A quantitative interpretation of the saturation exponent in Archie’s equations

Saturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

Early-time jet formation in liquid–liquid impact problems: theory and simulations

We perform a thorough qualitative and quantitative comparison of theoretical predictions and direct numerical simulations for the two-dimensional, vertical impact of two droplets of the same fluid. In particular, we show that the theoretical predictions for the location and velocity of the jet root are excellent in the early stages of the impact, while the predicted jet velocity and thickness profiles are also in good agreement with the computations before the jet begins to bend. By neglecting the role of the surrounding gas both before and after impact, we are able to use Wagner theory to describe the early-time structure of the impact. We derive the model for general droplet velocities and radii, which encompasses a wide range of impact scenarios from the symmetric impact of identical drops to liquid drops impacting a deep pool. The leading-order solution is sufficient to predict the curve along which the root of the high-speed jet travels. After moving into a frame fixed in this curve, we are able to derive the zero-gravity shallow-water equations governing the leading-order thickness and velocity of the jet. Our numerical simulations are performed in the open-source software Gerris, which allows for the level of local grid refinement necessary for a problem with such a wide variety of length scales. The numerical simulations incorporate more of the physics of the problem, in particular the surrounding gas, the fluid viscosities, gravity and surface tension. We compare the computed and predicted solutions for a range of droplet radii and velocities, finding excellent agreement in the early stage. In light of these successful comparisons, we discuss the tangible benefits of using Wagner theory to confidently track properties such as the jet-root location, jet thickness and jet velocity in future studies of splash jet/ejecta evolution.

INFLUENCE OF TRACES ADDITION OF TIN ON THE GROWTH AND ON THE COARSENING OF THE GUINIER-PRESTON ZONES IN Al-10% at.Ag ALLOY

<p class="AMSmaintext"><span lang="EN-GB">The formation of the Guinier-Preston zones in aluminium alloys is closely linked with the excess vacancies. Traces of tin added to an Al-Ag alloy exert an influence on the Guinier-Preston zones precipitation. Due to their high binding energy with vacancies, tin atoms trap some of these available to promote the diffusion of silver atoms for the formation of the Guinier-Preston zones. At 125°C, tin microalloying slows down the reaction of the Guinier-Preston zones precipitation. The diffusion coefficient of the solute atoms in the Sn free alloy and in the Sn added alloy are determined during the coarsening regime which obeys to the Lifshitz, Slyosov and Wagner theory.</span></p>

Ostwald Ripening Process of Coherentβ′ Precipitates during Aging in Fe0.75Ni0.10Al0.15and Fe0.74Ni0.10Al0.15Cr0.01Alloys

The Ostwald ripening process was studied in Fe0.75Ni0.10Al0.15and Fe0.74Ni0.10Al0.15Cr0.01alloys after aging at 750, 850, and 950°C for different times. The microstructural evolution shows a rounded cube morphology (Fe, Ni)Alβ′ precipitates aligned in the ferrite matrix, which changes to elongated plates after prolonged aging. The variation of the equivalent radii of precipitates with time follows the modified Lifshitz-Slyozov-Wagner theory for diffusion-controlled coarsening. Thermo-Calc analysis shows that the chromium content is richer in the matrix than in the precipitates which causes higher hardness and coarsening resistance in the aged Fe0.74Ni0.10Al0.15Cr0.01alloy.

Three-dimensional oblique water-entry problems at small deadrise angles

This paper extends Wagner theory for the ideal, incompressible normal impact of rigid bodies that are nearly parallel to the surface of a liquid half-space. The impactors considered are three-dimensional and have an oblique impact velocity. A formulation in terms of the displacement potential is used to reveal the relationship between the oblique and corresponding normal impact solutions. In the case of axisymmetric impactors, several geometries are considered in which singularities develop in the boundary of the effective wetted region. We present the corresponding pressure profiles and models for the splash sheets.