Palierne equation

For the dilute emulsions Palierne equation looks like:

${\displaystyle G^{*}=G_{m}^{*}(1+5\phi H^{*})}$

where ${\displaystyle G^{*}}$ is the dynamic modulus of the emulsion, ${\displaystyle G_{m}^{*}}$ is the dynamic modulus of the continuous phase (matrix), ${\displaystyle \phi }$ is the volume fraction of the disperse phase and the ${\displaystyle H^{*}}$ is given as

${\displaystyle H^{*}={\frac {(G_{d}^{*}-G_{m}^{*})(19G_{d}^{*}+16G_{m}^{*})+(4\sigma /R)(5G_{d}^{*}+2G_{m}^{*})}{(2G_{d}^{*}+3G_{m}^{*})(19G_{d}^{*}+16G_{m}^{*})+(40\sigma /R)(G_{d}^{*}+G_{m}^{*})}}}$