Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid

Cieszko, M.; Kubik, J.

doi:10.1007/978-94-011-4579-4_20

Cited by 18 publications

(21 citation statements)

References 21 publications

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“…However, when the linearization procedure is performed in the neighborhood of a state in which some velocity fields are not vanishing then inertial terms cannot be neglected, even when Rayleigh modeling hypothesis applies. Finally one should remark that in Ochoa-Tapia and Whitaker (1998) some inertial effects at the interface are considered. However, they deduce no-slip conditions for tangential velocity and a normal-to-the-interface boundary condition by means of an averaging procedure involving "excess quantities".…”

Section: Discussionmentioning

confidence: 99%

“…in Baek and Srinivasa (2004) (the spirit of which is very similar to the one adopted here). Several versions of "surface balance of force" or "kinematical boundary conditions" can be found in Deresiewicz (1963), Ciezko and Kubik (1998a-b), Debergue et al (1999), Goyeau et al (2003), Haber and Mauri (1983), Kuznetsov (1997), Le Bars and Grae Worster (2006), Levy and Sanchez-Palencia (1975), Rajagopal and Tao (1995), Sharma (2008), Ochoa-Tapia and Whitaker (1998). Our boundary conditions seem suitable to describe (macroscopically) the behavior of solid material interfaces open to fluid flow.…”

Section: Introductionmentioning

confidence: 96%

“…Mandel (1953), Terzaghi (1943)) or the phenomena involved in earthquakes (see e.g. Yang (1999) or in the bradyseism and in the related micro-earthquakes in the Phlegraean Fields -Campi Flegrei region (South Italy) (see dell'Isola a et al (1998) and references there cited, Casertano et al (1976), Orsi et al (1999)). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluid Shock Wave Generation at Solid-Material Discontinuity Surfaces in Porous Media

Dell’Isola

Seppecher

Madeo

2011

Variational Models and Methods in Solid and Fluid Mechanics

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

Fluid Shock Wave Generation at Solid-Material Discontinuity Surfaces in Porous Media

Dell’Isola

Seppecher

Madeo

2011

Variational Models and Methods in Solid and Fluid Mechanics

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“…Such a system permits to study characteristic traits of the flows in beds of rivers (canals, pipes, lakes) with obstacles at the bottom (such as stones, plants or other structures), cf. [3][4][5][6][7][8][9][10].…”

Section: Motivation Of the Papermentioning

confidence: 99%

Laminar flow past the bottom with obstacles – a suspension approximation

Wojnar¹,

Bielski²

2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. From Albert Einstein's study (1905) it is known that suspension introduced to a fluid modifies its viscosity. We propose to describe the influence of obstacles on the Stokesian flow as a such modification. Hence, we treat the fluid flow through small obstacles as a flow with suspension. The flow is developing past the plane bottom under the gravity force. The spatial distribution of suspension concentration is treated as given, and is regarded as an approximation of different obstacles which modify the fluid flow and change its viscosity. The different densities of suspension are considered, beginning of small suspension concentration until 40%. The influence of suspension concentration on fluid viscosity is analyzed, and Brinkman's formula as fitting best to experimental data is applied.

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“…(1). In analogy to the contact force, a new penalty parameter ε p N is introduced for the efflux of the pore-fluid at the contact boundary as…”

Section: Theory Of Porous Mediamentioning

confidence: 99%

Numerical Modelling of Contact Problems with Application to Porous Media

Yang

Ehlers

Markert

et al. 2003

Proc Appl Math and Mech

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Contact problems are highly non-linear because of the non-penetration inequality in the contact interface. To solve such problems, different constraint methods are used to transform the inequality into an equality problem [4]. Concerning the contact of two isotropic fluid-saturated porous solids which consist of an immiscible mixture of a solid skeleton and a fluid pore content [3], the non-penetration constraint can be applied to the mixture approach by accounting additionally for the pore-fluid interchange between the contacting porous solids.

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Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid

Cited by 18 publications

References 21 publications

Fluid Shock Wave Generation at Solid-Material Discontinuity Surfaces in Porous Media

Fluid Shock Wave Generation at Solid-Material Discontinuity Surfaces in Porous Media

Laminar flow past the bottom with obstacles – a suspension approximation

Numerical Modelling of Contact Problems with Application to Porous Media

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