Mass-flow-rate-controlled fluid flow in nanochannels by particle insertion and deletion

A nonequilibrium molecular dynamics method to induce fluid flow in nanochannels, the insertion-deletion method (IDM), is introduced. IDM inserts and deletes particles within distinct regions in the domain, creating locally high and low pressures. The benefits of IDM are that it directly controls a physically meaningful quantity, the mass flow rate, allows for pressure and density gradients to develop in the direction of flow, and permits treatment of complex aperiodic geometries. Validation of IDM is performed, yielding good agreement with the analytical solution of Poiseuille flow in a planar channel. Comparison of IDM to existing methods indicates that it is best suited for gases, both because it intrinsically accounts for compressibility effects on the flow and because the computational cost of particle insertion is lowest for low-density fluids.

Figure 1

IDM schematic. Particles are inserted in ${\mathrm{\Omega }}_I$ (red), deleted in ${\mathrm{\Omega }}_D$ (blue), and flowing in ${\mathrm{\Omega }}_S$ (green).

Figure 2

Snapshots of particle positions at various times for the liquid system with ${\dot{m}}_{\text{set}}=40$.

Figure 3

Mass flow rate versus number of steps between insertion and deletion events. An event refers to the insertion and deletion of $k$ particles in ${\mathrm{\Omega }}_I$ and ${\mathrm{\Omega }}_D$, respectively. Standard error is smaller than marker size.

Figure 4

(a) Number density and (b) horizontal velocity versus vertical channel position for $L_x=41.04$. The mass flow rate for the liquid is ${\dot{m}}_{\text{set}}=40$ while the mass flow rate for the gas is ${\dot{m}}_{\text{set}}=20$.

Figure 5

(a, b) Normalized number density and (c, d) normalized pressure versus horizontal channel position for $L_x=41.04$. The density is normalized by the bulk density and the pressure is normalized by the BFM-C pressure before the hydrostatic portion is removed. The mass flow rate for the liquid (a, c) is ${\dot{m}}_{\text{set}}=40$, while the mass flow rate for the gas (b, d) is ${\dot{m}}_{\text{set}}=20$.

Figure 6

Percentage difference in (a) density and (b) pressure between IDM and BFM-C versus normalized horizontal channel position for the liquid. The mass flow rate is ${\dot{m}}_{\text{set}}=40$.

Figure 7

(a, b) Viscosity, (c, d) density gradient, and (e, f) pressure gradient versus set mass flow rate for the (a, c, e) liquid and (b, d, f) gas systems. The “$\times$,” “$■$,” “$▲$,” and “$⧫$” markers represent IDM, BFM-C, BFM-GD, and DCV-GCMD, respectively.

Figure 8

Runtime efficiency, defined as BFM-C runtime divided by IDM (or DCV-GCMD) runtime, for simulations of 10 000 time steps. The “$\times$” and “$○$” are IDM simulations with USHER acceptance criteria of 5% and 10%, respectively. The “$⧫$” and “$▲$” are DVC-GCMD simulations with 75 and 686 GCMC steps for every MD step, respectively.

Figure 9

Potential and kinetic (inset) energy distributions of inserted and deleted particles for (a) ${\dot{m}}_{\text{set}}=20$ and (b) ${\dot{m}}_{\text{set}}=40$ for the liquid system. One event refers to inserting or deleting one particle.

Figure 10

Normalized potential energy fluctuations for ${\dot{m}}_{\text{set}}=40$ for the entire liquid domain, $△$, and due to IDM, $\times$. The inset shows a finer resolution.