axisymmetric, self-similar manner, reducing the three-dimensional problem for the evolution of fault slip to a single self-similar dimension. The rupture radius grows as$$\lambda \sqrt {4\alpha _{hy} t}$$, where$$t$$is time since the start of injection and$$\alpha _{hy}$$is the hydraulic diffusivity of the pore fluid pressure. The prefactor$$\lambda$$is determined by a single parameter,$$T$$, which depends on the pre-injection stress state and injection conditions. The prefactor has the range$$0\lt \lambda \lt \infty$$, the lower and upper limits of which correspond to marginal pressurisation of the fault and critically stressed conditions, in which the fault-resolved shear stress is close to the pre-injection fault strength. In both limits, we derive solutions for slip by perturbation expansion, to arbitrary order. In the marginally pressurised limit ($$\lambda \rightarrow 0$$), the perturbation is regular and the series expansion is convergent. For the critically stressed limit ($$\lambda \rightarrow \infty$$), the perturbation is singular, contains a boundary layer and an outer solution, and the series is divergent. In this case, we provide a composite solution with uniform convergence over the entire rupture using a matched asymptotic expansion. We provide error estimates of the asymptotic expansions in both limits and demonstrate optimal truncation of the singular perturbation in the critically stressed limit. 

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5. Resistance and mobility functions for the near-contact motion of permeable particles

   https://doi.org/10.1017/jfm.2022.171  

   Reboucas, Rodrigo B; Loewenberg, Michael (May 2022, Journal of Fluid Mechanics)

   A lubrication analysis is presented for the resistances between permeable spherical particles in near contact,$$h_0/a\ll 1$$, where$$h_0$$is the minimum separation between the particles, and$$a=a_1 a_2/(a_1+a_2)$$is the reduced radius. Darcy's law is used to describe the flow inside the permeable particles and no-slip boundary conditions are applied at the particle surfaces. The weak permeability regime$$K=k/a^{2} \ll 1$$is considered, where$$k=\frac {1}{2}(k_1+k_2)$$is the mean permeability. Particle permeability enters the lubrication resistances through two functions of$$q=K^{-2/5}h_0/a$$, one describing axisymmetric motions, the other transverse. These functions are obtained by solving an integral equation for the pressure in the near-contact region. The set of resistance functions thus obtained provide the complete set of near-contact resistance functions for permeable spheres and match asymptotically to the standard hard-sphere resistances that describe pairwise hydrodynamic interactions away from the near-contact region. The results show that permeability removes the contact singularity for non-shearing particle motions, allowing rolling without slip and finite separation velocities between touching particles. Axisymmetric and transverse mobility functions are presented that describe relative particle motion under the action of prescribed forces and in linear flows. At contact, the axisymmetric mobility under the action of oppositely directed forces is$$U/U_0=d_0K^{2/5}$$, where$$U$$is the relative velocity,$$U_0$$is the velocity in the absence of hydrodynamic interactions and$$d_0=1.332$$. Under the action of a constant tangential force, a particle in contact with a permeable half-space rolls without slipping with velocity$$U/U_0=d_1(d_2+\log K^{-1})^{-1}$$, where$$d_1=3.125$$and$$d_2=6.666$$; in shear flow, the same expression holds with$$d_1=7.280$$. 

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