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• W1972336618 abstract "The structure of a Wood's metal [1] slow invasion front into homogeneous crushed glass is analyzed in the framework of a “gradient percolation” model allowing to account for the influence of gravity. We show that this model accounts quantitatively well for experimental observations and permits a detailed analysis of the experimental front structures. Invasion of a porous medium by a non-wetting fluid at low velocity and under zero gravity is correctly described by the “invasion percolation” model [2]. However, in most 3D systems, it is not possible to neglect the influence of gravity. The hydrostatic component adds up with the applied injection pressure: this creates a vertical gradient of the effective injection pressure. This missing gradient term has been recently introduced to analyse 2D and 3D diffusion processes [3]. In the “gradient percolation” model a linear variation of the percolation parameter is introduced along a lattice axis. As a consequence there appears a “front” connected to the high occupation region by a continuous chain of occupied sites. This “front” is equivalent to the front surface limiting the invaded volume in the invasion experiment [4]. Experiments can be shortly described as follows [1]: Wood's metal is injected at the bottom of a vertical evacuated crushed glass column. The flow velocity is kept low (a few mm/h) so that viscous pressure losses can be neglected. When the front has reached a given height, the injection is stopped and the liquid is solidified; then horizontal sections of the front corresponding to various heights z are analyzed. The pictures are digitized into a square lattice of pixels and “invaded” or “empty” pixels are discriminated by a threshold procedure. The correlation function C(r) of the metal distribution in horizontal planes is determined and compared to the corresponding quantity obtained from the numerical simulation for sites located on the gradient front: it is the key tool for comparing experimental and theoretical data. In both cases, close to pc in a range of r values between the individual grain size d and an upper limit γ (crossover length), C(r) varies roughly as: C(r) ∝ rDfr−2 indicating that the cut structure is fractal with a dimension Dfr at short distances. When r is larger than γ, C(r) is constant and equal to a value S proportional to the mean metal saturation. We show that the experimental 2D correlation function C(r) follows the universal behaviour predicted by the gradient percolation model. A good fit is obtained for realistic values of the geometric adjustable parameters; however the value Dfr = 2.4 obtained for the fractal dimension of the front is smaller than the value 2.54 expected for classical 3D percolation. The variations of the mean fluid saturation and crossover length γ with the cut height are in agreement with the numerical simulation results." @default.
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• W1972336618 date "1989-05-01" @default.
• W1972336618 modified "2023-10-01" @default.
• W1972336618 title "Invasion of a porous medium under gravity: A quantitative analysis" @default.
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• W1972336618 doi "https://doi.org/10.1016/0378-4371(89)90349-x" @default.
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