# 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_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.