Mechanical Properties of Fluids and Porous Media

Abstract

Fluids possess characteristic physical properties that govern how they behave when forces are applied to them. Of particular interest are properties that govern fluid responses to ordinary mechanical forces; thus we will not consider electrical and magnetic phenomena, and we will defer treating thermodynamical properties of fluids to the next chapter. Further, we will adopt a classic treatment of bulk behavior, as opposed to fluid behavior below the continuum scale. For example, we will examine how a Newtonian fluid deforms (in bulk) in a systematic way when it is subjected to shear stress, such that the rate of strain is proportional to the stress. In contrast, the same nominal fluid very close to a rock surface within a small pore may exhibit a much more complicated rheological behavior, from which we can infer that surface phenomena fundamentally alter the behavior of the fluid from that observed in bulk. We also will see how different types of real fluids respond differently to an applied shear stress, including how the rate of strain of certain fluids varies with the duration of stress as well as other factors. In this regard we will distinguish between time-independent and time-dependent behaviors; in the latter case the behavior of a fluid depends on its history of strain. These basic ideas of fluid behavior are a foundation for most of the material covered in the remainder of the text. Nonetheless, this initial treatment of fluid properties will provide sufficient insight to fluid behavior to begin using simple mathematical analyses to examine several important fluid-flow problems. Likewise, the description here of mechanical properties of porous media also is a foundation for later use. Coverage of this topic, however, is restricted to items that will be useful to understanding fluid behavior. Certain mechanical properties of fluids are defined in terms of the forces acting on them. In this context, it is useful to distinguish two types of forces: body forces and surface forces. A body force is one whose magnitude is proportional to the volume or mass of a fluid parcel.