New simple analytical method for flow enhancement predictions of pulsatile flow of a structured fluid

Abstract

In this work, a new simplified method to find the fluidity enhancement of a non-Newtonian liquid under a pulsating (time-dependent) pressure gradient is analyzed. The fluidity enhancement is predicted by means of a Taylor series expansion of the flow rate in the vicinity of the applied wall stress. This expansion is shown to render the same results as several perturbation techniques used at length in the literature. Both new and the conventional perturbation methods are equivalent in their predictions of the fluidity enhancement. Even though the flow and rheology behavior are modeled using the Bautista-Manero-Puig constitutive equation, it is shown that the prediction of the fluidity enhancement does not depend on the constitutive model employed, but a condition of shear thinning behavior of the fluid is necessary for it. Flow enhancement is predicted using rheological data for blood since this fluid naturally flows under a pulsatile pressure gradient. The flow enhancement equation is found to have a similar form as the equation of the Rabinowitsch formalism in fully developed Poiseuille flow. This simplified technique will help in saving machine time for numerical predictions in computational blood flow simulations.

Effects of multiple relaxation times in the annular flow of pulsatile electro-osmotic flow of a complex biological fluid: blood with low and high cholesterol

“…The effect of these anticoagulants can be predicted through constitutive modeling of blood (Moyers-Gonzalez et al, 2008). The complex circulatory system (heart, vein, and artery) can be modeled, at a first approach, as a capillary flow under a simple stochastic pulsating-pressure gradient (Herrera-Valencia et al, 2017, Herrera-Valencia et al, 2019. The occlusions are proposed here as a concentric cylinder system, where the central cylinder represents the occlusion and the diameter of such a cylinder represents the size of the occlusion, which is a simplification of the real case to study the analytical relations between the different variables involved as a first approximation to study this complex system, and flow is considered completely developed with no transitions (Collepardo-Guevara and Corvera-Poiré, 2007).…”

“…According to our material analysis (see, for example, Supplementary Appendix SA), the system can be classified into the following important modes. These modes are linked to the Lagrange multipliers and were previously studied by Herrera-Valencia et al (2017), Herrera-Valencia et al (2019.…”

“…To this end, another technique for controlling fluid flow is to use pulsatile or oscillating flow . Enhancement of the volumetric flow by the time-pulsating force has found application in different branches of science, such as DNA dynamics (Jendrejack et al, 2013), microcapillaries with slip conditions (Sanchez et al, 2013), blood with cholesterol (Herrera-Valencia et al, 2017), structured fluids (Herrera-Valencia et al, 2019), flexoelectric membranes (Herrera-Valencia and Rey 2023), and mass transfer (Mederos et al, 2020).…”

Normal Stress Differences of Human Blood in Unidirectional Large-Amplitude Oscillatory Shear Flow

“…To investigate hemorheology, some use blood biochemistry and microstructures to model blood [17][18][19][20][21][22]. These molecular models can provide direct insights, but computational cost is generally [23]; [12,24]).…”