A second order fluid of the differential type

In this paper a new constitutive equation is proposed for viscoelastic fluids. It is based on the time derivatives of the left Cauchy-Green strain tensor and is thus believed to characterize a new material. From this constitutive equation, a second-order approximation is derived and it is shown that this second order fluid has a bounded and unique solution to the initial value problem of cessation of steady shear flow. This stability is in direct contrast with the presently well known second order models. Further, the natural time of the fluid is positive, making the theory consistent with the intuitive notion that phenomena in dissipative materials should depend on the past rather than the future. Finally, a test is proposed to distinguish the present second-order model from the earlier version.