Simulation of particles dissolution in the shear flow: A combined concentration lattice Boltzmann and smoothed profile approach

A coupled DEM‐IMB‐LBM model for simulating methane hydrate exploitation involving particle dissolution

“…In the present study, it is assumed that particles keep circular shape during the dissolution process, which is always adopted in the simulation of moving particle dissolution 26–29 . According to Fick's first law, the change rate of the i th particle mass during dissolution is calculated by integrating the mass flux of all boundary nodes associated to the particle as follows 26,28 : $$$$ \frac{d}{dt}\left[{\rho}_s^i\pi {\left({r}^i\right)}^2\right]=-{\int}_{S^i} JdS $$$$ where $$$ {r}^i $$$ and $$$ {\rho}_s^i $$$ are the radius and density of solid particle i , respectively; $$$ {S}^i $$$ is the surface of solid particle i .…”

“…Substituting Equation (29) into Equation (30), the change of the particle radius can be obtained as follows: $$$$ \frac{dr^i}{dt}=\frac{D}{2{\pi \rho}_s^i{r}^i}{\int}_{S^i}\frac{\partial C}{\partial n} dS $$$$ Furthermore, the new radius of the solid particle i is calculated as follows 28 : $$$$ {r}_{t+\Delta t}^i=\sqrt{{\left({r}_t^i\right)}^2+\frac{D\Delta t}{{\pi \rho}_s^i}{\int}_{S^i}\frac{\partial C}{\partial n} dS} $$$$ where $$$ {r}_{t+\Delta t}^i $$$ and $$$ {r}_t^i $$$ are the radius of the solid particle i at times t + ∆ t and t , respectively.…”

“…In the present study, it is assumed that particles keep circular shape during the dissolution process, which is always adopted in the simulation of moving particle dissolution. [26][27][28][29] According to Fick's first law, the change rate of the i th particle mass during dissolution is calculated by integrating the mass flux of all boundary nodes associated to the particle as follows 26,28 : d dt…”

“…In the present two‐dimensional case, the surface area A is $$$ 2\pi \kern0.1em {r}_p $$$. Then mass transport coefficient $$$ {k}_c $$$ is calculated as follows: $$$$ {k}_c=\frac{J}{A\left({C}_s-{C}_0\right)}=\frac{J}{2\pi\;{r}_p\left({C}_s-{C}_0\right)}=\frac{-D{\left.\frac{\partial C}{\partial n}\right|}_S}{2\pi\;{r}_p\left({C}_s-{C}_0\right)} $$$$ Finally, the Sh is given by 28 $$$$ Sh=\frac{-{\int}_S\frac{\partial C}{\partial n} dS}{\pi \left({C}_s-{C}_0\right)} $$$$ Figure 8 shows the Sherwood number Sh as a function of the Peclet number Pe at Sc = 300 for mass transport from a rotating cylinder in simple shear flow. In the present simulation, different Pe numbers is obtained by changing the velocity of two parallel plates ($$$ {u}_w $$$).…”

“…Rahmat et al 27 used the smoothed particle hydrodynamic (SPH) method to modeling particle dissolution in fluid flow. Safa et al 28 combined the SPM‐LBM to simulate circular particles dissolution. Furthermore, Safa et al 29 extended the SPM‐LBM to investigate double‐diffusive mixed convection related to the heat and mass transport during the hydrate particle dissolution.…”