Instabilities of nonisothermal nanocatalytic reactive flows in porous media

Instabilities of reactive miscible flows in homogeneous porous media are investigated in the presence of nanocatalysts undergoing $A+B+n\to C+n$ reaction. The analysis is conducted under both isothermal and nonisothermal conditions resulting from the heat of reaction. Ignoring double diffusive effects of the different components, a new set of conditions is introduced to predict the instability of the isothermal case based on the species mobility ratios. Validated with nonlinear simulations, these conditions predict well the instability of the system and how the chemical product develops after the reaction. Examination of flows that account for the heat of reaction with no effect on the mobility ratios reveals that these conditions are no longer valid. This result is in contrast with nanocatalyst-free flows. In these systems the stability condition is unaffected by the heat of reactions that has neutral effects on mobility ratios. This difference is attributed to the nanocatalysts transport phenomena and in particular to thermophoretic effects arising from the temperature gradients in the flow. These effects are analyzed for both exothermic and endothermic chemical reactions.

Figure 1

Schematic view of the medium.

Figure 2

One-dimensional Log-viscosity variation with respect to $\eta =\frac{x}{2\sqrt{t}}$ at asymptotically large times $(t\to \infty )$ along with insets of corresponding contours of $C_c$ derived from NLS. The contours are represented at $t=1000$ for intrinsically unstable and $t=1300$ for intrinsically stable systems.

Figure 3

Variation of the normalized first moment of the transversely averaged product concentration with the inset of contours of $C_c$. Dashed lines represent those systems with $\text{Da}=10$.

Figure 4

The effect of $R_c$ on the total amount of chemical products in the NP-laden isothermal reactive systems in the Log-Log scale.

Figure 5

The variation of $x_m$ with time at different thermophoretic diffusivities in both intrinsically unstable and stable reference systems along with the inset of the contours of $C_c$. The contours are depicted at identical times in each systems. The solid lines represent the systems with ${\delta }_T=0$.

Figure 6

The one-dimensional Log-viscosity variation in the reference systems in the presence (${\delta }_T=20$) and the absence of thermophoresis.

Figure 7

The one-dimensional NP concentration variation at different ${\delta }_T$ with constant $H_R=0.1$, and at two $H_R$ with constant ${\delta }_T=20,$ including the scaled convective and source/sink terms variation. The representative inset of the contours of $C_n$ derived from NLS are attached for ${\delta }_T=0$ and ${\delta }_T=20$.

Figure 8

Variation of ${\left(C_c\right)}_{r_i}$ in the representative systems at different thermophoretic diffusivities.