It will not foam
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Check the viscosity before the pump
The mesh is the mechanism and a liquid too thick to pass it will not foam no matter which foamer you fit. If the product was developed at hand soap thickness and then put in a foamer, this is the answer and the fix is the formula.
Then look for a clogged screen
Dried product, a particle, or an ingredient that settled can block the mesh. It shows as a pump that worked and then stopped, rather than one that never worked, which is the distinction that tells you which of the two you have.
Then the dip tube
Too short for the bottle and it loses prime as the level drops; kinked against the base and it draws nothing. Tube length is specified to the bottle height, and it is what gets forgotten when a format changes and the closure order does not.
Air is half the mechanism
A foamer draws air as well as liquid, so a closure that is not seated properly or a bottle that cannot vent will foam poorly. If the pump works off the bottle and not on it, this is where to look.
Cold thickens it
A product that foams in a warm room may not in a cold bathroom in winter, because viscosity rises as temperature falls. Testing only at workshop temperature hides a seasonal failure that arrives as complaints in January.
Test the real combination through a whole bottle
The first dose and the last dose behave differently, and a pump that primes easily when full can lose prime at a quarter full. One bottle used end to end answers more than any amount of bench testing.