Color
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The first thing a customer sees, and a set of pigments behaving in a strongly alkaline medium.
Three sources
Micas, for shimmer and bright color.
Oxides and ultramarines, for solid opaque color.
Natural colorants: clays, botanicals, spices, charcoal, indigo.
Each behaves differently in soap, and "behaves" mostly means "survives or does not".
Micas and oxides
Buy colorants stated as suitable for cold process soap, because many micas are not stable in it: they morph, fade or vanish entirely in an alkaline environment.
A supplier who says "soap stable" is telling you something useful, and one who does not is selling for another application.
Disperse in a light oil or in glycerine before adding. Dry powder stirred into a traced batch gives specks and streaks and never fully disperses.
And note the labeling consequence: color additives are regulated, and permitted uses matter, which is a cosmetic question if the bar is a cosmetic.
Natural colorants
Clays are reliable and muted.
Charcoal gives gray to black and is easy to overdose into a bar that marks a cloth.
Indigo and madder work and take practice.
Spices are unpredictable: turmeric can be yellow or orange or brown depending on the batch and the heat, and paprika frequently disappoints.
Most botanicals brown in soap. A green herb infused into oil gives a khaki bar, not a green one, and accepting that is better than fighting it.
What color does in an alkaline bar
pH shifts hue in anything pH-sensitive, which is most natural color.
Gel phase deepens and intensifies color, so a gelled and an ungelled batch of the same soap are different colors, which is why partial gel is so visible.
And vanillin in a fragrance browns the soap regardless of what you colored it with, sometimes over weeks, which catches makers who approved the bar on day one.