DropletCollisions

Through the use of

• ParticleInteraction
• %BND_COLLISION%

one may define the parameters of a collision model between droplets and boundaries. In this case, droplets will, assuming sensible choices of parameters, no longer pass through each other and behave more closely to granular matter.

Repulsive Normal Forces

The two parameters k_n, e_n in determine the constants \( k_n\) and \( c_n\) within the linear spring-damper model \begin{align} \mathbf{f}_{ij}^n = \begin{cases} -\left[ k_n \delta_{ij} - c_n (\mathbf{v}_{ij}\cdot\mathbf{n}_{ij}) \right] \mathbf{n}_{ij} & \delta_{ij}>0 \\ 0 & \text{else} \end{cases} \end{align} which is employed to calculate forces along contact normal \( \mathbf{n}_{ij}\) from overlap \( \delta_{ij}\) and relative velocity \( \mathbf{v}_{ij}\). In particular, e_n represents the coefficient of restitution, i.e. the ratio of post- to pre-collisional velocity, from which the damper constant \( c_n\) is calculated internally. Defaults:

• If e_n is set to a negative value, the damping coefficient c_n will be set to the absolute value of e_n.
• If k_n is set to zero or a negative value, no collision forces will be calculated.

Notes:

• Interacting DROPLETPHASE particles are allowed to have different size and spring stiffness, however the coefficient of restitution must be identical.
• During the separation phase, the damper force might produce attractive contributions which lead to a reversal of sign. By default, this is prevented by setting the total force to zero as soon as the attractive damper force becomes larger in magnitude than the repulsive elastic force. See DP_UseOnlyRepulsiveContactForce.

Attractive normal forces

The two parameters E_a, R_a in are reserved for attractive forces along the normal direction. While R_a determines the range of adhesive forces (relative to the particle diameter \( D_i\)), E_a determines the energy level of the adhesive potential \begin{align} \mathbf{f}_{ij}^{a} = \begin{cases} -k_{a} \delta_{ij} \mathbf{n}_{ij} & -\frac{1}{2}R_{a}D_i<\delta_{ij}<0\\ \left[-2F_{max}^{a}-k_{a} \delta_{ij}\right] \mathbf{n}_{ij} & -R_{a}D_i<\delta_{ij}<-\frac{1}{2}R_{a}D_i \\ 0 & \text{else} \end{cases} \end{align} i.e. \( k_{a}\) and \( F_{max}^{a}\) are chosen so that the integral over this force expression is given by E_a: \( F_{max}^{a}=2\frac{E_a}{R_{a}D_i}\) Defaults:

• If E_a is set to zero or a negative value, no attractive forces will be calculated.
• If R_a is set to zero or a negative value, it is overwritten by the default value of one.

Frictional forces

The parameter mu in determines the coefficient of friction \( \mu\) in Coulombs law of friction \begin{align} \mathbf{f}_{ij}^t = -\mu \lVert \mathbf{f}_{ij}^n \rVert \mathbf{t}_{ij} \end{align} which is used to calculate forces along the tangential direction \( \mathbf{t}_{ij}\) due to friction between the particles or between particles and boundaries. Defaults:

• If mu is set to zero or a negative value, no friction forces will be calculated.

Notes:

• The coefficients of friction must be identical for all interacting DROPLETPHASE particles.

Important notes

Choice of smoothing length

• In order to resolve the collision dynamics correctly, the smoothing length h has to be at minimum 1.5 * D30. Otherwise the neighborhood lists are not correct and collision detection might be late or missed.
• Generally: other than in LIQUID the smoothing length generally does not refine the resolution of the simulation, but is the quantity to define the neighborhood information.

Timestep Management

• The stability of a simulation of interacting droplets can be improved by decreasing the value of COEFF_dt_d30 and COEFF_dt_coll.
• If the DROPLETPHASE timestep becomes too small, one may use a subcycling as described in COMP_DropletphaseSubcycles

Simulation Model

• As the collision forces are the basis for the dynamics for the particle wall interaction, boundary particles are not needed and hence the particles are usually inner particles with %ind_kob% equal %IDENT_none%.
• Use %TOUCH_reflection% as backup if the collision dynamics allow the particles to cross the boundary accidentally.