Glycerine rivers
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Translucent crackled veins running through the cut face, most visible in a colored bar.
Crackled lines through the bar
A pattern like crazed glass or a dry riverbed, in a lighter or more translucent shade than the surrounding soap.
Structurally the bar is fine. This is purely appearance.
What they are
Areas where the soap gelled differently, leaving a different crystal structure and a different translucency.
They are called glycerine rivers by convention rather than by chemistry: glycerine is present throughout, not concentrated in the veins.
What causes them
Overheating during gel, which is the main one.
A water discount, which concentrates everything and makes the effect more pronounced.
Titanium dioxide specifically, which is strongly associated with them and which many makers use for white and pastel bars.
A high gel temperature generally.
Whether to fight them
Some makers do it deliberately. In a rustic or marbled bar they read as character.
In a crisp geometric design they read as a fault, and the customer cannot tell the difference between intentional and not.
To avoid them: soap cooler, do not insulate, use less titanium dioxide, and consider preventing gel entirely.
To get them: the opposite.
What matters commercially is consistency, because a range where some bars have them and some do not looks like a process that is not in control, which it is.