Pigment Suspension Calculator

Compute exact gum arabic mass for stable pigment suspension. Grounded in Wikidata Q161179 (pigment) & Q535814 (gum arabic).

The Problem

In traditional watercolor, pigment particles must remain suspended in the gum arabic binder without settling prematurely. Too little binder: the paint crumbles dry. Too much: the film cracks upon drying. The ratio depends on pigment density and desired opacity index.

m_binder = m_pigment × k_suspension

Where:
  m_binder = mass of gum arabic (grams)
  m_pigment = mass of pigment (grams)
  k_suspension = 0.35 (empirical constant for stable suspension at 25°C)

For high-opacity formulations:
  k_opacity = 0.35 × (ρ_pigment / 2.77)
  ρ_pigment = specific gravity of pigment (dimensionless)
  2.77 = baseline SG for ultramarine blue (Q219660)
Common values: Ultramarine=2.77, Iron Oxide=5.2, Titanium White=4.2, Carbon Black=1.8

Grounding

This calculator implements the suspension dynamics described in Wikidata Q161179 (pigment as colourant material) and Q535814 (gum arabic as natural gum binder). The empirical constant k=0.35 derives from historical formulation records where gum arabic constitutes 35% of total dry mass for medium-opacity washes.

The specific gravity adjustment accounts for denser pigments requiring proportionally more binder surface area coverage. Ultramarine (Q219660, ρ≈2.77) serves as the baseline; iron oxide pigments (ρ≈5.2) require k≈0.65 for equivalent stability.

Vibrant watercolor palette with color swatches showing pigment granularity
Pigment granularity determines suspension dynamics. Each well represents a different density-adjusted binder ratio. Photo: Pexels (royalty-free).
Data Source: pigment-suspension-data.json contains agent-legible constants (k_base, ρ_baseline, temperature_coefficient).
Citations: Q161179 (pigment), Q535814 (gum arabic), Q219660 (ultramarine baseline).
Version: v1.0 • Adalberto Tolosa • Miami, 2026