Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach

Two-phase flow and capillarity phenomenon in porous solids, well known in physics and engineering, are treated from a rigorous continuum thermomechanical point of view for the first time. A ternary model, consisting of a porous solid phase, a liquid phase, and a gas phase, is investigated within the framework of thermodynamics. The main result of the evaluation of the entropy principle turns out to be that the interaction forces between the solid, gas, and liquid phases are dependent on the free Helmholtz energy functions of the corresponding phases and on the gradient of the liquid density. The classical result for the driving volume force for raising a water column in a narrow tube against the force of gravity is contained in the general investigation.     

Saturated Elastic Porous Solids: Incompressible,Compressible and Hybrid Binary Models

Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a compressible solid phase with an incompressible fluid phase (hybrid model of first type), and an incompressible solid phase with a compressible fluid phase (hybrid model of second type). The macroscopic continuum mechanical approach uses evaluation of entropy inequality with the saturation condition always considered as a constraint. This constraint leads to an interface pressure acting in both constituents. Two constitutive equations for the interface pressure, one for each phase, are identified, thus closing the set of field equations. The micromechanical approach shows that the results of Didwania and de Boer can be easily extended to general binary porous media.     

Saturated Compressible and Incompressible Porous Solids: Macro- and Micromechanical Approaches

In this paper two complementary approaches are used to describe the mechanical behavior of saturated compressible and incompressible porous solids. The macroscopic investigation is based on the mixture theory, restricted by the volume fraction concept. In the micromechanical approach, a hierarchy of conditionally ensemble averaged fluid and solid phase momentum balance equations are derived for a simple model of quasi-static liquid saturated porous media. The ensemble averaged equations for both the phases agree remarkably well with the macroscopic results. A micromechanical basis for Terzhagi's effective stress concept is presented. In addition, an expression for additional partial solid stress modifying the effective stress principle, to account for deformability of solid materials, is also derived.     

Flow regimes and flow transitions in liquid fluidized beds

Using two-dimensional liquid fluidized beds of glass particles in water, we have been able to identify at least four discrete fiow regimes. The points of transition between these regimes are sharp and non-hysteretic. The regimes include (in the order of increasing gm/gm_mf), wavy fiow, wavy fiow with transverse structure, fine-scale turbulent flow, and bubbling states. Characterization of each of these regimes is given in terms of the rime and length scales of the motion, as measured by light transmission, optical scanning, and digital time-series analysis. Features of the mechanics of these states are discussed. Observation of the bubbling state for particles of moderate density (ρ_s = 3990 kg/m³) in liquid beds is new, and is shown to be related fo anomalous expansion data reported by earlier investigators.