Snapshots from network simulations with Bond numbers comparable to those set by the inclinations in the experiments. Invading air is in white; dense wetting defending fluid is in black. The first two columns show the displacement structure after, respectively, 8% and 16% of air has saturated the medium; the two last ones show the breakthrough and final configurations.

Snapshots from network simulations with Bond numbers comparable to those set by the inclinations in the experiments. Invading air is in white; dense wetting defending fluid is in black. The first two columns show the displacement structure after, respectively, 8% and 16% of air has saturated the medium; the two last ones show the breakthrough and final configurations.

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We experimentally and numerically study the influence of gravity and finite-size effects on the pressure-saturation relationship in a given porous medium during slow drainage. The effect of gravity is systematically varied by tilting the system relative to the horizontal configuration. The use of a quasi two-dimensional porous media allows for dire...

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... 2 of 16 notable role (Ayaz et al., 2020;Kuang et al., 2011;Luo et al., 2020). Moreover, there are now published datasets consisting of stacks of many tomograms taken at different elevations of the sample (Jackson, 2019) resulting in very tall images. ...
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... Let L be the length of the porous model and assume L > w. The final saturation behind the front of the invading fluid and its dependence on the pressure across the model has been studied in Ref. [81]. In this study, we considered the volume of the invaded fluid in boxes with size corresponding to the width of the invading front. ...
... On length scales below this size, the structure of the invading fluid is fractal, while on length scales larger than this size, the structure is homogeneous. For sufficiently large F, when η is the characteristic length scale of the front, the saturation S F nw of the nonwetting fluid behind the front becomes [81]. ...
... (50) Figure 11 shows a two-dimensional invasion percolation simulation with a gravitational field together with drainage experiments performed by Ayaz et al. [81]. The red dash-dotted line confirms the predictions of the theoretical scaling in Eq. 49. ...
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We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In the theoretical framework presented, the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invading structure and its boundary, and the exponent describing the divergence of the correlation length in percolation. Furthermore, our theoretical description explains how the Haines jumps’ local activity and dissipation relate to dissipation on larger scales.
... Let L be the length of the porous model and assume L > w. The final saturation behind the front of the invading fluid and its dependence on the pressure across the model has been studied in reference [62]. In those studies we considered the volume of the invaded fluid in boxes corresponding to the width of the invading front. ...
... On length scales below this length scale, the structure of the invading fluid will be fractal, while on length scales larger than this length scale the structure will be homogeneous. For sufficient large F , when η is the characteristic length scale of the front, the saturation S F nw of the non-wetting fluid behind the front will be [62] S F nw ∝ where d is the spatial dimension (2 or 3). Hence using Eq. ...
... However, when the fluctuation number F is sufficient small, η > w, and the width of the model w will be the characteristic length scale in the problem. Then Fig. 11 shows two dimensional invasion percolation simulation with a gravitational field and experiments, by Ayaz et al. [62]. In the equations above we have neglected the boundary effects at the inlet and outlet since L/w 1. ...
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We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In this theory the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invasion front and the invading structure, and the exponent describing the divergence of the correlation length in percolation. This theoretical description explains how the Haines jumps' local activity and dissipation relate to dissipation on larger scales.
... Let L be the length of the porous model and assume L > w. The final saturation behind the front of the invading fluid and its dependence on the pressure across the model has been studied in Ref. [82]. In this study, we considered the volume of the invaded fluid in boxes with size corresponding to the width of the invading front. ...
... On length scales below this size, the structure of the invading fluid is fractal, while on length scales larger than this size, the structure is homogeneous. For sufficiently large F , when η is the characteristic length scale of the front, the saturation S F nw of the nonwetting fluid behind the front becomes [82] S F nw ∝ ...
... However, when the fluctuation number F is sufficient small, η > w, and the width of the model w will be the characteristic length scale in the problem. Then Fig. 11 shows a two-dimensional invasion percolation simulation with a gravitational field together with drainage experiments performed by Ayaz et al. [82]. The red dash-dotted line confirms the predictions of the theoretical scaling in Eq. (49). ...