Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition

Khabthani, Sondes; Sellier, Antoine; Feuillebois, François

doi:10.1017/jfm.2019.169

Cited by 5 publications

(4 citation statements)

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“…Hydrodynamic interactions between spherical particles and thin, permeable layers have been analysed as a model for filtration (Goren 1979;Nir 1981;Debbech, Elasmi & Feuillebois 2010;Ramon & Hoek 2012;Ramon et al 2013;Khabthani, Sellier & Feuillebois 2019). Several studies explored the hydrodynamic interactions of spherical particles with permeable half-spaces Damiano et al 2004), conversely, others considered the interactions of permeable spheres with impermeable walls (Payatakes & Dassios 1987;Burganos et al 1992;Davis 2001;Roy & Damiano 2008), and a few analysed hydrodynamic interactions between pairs of permeable spheres (Jones 1978;Michalopoulou, Burganos & Payatakes 1993;Bäbler et al 2006).…”

Section: Introductionmentioning

confidence: 99%

“…Some used Darcy's law to describe the fluid flow in the permeable medium, others used Brinkman's equation (despite its limitations discussed above), the choice usually related to the porosity of the material (Auriault 2009). Most of the prior studies consider axisymmetric motion and the results show that permeability reduces hydrodynamic resistance (Goren 1979;Nir 1981;Payatakes & Dassios 1987;Burganos et al 1992;Michalopoulou et al 1992Michalopoulou et al , 1993Davis 2001;Debbech et al 2010;Ramon & Hoek 2012;Ramon et al 2013;Khabthani et al 2019).…”

Section: Introductionmentioning

confidence: 99%

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

Rebouças

Loewenberg

2022

J. Fluid Mech.

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Rebouças

Loewenberg

2022

J. Fluid Mech.

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“…A significant amount of work has focused on analyses of suspended spherical particles moving towards thin, permeable layers as a model for particle capture in filtration (Goren 1979; Nir 1981; Debbech, Elasmi & Feuillebois 2010; Ramon & Hoek 2012; Ramon et al. 2013; Khabthani, Sellier & Feuillebois 2019). In these studies, it was assumed that the fluid velocity normal to the permeable layer is proportional to the local pressure difference across the layer with proportionality , where is the permeance, a characteristic property of the layer.…”

Section: Introductionmentioning

confidence: 99%

Near-contact approach of two permeable spheres

Rebouças

Loewenberg

2021

J. Fluid Mech.

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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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“…The investigations on the flow problems in the area of porous media are being paid attention for a long time [4][5][6][7][8][9] by considering different boundary conditions at the porous interface, including no-slip and slip conditions [10,11]. Moreover, including the Saffman's condition, the lubricating flow of a sphere nearing a porous thin slab was analyzed by Khabthani et al [12]. Furthermore, Lai et al [13] carried out the work discussing the simple projection technique to know the coupling of Navier-Stokes along with Darcy's flow by employing the Beavers-Joseph-Saffman condition.…”

Section: Introductionmentioning

confidence: 99%

Archive of Mechanical Engineering

Bucha,

Prasad

2021

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The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy's equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel's and Kuwabara's cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.

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Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition

Cited by 5 publications

References 29 publications

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

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

Near-contact approach of two permeable spheres

Archive of Mechanical Engineering

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