Fingering Instability of a Gravity-Driven Thin Film Flowing Down a Vertical Tube with Wall Slippage

Inspired by the antiwetting property of pitcher plants, specialists have designed different functional material with slippery surfaces, and a directional slippery surface has been fabricated. This paper considers a gravity-driven liquid film coating the interior surface of a vertical tube, and different slippery lengths in the azimuthal direction and the axial direction are taken into account. The evolution equation of coating flow is derived using the thin film model, and time responses for two dimensional flow are calculated. Linear stability analysis (LSA) is given based on the traveling wave solutions, demonstrating that the axial slippery effect suppresses the flow instability and causes a larger traveling wave speed. Simultaneously, the azimuthal slippery effect plays a destabilizing role for perturbations with small wavenumbers and it is stabilizing for large wavenumbers. Direct simulations of the fingering flow patterns agree well with the linear stability analysis. Our results offer insight into the influence of wall slippage on the flow stability of liquid in petroleum engineering.

WALL SLIPPAGE IN HIGH-PRESSURE CAPILLARY VISCOMETRY: EFFECTS OF MOLECULAR WEIGHT, COMPOUND COMPOSITION, AND CAPILLARY SURFACE COATING

ABSTRACT Flow behavior is of major importance in the extrusion processing of rubber compounds. It is evaluated by means of a series of tests on a high-pressure capillary viscometer (HCV). Adhesion between the polymer melt and the capillary wall is assumed in all current calculation models, although such adhesion does not always pertain to the case of rubber compounds. To date, no uniform model discussed in the literature on the topic extensively describes the wall slippage behavior of rubber compounds. The phenomenon of wall slippage is analyzed by determining the power-law parameters n (flow exponent) and K (consistency factor) from the flow curve in the subcritical flow range. This makes it possible to explicitly calculate first the slip velocity and then the slippage ratio relative to the total volume flow as a function of the given shear rate and temperature. The work is based on the testing of EPDM raw polymers of different molecular weights in the HCV. In addition, EPDM compounds containing either a carbon black or a softener were analyzed with regard to their flow behavior. The rheological analysis was carried out on three variously coated flow channels. It was observed that with attainment of a critical wall shear stress, the wall slippage effect becomes more pronounced; thus, occurrences of flow anomalies such as slip-stick or shark-skin significantly influence processing and flow behavior. Wall slippage effects are noticeable, however, even before the critical wall shear stress is attained.

Heterogeneous flow kinematics of cellulose nanofibril suspensions under shear

The coexistence of multiple flow bands, wall slippage and possible multidimensional effects in enzymatic and TEMPO cellulose nanofibril suspensions under shear were revealed using optical and ultrasonic speckle velocimetry (USV) rheometry techniques.