What Controls the Rheology of Granular Materials? [chapter]

Einat Aharonov
2004 Continuum Models and Discrete Systems  
Israel Tel: 972-3-9683432; Fax: 972-3-9604017 email: ASSOULINE Shmuel 2. 4 The impact of raindrops on the soil surface disturbs the soil upper layer and causes changes in its properties. The result is the sealing of the soil to water infiltration. A dynamic model is developed, that describes soil sealing in terms of the increase of the soil bulk density, being maximal at the soil surface and decreasing exponentially with depth. The formulation of the relationships between the soil bulk density
more » ... nd its hydraulic parameters allows the determination of the hydraulic functions at every point within the disturbed layer and at every moment during seal formation. It is, thus, possible to solve the flow equations not only for the undisturbed soil but also within the seal domain. Once calibrated, the predictive ability of the dynamic model was found to be rather good on basis of verification with extensive experimental results. Therefore, it can be used now to evaluate the effects of various variables affecting flow processes, like soil and rainfall properties, initial conditions, or chemical conditions of the soil-water system, on infiltration and runoff generation. The dynamic model is used to compare the effects of accounting for the nonuniformity with depth of the seal layer and the areal heterogeneity of the soil hydraulic properties under soil surface sealing conditions on infiltration are studied. The depth dependent properties of the non-uniform seal are expressed in terms of the exponential model of Mualem and Assouline (1989). The dynamics of seal formation are modeled according to Assouline and Mualem (1997). The soil areal heterogeneity is represented by a lognormal distribution of the saturated hydraulic conductivity of the initially undisturbed soil and by related distributions of the other soil parameters. Accounting for seal non-uniformity has only a minor effect on the infiltration curve during the first rainfall on an undisturbed soil profile, when the seal layer is formed. However, it has a significant effect regarding the dynamic changes of the water content in the soil surface, and consequently, within the seal layer. During subsequent rainfalls on a sealed soil profile, when the seal layer is completely developed, the effect on the infiltration curve is much more significant. Representing the seal as a non-uniform layer decreases the ponding time and the infiltration rates at the early stage of the process. The amplitude of these effects is increased when the rainfall rate is higher and the seal layer is thicker. Accounting for areal soil heterogeneity reduces the ponding time and the rate of infiltration decrease, while it increases the steady infiltration rate after a long exposure to rainfall. When soil surface sealing is considered, the ponding time is only slightly affected but significantly more runoff is produced. However, the effects of soil variability on the infiltration curve are reduced, compared to the unsealed field. The approximation that the infiltration curve is a unique function of cumulative rainfall independent of rainfall intensity is not valid in a sealing heterogeneous field case. On the other hand, one may disregard the variability of all soil parameters, except the hydraulic conductivity, when calculating infiltration. Tel: 972-2-6585680; Fax: 972-2-6584437 http://cond-mat.phys.huji.ac.il/balberg/ email: Isaac Balberg The electrical properties of carbon black-polymer composites are of great interest from both, the basic physics and the commercial-applications points of view. Correspondingly, these Convective Cahn-Hilliard models have been suggested for the description of phase separation of driven systems and instabilities of crystallization fronts. With the increase of the driving force, a transition from the coarsening regime to a chaotic behavior takes place via a plethora of stable patterns characterized by a complex spatial structure but simple time dynamics. The relation of the dynamic transitions to the phenomenon of kinetic roughening of interfaces is discussed. A phase field model is proposed which incorporates the effects of slowly varying internal variables via a delayed or time averaged response of the system to the ambient driving forces. The internal variables we have in mind could model such effects as: (a) slow structural relaxation in a viscous solvent with a miscibility gap in the proximity of a glass transition temperature, or (b) clusters of impurity already segregated out from a mixture which might have a tendency to relax after quench. We demonstrate that these memory effects can cause inertial effects giving rise for example to oscillation relaxation during grain shrinkage. The phase field model with memory can also be shown to be no more unstable that the classical phase field model, in an appropriate sense. Moreover, certain long time features of the system can be readily assessed via formal asymptotics. phone +972 4829-3086(o); fax +972 4823-0476 Web: http://pattern.technion.ac.il email: Len Pismen Catalytic reactions on oriented single crystals often exhibit rate oscillations and produce a variety of spatio-temporal patterns on a micron scale. The most thoroughly studied
doi:10.1007/978-1-4020-2316-3_52 fatcat:x4kh7xkf6fajloq6fffagbyp24