  In modelling of chemical, physical or biological systems it may occur that
the coefficients, multiplying various terms in the equation of interest, differ
greatly in magnitude, if a particular system of units is used. Such is, for
instance, the case of the Population Balance Equations (PBE) proposed to model
the Latex Particles Morphology formation. The obvious way out of this
difficulty is the use of dimensionless scaled quantities, although often the
scaling procedure is not unique. In this paper, we introduce a conceptually new
general approach, called Optimal Scaling (OS). The method is tested on the
known examples from classical and quantum mechanics, and applied to the Latex
Particles Morphology model, where it allows us to reduce the variation of the
relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then
solved by a novel Generalised Method Of Characteristics, and the OS is shown to
help reduce numerical error, and avoid unphysical behaviour of the solution.
Although inspired by a particular application, the proposed scaling algorithm
is expected find application in a wide range of chemical, physical and
biological problems.
