Effect of parallel electric field on the linear stability between a Newtonian and a power-law fluid in a microchannel

Applying an electric field to a two-fluid flow in a microchannel is an effective way to obtain microdroplets. For that purpose, the stability of the interface between a Newtonian and a power-law fluid flowing in a microchannel is studied. The fluids are either leaky dielectric or perfect dielectric. The effects of the applied voltage, the power-law index, and the strength of the base flow are investigated. Increasing the voltage may destabilize or stabilize the system depending on the electrical properties of the leaky dielectric fluids, similar to a system of two Newtonian fluids. When the electric field destabilizes the system, the maximum wavenumber increases, representing a droplet volume decrease. For perfect dielectric fluids, the electric field permanently stabilizes the flow independent of the electrical properties of fluids. The stability behavior of the power-law index depends on the fluids’ thickness ratio. When the power-law index is added as a new parameter, the base flow strength also affects the system stability, even when the thickness and viscosity ratios are unity, unlike two Newtonian fluid system. Depending on the fluids’ power-law index, and viscosity ratio, the base flow strength may stabilize or destabilize the system. Additionally, a sudden decrease in the droplet volume may be observed for some values of the power-law index and viscosity ratios

A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge

Initially motivated by the analysis of the flow dynamics of the synovial fluid, taken as non-Newtonian, this paper also reports on a numerical challenge which occurred unexpectedly while solving the momentum equation of the model. The configuration consists of two infinitely long horizontal parallel flat plates where the top plate is sheared at constant speed and the bottom plate is fixed. The synovial fluid shows a shear-thinning rheology, and furthermore it thickens with the hyaluronic acid (HA) concentration, i.e., it is also chemically-thickening. Accordingly, a modified Cross model is employed to express the shear rate and concentration-dependent viscosity, whose parameter values are determined from experimental data. Another significance of the study is the investigation of the effect of an external stimulus on the flow dynamics via a HA source term. The resulting flow exhibits peculiar features resulting from extremely large and small, but positive, numerical quantities, such as the viscosity and the shear rates. This requires constructing a parametrized zero-machine level solver, up to 300 accurate digits or so, for capturing the correct length scales of the flow physics. As a conclusion, the physical model, although simple, but original, leads to interesting results whose numerical determination turns out to be successful only once the real cause of the numerical trap is identified