The fastest capillary penetration of power-law fluids

Shou, Dahua; Fan, Jintu

doi:10.1016/j.ces.2015.07.009

Cited by 24 publications

(8 citation statements)

References 36 publications

(51 reference statements)

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“…Later fractal modeling of fluids’ flows in porous random media [ 49 ], including transport through tree-like networks and diffusion on fractals [ 50 ] was widely used in oil recovery studies [ 51 ]. This modeling was supported by theoretical and experimental studies demonstrating that fluid’s flow through tree-like networks is faster [ 52 , 53 ].…”

Section: Geophysics: From Fractal To Tree-like Modelsmentioning

confidence: 79%

“…Finally, we remark that the tree-like structure of capillary networks is not only very common in nature, but recently they started to be artificially manufactured—to speed up fluid’s propagation (see [ 56 ] and references herein). This applied research is theoretically justified by the works of Shou et al [ 52 , 53 ] on the tree-like basis of acceleration of fluid’s flows (see also [ 57 ] on p -adic modeling). Such industrial applications stimulate p -adic (and more general ultrametric) modeling of fluids’ propagation in tree-like capillary networks.…”

Section: Navier—stokes Equation On Tree-like Configuration Space Amentioning

confidence: 92%

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Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

Pourhadi

Khrennikov

Saadati

et al. 2019

Entropy

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P-adic numbers serve as the simplest ultrametric model for the tree-like structures arising in various physical and biological phenomena. Recently p-adic dynamical equations started to be applied to geophysics, to model propagation of fluids (oil, water, and oil-in-water and water-in-oil emulsion) in capillary networks in porous random media. In particular, a p-adic analog of the Navier–Stokes equation was derived starting with a system of differential equations respecting the hierarchic structure of a capillary tree. In this paper, using the Schauder fixed point theorem together with the wavelet functions, we extend the study of the solvability of a p-adic field analog of the Navier–Stokes equation derived from a system of hierarchic equations for fluid flow in a capillary network in porous medium. This equation describes propagation of fluid’s flow through Geo-conduits, consisting of the mixture of fractures (as well as fracture’s corridors) and capillary networks, detected by seismic as joint wave/mass conducts. Furthermore, applying the Adomian decomposition method we formulate the solution of the p-adic analog of the Navier–Stokes equation in term of series in general form. This solution may help researchers to come closer and find more facts, taking into consideration the scaling, hierarchies, and formal derivations, imprinted from the analogous aspects of the real world phenomena.

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Section: Geophysics: From Fractal To Tree-like Modelsmentioning

confidence: 79%

Section: Navier—stokes Equation On Tree-like Configuration Space Amentioning

confidence: 92%

Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

Pourhadi

Khrennikov

Saadati

et al. 2019

Entropy

View full text Add to dashboard Cite

show abstract

“…Theoretically, Shou & Fan (2015) had success studying non-Newtonian power-law fluids in different configurations of tubing networks and showed that the rising dynamics is influenced by the viscous and capillary forces while examining the conditions that ensure the quickest rise. Furthermore, using Stokesian dynamics, Kiradjiev, Breward & Griffiths (2019) mathematically analysed the viscous spreading of a -influenced liquid drop injected through a substrate and correlated the power-law injection time rate () with the film spreading.…”

Section: Introductionmentioning

confidence: 99%

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

et al. 2022

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The unsteady effects of transitioning surface tension, $\gamma (t)$ , on the dynamics of capillary imbibition in channels of arbitrary shape are analytically investigated with a focus on rectangular and circular channels. With proper scaling, two unsteady models for $\gamma (t)$ are defined and used to highlight this transient behaviour. The convoluted dynamics at the flow front are correctly captured in the governing equations, which are rigorously analysed using unsteady eigenfunction expansion. Then, the final solution and data are obtained by employing the Runge–Kutta fourth-order scheme elegantly applied simultaneously to two derived nonlinear ordinary differential equations. Ultimately, the results are more accurate compared with previous studies. Dynamics and kinematic similarity between rectangular and circular channels are investigated and discussed and the conditions for equivalence in both channels are highlighted. Using a small parameter ( $\epsilon$ ) that stretches the time scale, we successfully use a robust asymptotic analysis to develop and capture the long-time dynamics. Ultimately, we recover the Lucas–Washburn regime analysed in Washburn (Phys. Rev., vol. 17, 1921, pp. 273–283), Lucas (Kolloidn. Z., vol. 23, 1918, pp. 15–22) for steady surface tension where the variations of depth and rate with time result in $h\thicksim t^{1/2}$ and $v \thicksim t^{-1/2}$ . In the end, the three forces, namely the inertia, $F_{v}$ , the viscous, $F_{\mu }$ , and the surface tension, $F_{\gamma }$ , are briefly analysed and used to highlight three main distinct regimes. We show that at early times, $F_{v}/F_{\gamma } \thicksim 1$ , whereas at a long time, $F_{\mu }/F_{\gamma } \thicksim -1$ .

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“…Hence, the graphene/h-BN heterostructure is a promising form to open up new possibilities in different fields. It is necessary to explore the application of heterostructures as substrates to drive the spontaneous movement of water droplets [40][41][42].…”

mentioning

confidence: 99%

Spontaneous transport of water nanodroplets on graphene and hexagonal boron nitride in-plane heterostructure

Hao¹,

Wang²,

Kou³

et al. 2022

EPL

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Developing a surface inducing water droplets to transport spontaneously is very important to energy conversion. Here we demonstrate by the molecular dynamics simulations that a water nanodroplet on graphene and hexagonal boron nitride (h-BN) in-plane heterostructure can move spontaneously from the narrower end of the wedge-shaped h-BN track to the wider end. The driving force comes from the capillary force caused by the surface energy gradient at the edge of the connection, which is attributed to the different interactions of the water nanodroplet with graphene and h-BN. The energy analysis shows that the h-BN acts as a driving force, while graphene a hindrance. We analyze the forces exerted on the water droplet and propose a theoretical model which indicates that the moving speed of the water nanodroplet can be controlled by the wedge angle and temperature. The present study suggests that the graphene/h-BN heterostructure is a potential material for driving droplets motion and can be explored to applications in microfluidic systems.

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The fastest capillary penetration of power-law fluids

Cited by 24 publications

References 36 publications

Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

Spontaneous transport of water nanodroplets on graphene and hexagonal boron nitride in-plane heterostructure

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