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Lattice Boltzmann implementation of the three-dimensional Ben-Naim potential for water-like fluids
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Image of FIG. 1.
FIG. 1.

The unit cell of the D3Q27 lattice. The nearest neighbors, next-nearest neighbors and next-next nearest neighbors are shown in green, blue, and red, respectively. The weighting factors, w i , for the D3Q27 are: w 0 = 8/27 (the cell-center), w i = 2/27 (i = 1 − 6), w i = 1/54 (i = 7 − 18), and w i = 1/216 (i = 19 − 26).

Image of FIG. 2.
FIG. 2.

Tetrahedral representation of water-like molecules sitting at lattice site x and its neighbor x i . The four arms are denoted by the corresponding normals n k , k = 1, 4 (unprimed) and n l , l = 1, 4 (primed), respectively. Blue and red code for donor and acceptor arms, respectively. Here the index i corresponds to i = 23 in Fig. 1 .

Image of FIG. 3.
FIG. 3.

Radial shape functions for the case σ R = 0.28 and . Note that nearest-neighbor interactions are roughly an order of magnitude weaker than next and next-next nearest neighbor ones.

Image of FIG. 4.
FIG. 4.

The angular potential V ikl for σθ = 0.28. θ ik and θ il are shown in degrees.

Image of FIG. 5.
FIG. 5.

The torque acting on the arm n k has two components in the direction of e ϕ(n k ) and e θ(n k ). The total torque acting on the tetrahedron is then the vector sum of the torques acting on all 4 arms.

Image of FIG. 6.
FIG. 6.

Time evolution of the total potential energy vs the LB time steps together with the number of hydrogen bonds for four different effective temperatures, at (a) β−1 = 10−4, (b) β−1 = 4 × 10−4, (c) β−1 = 5.5 × 10−4, and (d) β−1 = 7 × 10−4. Main parameters are as follows N = 103, σ R = 0.28, σθ = 0.28, and .

Image of FIG. 7.
FIG. 7.

(a) Initial random distribution of tetrahedrons and the corresponding final distribution at steady state with and without thermal fluctuations in (b) and (c), respectively.

Image of FIG. 8.
FIG. 8.

Comparison of LB-ADR (blue) and MC (green) simulated annealing as energy minimizers. Main parameters are as follows N = 63, , σ R = 0.28, σθ = 0.28.


Generic image for table
Table I.

Extremal values of the angular potential , corresponding to cos θ ik = 1, 0, −1 and cos θ il = − 1, 0, 1 for the case σθ = 1.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lattice Boltzmann implementation of the three-dimensional Ben-Naim potential for water-like fluids