Convective mixing of carbon dioxide in geological formations follows different regimes During a regime in which the flux is constant, mixing in 3D simulations is 13% larger than in 2D simulations...

Convective mixing of carbon dioxide in geological formations follows different regimes During a regime in which the flux is constant, mixing in 3D simulations is 13% larger than in 2D simulations...

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The case shown here is We = 40, Oh = 0.0025. Paper: https://doi.org/10.48550/arXiv.2311.03012 Full description: Comparison of the drop impact force $F(t)$ obtained from experiments and simulations for the three typical cases with impact velocity $V_0 = 1.2\,\si{\meter}/\si{\second}, 0.97\,\si{\meter}/\si{\second}, 0.96\,\si{\meter}/\si{\second}$, diameter $D_0 = 2.05\,\si{\milli\meter}, 2.52\,\si{\milli\meter}, 2.54\,\si{\milli\meter}$, surface tension $\gamma = 72\,\si{\milli\newton}/\si{\meter}, 61\,\si{\milli\newton}/\si{\meter}, 61\,\si{\milli\newton}/\si{\meter}$ and viscosity $\eta_d = 1\,\si{\milli\pascal\second}, 25.3\,\si{\milli\pascal\second}, 80.2\,\si{\milli\pascal\second}$. These parameter give $Oh = 0.0025, 0.06, 0.2$ and $We = 40$. For the three cases, the two peak amplitudes, $F_1/(\rho_dV_0^2D_0^2) \approx$ 0.82, 0.92, 0.99 at $t_1 \approx 0.03\sqrt{\rho_dD_0^3/\gamma}$ and $F_2/(\rho_dV_0^2D_0^2) \approx$ 0.37, 0.337, 0.1 at $t_2 \approx 0.42\sqrt{\rho_dD_0^3/\gamma}$, characterize the inertial shock from impact and the Worthington jet before takeoff, respectively. The drop reaches the maximum spreading at $t_{\text{max}}$ when it momentarily stops and retracts until $0.8\sqrt{\rho_dD_0^3/\gamma}$ when the drop takes off ($F = 0$). The black and gray dashed lines in panel (a) mark $F = 0$ and the resolution $F = 0.5\,\si{\milli\newton}$ of our piezoelectric force transducer, respectively. We stress the excellent agreement between experiments and simulations without any free parameters. The left part of each numerical snapshot shows (on a $\log_{10}$ scale) the dimensionless local viscous dissipation function $\tilde{\xi}_\eta \equiv \xi_\eta D_0/\left(\rho_dV_0^3\right) = 2Oh\left(\boldsymbol{\tilde{\mathcal{D}}:\tilde{\mathcal{D}}}\right)$, where $\boldsymbol{\mathcal{D}}$ is the symmetric part of the velocity gradient tensor, and the right part the velocity field magnitude normalized with the impact velocity.