Quantitative Biofouling Diagnosis in Reverse Osmosis Membrane Systems.¶
Vrouwenvelder, J. S. (2009). Quantitative Biofouling Diagnosis in Reverse Osmosis Membrane Systems. Water Research, 43(3), 583-594.
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Primes¶
- Biofouling
- Deposition adds area at a rate proportional to clean surface, $d \cdot (1 - A)$, while cleaning removes it at rate $r \cdot A$; the governing quantity is deposition net of removal, and the interface stabilises only at $A^* = d/(d+r)$ — exactly the prime's rate-balance invariant.
This sourceEstablishes that biofilm accumulation on a working membrane surface follows deposition-minus-removal dynamics reaching a balance, supporting the rate-balance occupancy form (deposition proportional to clean surface, removal proportional to coverage, equilibrium where they match).
- Deposition adds area at a rate proportional to clean surface, $d \cdot (1 - A)$, while cleaning removes it at rate $r \cdot A$; the governing quantity is deposition net of removal, and the interface stabilises only at $A^* = d/(d+r)$ — exactly the prime's rate-balance invariant.
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