Simulation of slot-coating of nanocellulosic material subject to a wall-stress dependent slip-velocity at die-walls

Bio-based nanocellulosic materials are non-toxic, renewable, exhibit excellent barrier properties, and are suitable candidates for sustainable food packaging applications. Sizing and designing coating parameters for slot-coating process using nanocellulose suspensions is challenging due to complex shear-thinning rheology and the presence of a water-rich boundary layer, effecting significant apparent slip at the wall. Previous studies have shown that the flow inside the coating bead can be complex, with occasional stagnation regions and a rheological model incorporating yield stress which should be considered while analyzing slot coating of nanocellulosic flows. This work extends earlier investigations by including the effects of the particle depleted water-rich boundary layer. The suspension is modeled as a Casson fluid with a shear-thinning viscosity, and the particle depletion at the wall is represented by an infinitely thin layer modeled as a local shear-dependent nonlinear slip law. The resulting two-phase flow equations are solved using a Finite Volume Method (FVM) coupled with the Volume of Fluid (VoF) method for tracking the free surface interface. It is observed that slip alters the flow’s dynamics in the coating bead, and the effect of slip cannot be ignored, especially at high shear rates. For thin films, the presence of slip enhances the flow, leading to more material coated on the substrate. In contrast, for thicker coatings, apparent slip leads to an augmentation in stagnant, non-yielded regions, potentially generating uneven surfaces.

Quaternary Displacement on the Joiner Ridge Fault, Eastern Arkansas

ABSTRACT The New Madrid seismic zone of the central United States is an intraplate seismic zone with blind structures that are not seismically active but may pose seismic hazards. The Joiner ridge fault (JRF) is the 35‐kilometer‐long east‐bounding fault of the Joiner ridge blind horst located in eastern Arkansas ∼50 km northwest of Memphis, Tennessee. Shallow S‐wave (SH‐mode) seismic reflection profiles, continuous cores, and radiometric dating of Quaternary alluvium across the JRF reveal down‐to‐the‐east reverse faulting and folding of Eocene strata and overlying Quaternary Mississippi River alluvium. The base of the Quaternary alluvium has an age of 20.3 ka and is vertically displaced 12 m, resulting in an average slip rate of 0.6±0.1 mm/yr over the past 20.3 ka. The overlying upper Wisconsinan and Holocene alluvial facies are also displaced by the JRF. These facies increase in thickness across the JRF and were used to calculate late Wisconsinan and Holocene slip histories. The JRF slipped 7 m between 20.3 and 17.5 ka, 3 m between 12.3 and 11.5 ka, and 2 m between 11.5 and 8.9 ka. No apparent slip occurred on the JRF within the last 8.9 ka. This research illustrates that slip has been intermittent and that slip magnitudes on the JRF diminished through the late Wisconsinan and early Holocene.

On the Effect of Trailing Edge Under-Filing on the Apparent Slip Factor of Centrifugal Impellers

The trailing edge flow in a centrifugal impeller is of great importance as it determines the exit flow velocity triangle and therefore the work transferred to the fluid. The present study deals with the impact of trailing edge under-filing on the impeller exit flow and the resulting slip factor. Different under-filed trailing edge shapes are investigated by means of numerical simulations. 2D-RANS simulations are performed for a wide range of blade angles. For the default cut-off trailing edge configuration an attached and a separated flow regime around the blade trailing edge can be distinguished, mainly depending on the blade exit angle. The occurrence of the separated flow regime is associated with a significant change in performance, mainly due to the reduced flow deflection at the impeller exit. Under-filing of the trailing edge leads to less apparent slip for blade angles up to 40 degrees. This can be attributed to the fact that under-filing prevents the attached flow regime occurring in case of the default trailing edge. Additional DES simulations provide deeper insight into the detailed flow structures involved in this phenomena and reveal the turbulent flow structures in the trailing edge and wake flow. The obtained results provide a deep insight into trailing edge flows in centrifugal pump impellers and help to get a better understanding of the phenomena involved. Moreover, the results can provide an explanation to the often observed deviation of the apparent impeller slip from the theoretical slip predicted by slip factor models.

The sinkage characteristics and prediction of a planetary rover based on a similarity model experiment

The environment on an extraterrestrial planet is complex, with soft surfaces and low gravity, which make it easy for rovers to sink and skid. Excessive sinkage may occur under large slip conditions of probe rovers and could influence the survey mission. Predicting the sinkage performance of wheels under slip conditions is important for the development and performance evaluation of exploration rovers. This paper presents a dimensional analysis on the main parameters of the wheel–soil interaction system; the analysis was performed based on the similarity law, for which corresponding similar scale values were obtained. Referring to the lunar surface gravity environment, we have produced a 1/2 scaling model rover. To investigate the sinkage characteristics of the model rover, tests were performed with different wheel loads (5 N, 7 N, and 9 N) and soil states (loose, natural, and compact). The characteristic parameters of a rear wheel rut were also analyzed, including rut depth (hereinafter referred to as apparent sinkage) and slip ratio (hereinafter referred to as apparent slip ratio). Experimental results were analyzed to evaluate the sinkage characteristics and to draw conclusions. Sinkage models for the rover under different soil states were proposed, and verification and error analyses for the sinkage models were conducted using indices such as the mean relative error and root mean squared error. The experimental results and conclusions are useful for optimal rover design and improvement/verification of wheel–soil interaction mechanics models.

Analytical and Numerical Investigations of Friction Number for Laminar Flow in Microchannels

Analytical and computational fluid dynamics (CFD) analyses confirmed the presence of apparent slip for water flow in microchannels with equivalent hydraulic diameter, Dh < 103μm, markedly decreasing the friction number, fRein. The determined values of the slip length, β, from reported measurements of pressure losses in microchannels with aspect ratio, α = 1, 1.74, 2, and 40, are 0.9, 3.5, 1.6, and 0.125 μm, respectively. For Dh > 103μm, the apparent slip in microchannels diminishes, and the friction number approaches the theoretical Hagen–Poiseuille with no slip. The analytical solution for fully developed flow successfully benchmarked the CFD approach, which is subsequently used to investigate fRein and the flow development length, Le, for uniform inlet velocity in microchannels. For fully developed flow, the analytical and CFD values of fRein are in excellent agreement. For microchannels with Dh < 103μm, fRein decreases below that of the theoretical Hagen–Poiseuille with no slip, almost exponentially with decreased Dh. The difference increases with decreased Dh, but increased α and β. The friction number for uniform inlet velocity is identical to that for fully developed flow when Dh ≤ 100 μm, but is as much as 9% higher for larger Dh. For uniform inlet velocity, Le negligibly depends on α and β, but increases with increased Rein. The obtained values are correlated as: Le/Dh = 0.068 Rein.

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

We use interface-resolved numerical simulations to study finite-size effects in turbulent channel flow of neutrally buoyant spheres. Two cases with particle sizes differing by a factor of two, at the same solid volume fraction of 20 % and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501), a particle–wall layer is responsible for deviations of the mesoscale-averaged statistics from what is observed in the continuum limit where the suspension is modelled as a Newtonian fluid with (higher) effective viscosity. Here we investigate in detail the fluid and particle dynamics inside this layer and in the bulk. In the particle–wall layer, the near-wall inhomogeneity has an influence on the suspension microstructure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the scaling laws in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501) to second-order Eulerian statistics in the homogeneous suspension region away from the wall. The results show that finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that single-point dispersion is dominated by particle–turbulence (and not particle–particle) interactions, while differences in two-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.