Particle Motion in a Shear Flow

Particles in a nonuniform velocity field are subjected to lift and drag forces. The drag force acts in the direction opposite the relative velocity of the particle with respect to the fluid. The lift force acts along the direction of the gradient of the fluid velocity. These forces change significantly as the particle approaches a wall.

Use the Lift Force feature to exert a lift force on the particles. Two formulations of the lift force are available. Both expressions for the lift force are valid when the angular velocity of the particle can be neglected and a no-slip boundary condition applies at the particle surface.

The following sections describe the available lift force models. Each of these models can be used by selecting the appropriate option from the list in the settings window for the Lift Force node. Use the lift force when particles are in a nonuniform velocity field far from walls. The lift force applies to particles close to the walls of a flow channel.

Saffman Lift Force

The lift force FL (SI unit: N), described in Ref. 13, is given by

where

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rp is the particle radius (SI unit: m)

•

μ is fluid viscosity (SI unit: Pa·s)

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v is the velocity of the particle (SI unit: m/s)

•

u is the fluid velocity (SI unit: m/s)

The lift force is only nonzero for particles that have not yet been entrained in the surrounding fluid. Once a particle has reached equilibrium with the surrounding fluid velocity, the Saffman lift force is zero. To model the inertial lift force on particles in a flow channel, which is typically nonzero even after the particles become entrained in the flow, consider using the lift force described in the following section.

Wall Induced Lift Force

The lift force model described in Ref. 14 uses a first order correction to the velocity profile at the channel walls and a second order correction at the surface of the particle in order to account for higher-order derivatives of the fluid velocity, compared to the model. It is given by

where

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rp is the particle radius (SI unit: m)

•

μ is fluid viscosity (SI unit: Pa·s)

•

u is the fluid velocity (SI unit: m/s)

•

I is the identity matrix (dimensionless),

•

n is the wall normal at the nearest point on the reference wall (dimensionless)


	Here the term “reference wall” refers to the set of boundaries selected in the Parallel Boundary 1 section in the settings window for the Lift Force node.

•

D is the distance between the channel walls (SI unit: m)

•

s is the nondimensionalized distance from the particle to the reference wall, divided by D so that 0 < s < 1 for particles in the channel

•

G1 and G2 are functions of nondimensionalized wall distance s as given in Ref. 14 (dimensionless). They are plotted in Figure 5-6 and Figure 5-7 below.

Figure 5-6: G1 coefficient for the lift force.

Figure 5-7: G2 coefficient for the lift force.

Figure 5-8: Dimensions used to define the wall induced lift force. Here the bottom wall has been selected in the Parallel Boundary 1 section and the top wall has been selected in the Parallel Boundary 2 section.