Variational formulation of oscillating fluid clusters and oscillator-like classification. I. Theory

Kurzeja, Patrick; Steeb, Holger

doi:10.1063/1.4871486

Cited by 13 publications

(13 citation statements)

References 29 publications

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“…The first term in (5) implies interfacial viscous coupling whereas the second term introduces a pressure jump condition according to the Young-Laplace equation [49].…”

Section: Direct Numerical Simulation Approachmentioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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We perform pore-scale resolved direct numerical simulations of immiscible two-phase flow in porous media to study the evolution of fluid interfaces. Using a Smoothed-Particle Hydrodynamics approach, we simulate saturation-controlled primary drainage in heterogeneous, partially wettable 2D porous microstructures. While imaging the evolution of fluid interfaces near capillary equilibrium becomes more feasible as fast X-ray tomography techniques mature, imaging methods with suitable temporal resolution for viscous-dominated flow have only recently emerged. In this work, we study viscous fingering and stable displacement processes. During viscous fingering, pore-scale flow fields are reminiscent of Bretherton annular flow, that is, the less viscous phase percolates through the core of a pore-throat forming a hydrodynamic wetting film. Even in simple microstructures wetting films have major impact on the evolution of fluid interfacial area and are observed to give rise to nonnegligible interfacial viscous coupling. Although macroscopically appearing flat, saturation fronts during stable displacement extend over the length of the capillary dispersion zone. While far from the dispersion zone fluid permeation obeys Darcy's law, the interplay of viscous and capillary forces is found to render fluid flow within complex. Here we show that the characteristic length scale of the capillary dispersion zone increases with the heterogeneity of the microstructure.

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“…The first term in (5) implies interfacial viscous coupling whereas the second term introduces a pressure jump condition according to the Young-Laplace equation [49].…”

Section: Direct Numerical Simulation Approachmentioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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“…For example, the dispersion of phase velocities in multiphase media is closely related to the decoupling process of solid and fluid and therefore depends on the frequency-dependent flow profiles [1,4]. In the case of residual saturation, the material and geometrical fluid cluster properties determine their resonance effects and can be characterized by their dynamic response in the frequency domain [3,6,7]. In all cases, a smart focus on the frequency regime of the relevant phenomena supports fundamental research as well as applications in classical and modern materials.…”

Section: Discussionmentioning

confidence: 99%

“…They determine capillary pressure and resonance effects of enclosed fluid conglomerations [2,3]. Frequency dependence was also proven for fluid-fluid interactions such as the resonance behavior of fluid clusters [6,7]. The corresponding characteristic number is the capillary number.…”

Section: Needs and Effective Usementioning

confidence: 99%

“…In all cases, an accurate description is of vital importance for reliable predictions and interpretation. For example, changing flow profiles can lead to modified attenuation regimes and multiple oscillations modes yield distinct stimulation regimes of enclosed fluid clusters [6,9]. Moreover, wrong assumptions can lead to errors of several hundred percent when estimating characteristic frequencies, for instance, in the case of osteoporotic bone or high-porosity foams [4].…”

Section: Needs and Effective Usementioning

confidence: 99%

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Frequency‐dependent properties of multiphase materials: origins, needs, and effective use in geophysics and modern synthetic materials.

Kurzeja

Steeb

2014

Proc Appl Math and Mech

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Dynamic processes in multiphase materials, e.g., fluid-filled sandstones or bones, are described by models that include frequency-dependent properties. The origin of such properties is introduced as an averaged representation of frequencydependent microscale motions. In addition to classical frequency-dependence of fluid flow, the influence of weak, highporosity materials and fluid-fluid interfaces is discussed. The relevant characteristic numbers are contrasted and specific situations are demonstrated, in which frequency dependence has to be considered or not.

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“…Among the modelling approaches using an energy potential, a common limiting case is a free energy that is proportional to surface tension and interfacial areas yielding p c|A eq = σ ∂a wn ∂s w , ( 3.4) which may also be introduced as an a priori definition in compliance with assumptions I-X. Also note the analogous counterpart in the microscopic virtual work p c,micro dV micro = σ dA micro [57,58].…”

Section: (B) Definitions Of Macroscopic Capillary Pressurementioning

confidence: 97%

The criterion of subscale sufficiency and its application to the relationship between static capillary pressure, saturation and interfacial areas

Kurzeja

2016

Proc. R. Soc. A.

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Modern imaging techniques, increased simulation capabilities and extended theoretical frameworks, naturally drive the development of multiscale modelling by the question: which new information should be considered? Given the need for concise constitutive relationships and efficient data evaluation; however, one important question is often neglected: which information is sufficient? For this reason, this work introduces the formalized criterion of subscale sufficiency. This criterion states whether a chosen constitutive relationship transfers all necessary information from micro to macroscale within a multiscale framework. It further provides a scheme to improve constitutive relationships. Direct application to static capillary pressure demonstrates usefulness and conditions for subscale sufficiency of saturation and interfacial areas.

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Variational formulation of oscillating fluid clusters and oscillator-like classification. I. Theory

Cited by 13 publications

References 29 publications

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Frequency‐dependent properties of multiphase materials: origins, needs, and effective use in geophysics and modern synthetic materials.

The criterion of subscale sufficiency and its application to the relationship between static capillary pressure, saturation and interfacial areas

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