3.2. Initial composition

The value of the following input key determines the choice of initial order parameter \(\phi(\mathbf{r}; t=0)\)

phi_initialisation       choice

The available choices are set out below with other relevant input parameters in each case. Some parameters have default values (where stated) and may be omitted.

3.2.1. Uniform composition

phi_iniitialisation        uniform
phi0                       -1.0

The initial order parameter will be set uniformly at all fluid sites to the specified value \(\phi_0\).

3.2.2. Spherical droplet

phi_initialisation         drop
phi_init_drop_radius       8.0      # default 8.0 lattice units
phi_init_drop_amplitude    1.0      # default 1.0

A spherical droplet with radial profile \(\phi^\star \tanh (r-r_0)/\xi\) is initialised. The drop radius can be set in the input, while the centre is always the centre of the system. The amplitude \(\phi^\star\) may be positive or negative (the centre of the drop will have \(\phi = -\phi^\star\)).

The interfacial width \(\xi\) will take on the value determined by the current symmetric free energy parameters.

3.2.3. Emulsion droplets

phi_initialisation          emulsion
phi_init_emulsion_ndrops       4
phi_init_emulsion_radius     4.0       # radius
phi_init_emulsion_d_centre  12.0       # distance between centres > 2R
phi_init_emulsion_amplitude  1.0       # phi at drop centres

Intended to initialise an array of small quasi-two-dimensional droplets (actually cylinders) in the y-z plane. The input specifies the total number of droplets, their radius, the distance between the centres and the amplitude \(\phi^\star\) at the centre.

3.2.4. Block structure

phi_initialisation         block

This initialises a configuration with flat interfaces at \(z = L_z/4\) and \(z = 3L_z/4\). The interfacial width is that set by the current free energy parameters.

More general configurations are available via

phi_initialisation         block_X
phi_init_block_dimension   2.0       # Extent in x-direction

phi_initialisation         block_Y
phi_init_block_dimension   4.0       # Extent in y-direction

phi_initialisation         block_Z
phi_init_block_dimension   10.0      # Extent in x-direction

In each case, the block entends either side of the centre of the system by half the input value. The interface profile is \(\tanh\) with width determined by the current free energy parameters.

3.2.5. Layer structure

phi_initialisation         layer_X   # or Y or Z
phi_init_layer_size        0.2       # 0 < fraction < 1

Similar to the block initialisation except one specifies a fraction of the extent in the required dimension for the central layer.

3.2.6. Single interface

phi_initialisation         bath

A special case where a single interface is initialised in the system system with normal in the z-direction. This is intended for cases without perioidic boundary conditions (e.g., a box), where this configuration makes sense.

3.2.7. Random noise

phi_initialisation         spinodal    # e.g., for spinodal decomposition
phi0                       0.0         # mean order parameter
noise                      0.05        # amplitude
random_seed                1234567     # random seed

Initialises a uniform field \(\phi_0\) modulated at each lattice position by a small random component drawn from a uniform distribution. Different random configurations may be generated by changing the seed.

This is useful to initiate spinodal decomposition, and mimics the effect of a quench in temperature in a real system. Here we have no temperature.

3.2.8. Random patches

phi_initialisation         patches    # random patches
phi_init_patch_size        4          # patch size lattice units
phi_init_patch_vol         0.1        # volume fraction minority phase
random_seed                1234567    # random seed

Initialises random patches in order parameter (value) of a characteristic size. The total volume fraction of the minority phase (\(\phi = -1\)) is also set. Different random configurations can be generated by changing the seed.

This is intended to allow spinodal decomposition to start in cases where the composition is far from 50:50. If the simple spinodal method is used in such a case, diffusive effects may prevent domains forming. The larger initial patches promote effective spinodal decomposition.

3.2.9. Composition from file

phi_initialisation      from_file

An arbitrary order parameter field may be supplied from file of appropriate format. See sections on I/O for details.