Research on Interaction between Asphalt and Filler Based on DSR Test

To explain the interactive effect between asphalt and fillers in the asphalt mastic, it is probably to start with an assessment of the rheology properties, since asphalt mastics are viscoelastic materials. In this study, firstly prepare the asphalt mastics with different dosage of limestone filler, and the volume fractions of fillers were 0, 14, 24, 32, 39 and 45%. And then, the same asphalt is mixed with different fillers, such as cement and hydrated lime, and the volume fractions of fillers were 18, 23, 28and 33%. DSR test was conducted on all of the asphalt mastic specimens to measure the complex shear modulus G* at different temperature. The volume filling effects and interaction between asphalt and filler are discussed on the analysis of complex shear modulus coefficient and Nielsens model model. It is obviously that G* of asphalt mastics decrease with the test temperature, but increase with the volume fraction of filler. A function relation between complex shear modulus coefficient and volume fraction of fillers is established, and the interaction coefficient α is proposed. For limestone, cement and hydrated lime filler, the interaction coefficient α values are 0.301, 0.317 and 0.429 respectively. Based on Nielsens model and DSR test data, the Einstein coefficient KE is calculated, and Einstein coefficients are 3.761, 5.09 and 7.44 for asphalt-limestone mastic, asphalt-cement mastic and asphalt-hydrated lime mastic respectively. Both the interaction coefficient α and Einstein coefficient KE can be used to represent the interaction between asphalt binder and filler. The bigger value means the better interaction.

Kinetic description of a wiggler-pumped ion-channel free-electron laser by applying the Einstein coefficient technique

A kinetic theory is used to investigate the theory of a free-electron laser with a helical wiggler and an ion channel based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency, propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.

Micromechanical-Rheology Model for Predicting the Complex Shear Modulus of Asphalt Mastic

The dynamic shear rheometer (DSR) was used to measure viscoelastic properties of asphalt mastic. Mechanical volume filling effects and additional interacting mechanisms within mastic systems are discussed on the basis of micromechanical-rheology model to predict the complex shear modulus of asphalt mastic from the measured mastic data. The Einstein coefficient is 3.761, and the maximum volumetric packing fraction is 0.562 for the measured asphalt mastic. The predicted G* of asphalt mastics is very close to the actual value, and the relative error is not exceeding 10%. The micromechanical-rheology model can predict the complex shear modulus of the asphalt mastic from the viscoelastic property of neat asphalt, the volumetric filler effect and an interactive effect between the filler and the asphalt.

The rheology of suspensions of solid particles

We present data for the rheology of suspensions of monodisperse particles of varying aspect ratio, from oblate to prolate, and covering particle volume fractions ϕ from dilute to highly concentrated. Rheology is characterized by fitting the experimental data to the model of Herschel & Bulkley (Herschel & Bulkley 1926 Kolloid Z. 39 , 291–300 ( doi:10.1007/BF01432034 )) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ 0 . The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron & Pierce (Maron & Pierce 1956 J. Colloid Sci. 11 , 80–95 ( doi:10.1016/0095-8522(56)90023-X )) with the maximum packing fraction ϕ m as the only fitted parameter. We derive empirical relationships for ϕ m and n as a function of average particle aspect ratio r p and for τ 0 as a function of ϕ m and a fitting parameter τ *. These relationships can be used to predict the rheology of suspensions of prolate particles from measured ϕ and r p . By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery’s (Jeffery 1922 Proc. R. Soc. Lond. A 102 , 161–179 ( doi:10.1098/rspa.1922.0078 )) theory. We extend Jeffery’s work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as ϕ increases.