Every liquid and every material has three Hansen Solubility Parameters (HSP), in MPa0.5: dispersion δD (van der Waals forces), polarity δP (dipole interactions) and hydrogen-bonding δH. Together they place a substance as one point in 3D "Hansen space".
A solute (polymer, resin, API, dye) is dissolved well by any solvent whose point falls inside its solubility region, centered at the solute's own (δD₀, δP₀, δH₀) with radius R₀. The interaction distance is:
Ra² = 4(δD1−δD2)² + (δP1−δP2)² + (δH1−δH2)²
RED = Ra / R₀
RED < 1 → good solvent (inside the region). RED > 1 → poor solvent. The factor of 4 on the δD term exists because Hansen's original regression found dispersion differences need that weight to match real solubility data.
Note on shape: because of that ×4 weighting, the true boundary in raw (δD, δP, δH) coordinates is not a sphere — it is an ellipsoid, squashed to a half-radius (R₀/2) along the δD axis and full radius R₀ along δP and δH. This 2D simulator draws that ellipse correctly in the δD–δP and δD–δH planes; the δP–δH plane (no δD involved) is a true circle. Verified numerically: for R₀ = 8, the boundary sits at Δ(δD) = 4 along a pure-δD offset but at Δ(δP) = Δ(δH) = 8 along a pure-δP or δH offset — a 2:1 ratio, confirmed by direct substitution into the Ra formula above.
- Target solute — switches the region's centre and its literature-typical radius R₀.
- R₀ slider — widens or shrinks the region, showing how a more solvent-tolerant material (larger R₀) accepts more solvents as "good".
- Solvent A / B + blend slider — a mixture's HSP is the volume-fraction-weighted average of its components' HSP. The blend marker moves along the straight line between A and B, and can cross into the good region even when neither pure solvent does.
- Custom probe — drag its three sliders to place any arbitrary point in Hansen space and read its own Ra / RED against the current solute, live, on all three planes at once.
- Drag / scroll on any plane — each of the three projection panels pans (drag) and zooms (scroll) independently.
Real-world relevance: this exact geometric test is how process chemists replace hazardous solvents (DMF, DCM, benzene) with safer ones (ethanol, ethyl lactate, water/scCO2 blends) without losing solvency — the basis of green-solvent selection guides used across the pharmaceutical and coatings industries.