Estimation of the Rheological Properties of a Suspension in a Gel Fluid

Abstract

M ODERN propelled flight requires constant improvement in two major areas: safety and performance. Gel fuels are considered as candidates that fulfill these requirements. Ideally, gel fuels can be used instead of liquids in existing aerospace engines like liquid rocket motors and ramjet engines. In aerospace applications, the term “gel” usually indicates a fluid that is shear thinning (the viscosity decreases with increasing shear rate) and in some cases has a yield stress [1]. The gel fuel structure is obtained by adding a small amount (2–20% weight) of gellant to a liquid fuel, thus altering the rheological properties of the liquid, i.e., increasing its zero-shear viscosity and introducing shear-thinning properties. The above-described behavior enhances both safety and performance. Additional safety is achieved due to the fact that yield stress and increased zero-shear viscosity inhibit involuntary flow [1]. The energetic improvement is achieved by enabling the addition of metal powders to the liquid. Metal particles are desired additives in rocket and ramjet motors due to their high-combustion energy release and density in comparison to hydrocarbons. However, using metal powders in liquid propulsion systems is problematic due to particle sedimentation. Therefore, the use of gel fuels that can be stored as “solids” and used as “liquids” seems most adequate. Assuming that these gels obey a kind of power–law (P–L) constitutive equation the desired P–L index should be as low as possible. Gels, with their high, yet controllable [2], zero-shear viscosity make this desired feature more feasible. Gel fuels introduce new challenges in the design of rocket or ramjet motors [3,4]. Instead of the familiar flow of a Newtonian fluid in the feeding system a two-phase, non-Newtonian flow needs to be taken into account. This influences the required pressures in the feeding system. The possibilities of powder deposition, erosion of the components in the supply line, phase separation, partial or full clogging, and other phenomena related to two-phase fluid-solid flow should be considered during the design of the feeding system. Shear stress, viscosity profile, and particle concentration profiles at the exit of the atomizer influence the atomization characteristics [5] of the fluids and must be accounted for. Suspensions in Newtonian fluids have been a subject for many studies. Einstein [6] found that the viscosity of the suspension is related to the viscosity of the pure liquid in the following form: