The variation of the scattering efficiencies are accurately fitted up to 20% PVC by a second-order polynomial function given by SD[empty set] = a1[empty set] + [a.
A complex challenge that paint formulators have to face is to establish whether it is more economically viable to increase the scattering efficiency of a given paint formulation by solely augmenting its PVC or by trying to improve the pigments' spatial state of dispersion, assuming that the latter is technically possible and financially viable.
The principal difficulty resides in the lack of theoretical and semi-empirical models that can accurately predict the maximum scattering efficiency of a given paint formulation, which corresponds to the optimum pigment spatial dispersion state (see typical variations in Fig.
b) The influence of the pigments' spatial state of dispersion is taken into account by expressing the paint scattering efficiency, denoted [s.
The limit [OMEGA] = 1 corresponds to the ideal case of independent scattering (curve (a) in Fig.
c) Measurements of the variations in the scattering efficiency as a function of the pigment's spatial state of dispersion are realized via the evaluation of a gain function, denoted G, defined as G =[s.
We have used numerical simulations based on a rigorous theoretical framework to show that contrary to some statements made in the literature, dependent scattering of light in white paint films containing rutile titanium dioxide pigments is a particular manifestation of multiple scattering.
We have also pointed out that the transition from independent-to-dependent scattering, as a function of the PVC is a continuous process that cannot be formally related to a specific concentration threshold.
Van de Hulst, RC, Light Scattering by Small Particles.
Fitzwaler, S, Hook, JW, III, "Dependent Scattering Theory: A New Approach to Predicting Scattering in Paints.
Ishimaru, A, Wave Propagation and Scattering in Random Media, Vols.
Tsang, L, Kong, JA, Ding, K-H, Scattering of Electromag-netic Waves: Theories and Application, Vol.