Micellar surfactant solutions are characterized by a distribution of aggregates made up predominantly of premicellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale re-equilibration following a system dilution, known as the $\tau_1$ and $\tau_2$ processes, whose dynamics may be described by the Becker–Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes.

MSC codes

  1. 45K05
  2. 82C70
  3. 35Q99


  1. Becker–Döring equations
  2. surfactant systems
  3. micellar kinetics
  4. asymptotic analysis

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Information & Authors


Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 201 - 215
ISSN (online): 1095-712X


Submitted: 22 July 2011
Accepted: 17 November 2011
Published online: 24 January 2012

MSC codes

  1. 45K05
  2. 82C70
  3. 35Q99


  1. Becker–Döring equations
  2. surfactant systems
  3. micellar kinetics
  4. asymptotic analysis



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