The pressure gradient force is an optional term that can be defined by the Drag Force node by clicking the Include virtual mass and pressure gradient forces check box.

For a particle of velocity v (SI unit: m/s) in a fluid of velocity u (SI unit: m/s), the pressure gradient force term Fp (SI unit: N) is (Ref. 19)

where, as in the Virtual Mass Force in the previous section, mf (SI unit: kg) is the mass of the fluid displaced by the particle volume,

dp (SI unit: m) is the particle diameter, and ρ (SI unit: kg/m3) is the density of the fluid at the particle’s position.

Unlike the virtual mass force, however, the material derivative D (not d) follows the fluid velocity direction rather than the particle velocity direction. That is,