Interdisciplinary Applied Mathematics

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FIGURE 16.9. Velocity profile across the channel for case 6 (W = 10.00 nm, as = +0.124    C/m2).    The    velocity in    the    region    within    S    from    the    channel wall is

obtained using equation (16.33) and the MD velocity within the same region from case 4    (W    =    2.22    nm,    as = +0.120    C/m2).    The    velocity    in    the    central    portion

of the channel is computed using a constant viscosity of 0.743 mPa-s.

the MD    velocity    profile    for    case 4    (i.e.,    in the MD    velocity    of    a    2.22-nm

channel), the velocity obtained using equation (16.33) matches the MD simulation results reasonably well.

16.4 Dissipative Particle Dynamics (DPD)

So far, we have discussed the molecular dynamics (MD) method and the lattice Boltzmann method (LBM) for simulations in the atomistic and mesoscopic regimes, respectively. A potentially very powerful alternative to both methods has more recently emerged: the dissipative particle dynamics method (DPD), which combines features from both MD and LBM. The initial model was proposed by Hoogerburgge and Koelman as a simulation method to avoid the artifacts associated with traditional LBM simulations while capturing spatiotemporal hydrodynamic scales much larger than those achievable with MD (Hoogerburgge and Koelman, 1992).

The DPD model consists of particles that correspond to coarse-grained entities, thus representing molecular clusters rather than individual atoms. The particles move off-lattice, interacting with each other through a set of prescribed and velocity-dependent forces (Hoogerburgge and Koelman, 1992; Espanol and Warren, 1995). Specifically, there are three types of forces acting on each dissipative particle:

A purely repulsive conservative force,

A dissipative force that reduces velocity differences between the particles, and

A stochastic force directed along the line connecting the center of the particles.

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