Thin-layer chromatography (TLC) is the standard forensic technique for questioned-document ink examination. A spot of ink sits near the base of a silica plate stood in a shallow solvent reservoir. Capillary action pulls solvent up the plate; the solvent front rises following the Lucas–Washburn relation:
h(t) ≈ √(k · t)
k depends on solvent surface tension, plate pore size, and viscosity (falls with temperature)
Each dye in the ink partitions between the moving solvent (mobile phase) and the silica coating (stationary phase). A dye that prefers the solvent travels almost with the front; a dye that clings to the silica lags behind. The ratio of the two distances is the retardation factor:
Rf = (distance travelled by dye spot) / (distance travelled by solvent front)
Rf is intrinsic to a given dye/solvent/plate combination — it does not depend on how far the plate has run. This is what makes it useful forensically: examiners run a questioned ink and a known reference ink side by side under identical conditions and compare the resulting Rf patterns. A matching band count at matching Rf values is evidence the two samples share the same ink formulation; a differing pattern — for example a signature added in a different pen than the body text — is physical evidence of alteration, even when the two inks look the same color to the eye.
- Lane A / Lane B — pick which ink formulation develops in each lane.
- Solvent polarity — a more polar mobile phase out-competes the silica for polar dyes, raising their Rf; this is why real examiners try several solvent systems.
- Plate temperature — raises the Lucas–Washburn rate constant k (faster front, see the rise-curve panel) and the diffusion coefficient (more band spreading), exactly as in a real developing tank.
- Rf bar chart — plots every dye's Rf side by side for both lanes so a mismatched band jumps out visually, not just numerically.
- Mean ΔRf — the average absolute Rf difference between best-matched bands once development completes; forensic labs typically treat ΔRf below ~0.03–0.05 as consistent with a common ink source.