Nanocatalytic chemohydrodynamic instability: Deposition effects

Due to the high surface area to volume ratio of nanoparticles, nanocatalytic reactive flows are widely utilized in various applications, such as water purification, fuel cell, energy storage, and biodiesel production. The implementation of nanocatalysts in porous media flow, such as oil recovery and contaminant transport in soil, can trigger or modify the interfacial instabilities called viscous fingering. These instabilities grow at the interface of the fluids when a less viscous fluid displaces a high viscous one in porous media. Here the flow dynamics and the total amount of chemical product are investigated when two reactive miscible fluids meet in a porous medium while undergoing $\mathrm{A}+\mathrm{B}+\mathrm{n}$ $\to$ $\mathrm{C}+\mathrm{n}$ reaction. Nanocatalysts (n) are dispersed in the displacing fluid and deposited gradually with time. Four generic regimes are observed over time as a result of the particle deposition: (1) the initial diffusive regime, where the flow is stable with decreasing production rate, (2) the mixing-dominant fingering regime, where the flow is unstable and the production rate generally increases, (3) the transition regime, where the production rate generally decreases regardless of whether the system is stable or unstable, and (4) the final zero-production regime, where the product diffuses and fades away in the channel. Although the general trend shows a decreasing reaction rate with nanocatalysts deposition, there is a period in which the production rate increases due to the moderate deposition rates. Such an increase of production, however, is not observed in two groups: first, those systems in which the nanocatalysts do not change the viscosity of the base fluid and, second, a subgroup of the systems that are stable before and after the reaction in the absence of deposition.

Figure 1

Schematic diagram of the numerical simulation of nanocatalytic reactive flow undergoing $\mathrm{A}+\mathrm{B}+\mathrm{n}$ $\to$ $\mathrm{C}+\mathrm{n}$ reaction in a porous medium.

Figure 2

The general trends of (a) the variation of total amount of chemical product in log-log scale and (b) the rate change of total amount of chemical product with time, in an intrinsically unstable system with $R_c=1$, ${\text{Da}}_{dep}=0.008$. The snapshots are the contours of $C_c$ at $t=100,300,600$, and 1500, corresponding to each of the four generic regimes observed: diffusive, mixing-dominate, transition, and zero-production, respectively.

Figure 3

Variation of the total amount of chemical product, ${\left(C_c\right)}_t\left(t\right)$, over time at different deposition rates, ${\text{Da}}_{dep}$, in the intrinsically unstable system with $R_c=1$, plotted in a log-log scale.

Figure 4

Contours of $C_c$ at different deposition rates, ${\text{Da}}_{dep}$ in two intrinsically unstable systems, with $R_c=1$ (left) and $R_c=7$ (right); $t=1500$.

Figure 5

Contours of $C_a$ (left) and $C_c$ (right) in the intrinsically unstable system with $R_c=1$ and ${\text{Da}}_{dep}=0.004$. The corresponding time of the snapshots: $t=500,600,800,1000,1400,1800,2000,$ and 2500 from the top to bottom, respectively.

Figure 6

Variation of the total amount of chemical product, ${\left(C_c\right)}_t$, with deposition rate, ${\text{Da}}_{dep}$, in two intrinsically stable systems: (a) $R_c=-3$, and (b) $R_c=-0.5$, plotted in a log-log scale.

Figure 7

Contours of $C_c$ at different deposition rates, ${\text{Da}}_{dep}$, in the intrinsically stable-stable system for (a) $R_c=-3$ and (b) $R_c=-0.5$; Here $t=4000$.