Model Lewis-Nielsen

S.E. Jorgensen, Halling-Sorensen and S.N. Nielsen (Eds.) 1995. Handbook of Environmental and Ecological Modeling. Lewis Publishers, Boca Raton, 672 pp. 

The Lewis-Nielsen model considers the effect of the shape of the filler and the orientation or type of packing for a two-phase system or single-phase reinforcement composite, resulting in equation (11.8) for effective thermal conductivity (Tavman... 

As discussed previously, a number of mathematical models for prediction of the mechanical reinforcement in polymer matrices exist. Halpin-Tsai (Halpin and Kardos 1976 Cadek et al. 2002) and Lewis-Nielsen (Lewis and Nielsen 1970) equations are based on simple approximations and provide reliable predictions of the modulus of reinforced matrices where the filler is unidirectional or randomly distributed. Therefore one can utilise these predictions to quantify the level of dispersion and the possible orientation of the filler particles in the matrix (see Fig. 8.10). 

Lewis-Nielsen or modified Kerner equation [17] is one of the most successful models ... 

The thermal conductivity (Ke) of a filled adhesive may be predicted from the Lewis and Nielsen model. °... 

Interpretation of the mechanical tests in terms of the simplified models proposed by Smith (cy), Nielsen (oy), Lewis and Nielsen (E) and in terms of the simple distribution of the energetic contributions to W among the phases proposed in this paper, suggests that the adhesion related to our treatments of glass A beads increases in the order TTS, SIC. Untreated beads were found to have low adhesion. 

Some additional experimental considerations were introduced in the Lewis and Nielsen model [17] through adjustable parameters A and Om as described in Eq 6. 

Maxwell model underestimates the thermal conductivity of PLA-eGR composites however Halpin-Tsai, Lewis and Nielsen and Hamilton models ensure a good fitting of experimental values. 

Many equations have been proposed for the transport properties of two-phase systems and in-depth details of the existing models are discussed elsewhere [4]. Noticing that virtually all the early theories neglected the effects of the particle shape, their packing density, and the possible formation of anisotropic clusters, Lewis and Nielsen modified the Halpin-Tsai equation for the elastic modulus of composite materials by incorporating the maximum volume fraction of filler cpm while still maintaining a continuous matrix phase [33,34]. Transposed to thermal conductivity Lewis and Nielsen s equation becomes... 

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