Water Membranes

Water Membranes Domain

The water domain provides evaluation models for polymeric separation membranes used in water treatment and desalination. It covers reverse osmosis (RO), ultrafiltration (UF), and forward osmosis (FO) membrane design.

Physics Model

The water domain's evaluation function combines the solution-diffusion model with structure-property correlations:

• Permeability is modeled using a modified Hagen-Poiseuille equation that accounts for pore size distribution, membrane thickness, porosity, and tortuosity.
• Salt rejection is modeled using the Kedem-Katchalsky transport equations with reflection coefficients derived from pore size relative to hydrated ion radii.
• Mechanical strength is estimated from polymer concentration, crosslink density, and thickness using empirical correlations from the membrane literature.

Default Parameters

| Parameter | Type | Bounds | Unit | Description | |—————-|———|————|———|——————-| | polymer_concentration | continuous | [0.08, 0.40] | wt% | Polymer in casting solution | | crosslinker_ratio | continuous | [0.01, 0.15] | mol/mol | Crosslinker to monomer ratio | | pore_size_nm | continuous | [0.3, 100.0] | nm | Mean pore diameter | | membrane_thickness_um | continuous | [5.0, 300.0] | um | Active layer thickness | | annealing_temp_c | continuous | [50.0, 180.0] | C | Post-treatment temperature | | support_porosity | continuous | [0.20, 0.85] | — | Substrate layer porosity | | tmpc_concentration | continuous | [0.05, 0.50] | wt% | TMC monomer concentration |

Default Objectives

| Objective | Direction | Unit | Description | |—————-|—————-|———|——————-| | permeability | maximize | L/(m2hbar) | Pure water permeability | | salt_rejection | maximize | % | NaCl rejection at 15.5 bar |

Templates

The water domain includes three templates:

materia init my-ro --template water/ro-membrane
materia init my-uf --template water/uf-membrane
materia init my-fo --template water/forward-osmosis

• ro-membrane: Reverse osmosis thin-film composite. 5 parameters, 2 objectives. Targets desalination-grade rejection (>97%).
• uf-membrane: Ultrafiltration membrane. 4 parameters, 2 objectives. Targets high flux with molecular weight cutoff control.
• forward-osmosis: FO draw solution and membrane co-optimization. 6 parameters, 2 objectives.

Example Campaign

name: high-flux-ro
domain: water
description: Maximize permeability while maintaining >97% NaCl rejection

parameters:
  - name: polymer_concentration
    type: continuous
    bounds: [0.12, 0.30]
  - name: crosslinker_ratio
    type: continuous
    bounds: [0.03, 0.10]
  - name: pore_size_nm
    type: continuous
    bounds: [0.3, 5.0]
  - name: membrane_thickness_um
    type: continuous
    bounds: [20.0, 150.0]
  - name: annealing_temp_c
    type: continuous
    bounds: [70.0, 140.0]

objectives:
  - name: permeability
    direction: maximize
    unit: L/(m2*h*bar)
  - name: salt_rejection
    direction: maximize
    unit: "%"

constraints:
  - expression: membrane_thickness_um >= 30
    description: Minimum for mechanical handling

optimizer:
  method: cma-es
  budget: 250
  batch_size: 15
  seed: 42

Key Trade-Offs

The fundamental trade-off in membrane design is between permeability and selectivity. Larger pores increase flux but allow more solute to pass. The Pareto front of this domain typically shows:

• High-rejection region (>99%): Low permeability (~5-15 L/(m2hbar)), dense polymer matrices, small pores.
• High-flux region (>30 L/(m2hbar)): Lower rejection (91-95%), thinner membranes, larger pores.
• Knee point: Typically around 20 L/(m2hbar) permeability and 97% rejection.

Validation Rules

The water domain enforces:

• Polymer concentration must be positive and less than 1.0
• Pore size must be positive
• Membrane thickness must be at least 5 micrometers
• Annealing temperature must be below the polymer degradation temperature

Source Code

The water domain implementation is at materia/plugins/water/physics.py. The evaluation function and its physics model are documented inline.