Radial Spreading Research Articles

Experimental investigation of the precessing vortex core in annular swirling jet flows in the transitional regime

In this paper, we study the flow structures and associated dynamics of an annular swirling jet in the transitional flow regime at Re = 520. In literature, studies on fully laminar or turbulent jets are plentiful, but detailed quantitative data for transitional jets are very scarce. Time-resolved stereoscopic particle image velocimetry measurements are employed to study the flow dynamics in combination with a spectral proper orthogonal decomposition analysis to extract the large-scale motions. Three different swirl numbers Sw are measured: Sw = 0.38, 0.47 and 0.57, with the lowest one very close to the critical swirl number for vortex breakdown to occur. Swirl has a significant impact on the flow field. For the lowest swirl number (Sw = 0.38), a vortex breakdown bubble appears/disappears periodically corresponding to a Strouhal number St = 0.023. If the swirl is increased to Sw = 0.47, the breakdown bubble remains permanently present in the flow field, accompanied with a large-scale vortical structure called the Precessing Vortex Core (PVC). The PVC precesses around the central axis of the jet at a Strouhal number of 0.23. It was observed that the precessing frequency of this spiral vortex core decreases to St = 0.146 as the swirl is increased to Sw = 0.57. This decrease of precession frequency finds its origin in the increased radial spreading of the jet, reducing the rotation rate of the flow near the centre. The 3D structure of the PVC is reconstructed from the planar stereo-PIV measurements by rotating the measurement plane around the central axis of the jet geometry in synchronisation with the precession. It is shown that the PVC is wrapped around the central vortex breakdown bubble and the windings are directed opposite to the swirl direction. This geometrical structure is also found in fully laminar or turbulent swirling jets and this paper shows it is the same for transitional jets.

Surface Orientation Effect on Local Heat Transfer by Round Water Jet Impingement

This paper describes local heat transfer for a round water jet on upward-facing and downward-facing static plates. Impinging liquid jets have high heat transfer rates. One of the technological issues in the steel making process is uniformity in cooling between the top and bottom sides of a plate. The objective of this study is to investigate the surface orientation effect on transient heat transfer experimentally. Experiments were conducted for a range of water flow rate, surface orientation. Both surface orientations were conducted on the same apparatus. The heat transfer plate was stainless steel to deal with both supercritical flow and subcritical flow regions. The plate length was wide for laboratory scale. Initial plate temperature was 800 degrees Celsius. Pipe Reynolds numbers were laminar flow regime. Inverse solution was employed to estimate transient local surface temperature and heat flux. Heat transfers between upward-facing and downward-facing surfaces are the same in the order of magnitude at downward-facing surface flow rate from 1.2 times to twice that of upward-facing surface. Local downward-facing surface temperature is higher than that of upward-facing temperature at the same flow rate. The following points can be given as reasons. Downward-flowing impinging jet velocity is larger than that of upward-flowing jet at the same flow rate due to gravity direction. Heat transfer is affected by a geometric arrangement relation of radial spreading liquid film, vapor and hot plate.

Morphological, structural and mechanical characterization of cold sprayed hydroxyapatite coating

The present paper investigates the deposition behavior of cold spraying agglomerated hydroxyapatite (HA) particles on stainless steel (SS) and HA substrates; for that purpose, the surface morphologies and cross-section microstructures of splats were investigated and compared to that of original HA particles. Full characterization of the coating was performed through the evaluation of (i) phase constitutions, crystallographic structure and composition, and coating/substrate interface as well as (ii) nanohardness of the powder, microhardness, tensile strength and the abrasive wear properties of the coating. HA splats on both substrates exhibited cap-like shape morphology with rough surface, and had some ring grooves on surface and some radial stripes on periphery composing of tiny HA granules. The cross-section of HA splats presented an asymmetric ellipsoid morphology with a flat bottom surface and convex up surface as well as compact area near bottom interface. Bonding of splats/substrate interface was related to the splats size and substrate materials. CS HA coating possessed a dense and homogeneous microstructure with reduced pores and crystal size, similar chemical structures, phase constitutions and chemical compositions to original powder. These microstructure evolutions were related to the deformation behavior of HA splats, i.e. radial spreading and compacting in impact direction by the un-continuous moving of agglomerates or granules in low temperature. Microhardness, tensile strength and the abrasive wear rate of the coating were 59.0 ± 5.6 kg/mm2, 10.9 ± 1.1 MPa and 1.3 ± 0.2 × 10−1 mg/(m·N), respectively.

Temporal changes in the internal stresses and pore pressures in a large-scale submarine mass transport deposit

We examined the temporal changes in the internal stresses and pore fluid pressures of a submarine mass transport deposit (MTD) in the Akkeshi Formation of the Upper Cretaceous–Paleocene Nemuro Group, eastern Hokkaido Island, Japan. We first analyzed previous paleostress field results from meso-scale faults in the MTD blocks, which indicated two phases during the evolution of the debris flow: phase I, radial spreading of the flow body during downslope movement; phase II, the flow body underwent compression during deposition on the basin plain. We also estimated the pore fluid pressure ratio from the fault orientation distribution. There was a large increase in the pore fluid pressure ratio during the transition from phase I to phase II that continued to rise during the initial stage of phase II and then decreased in its latter stages, whereas the maximum horizontal compressive stress increased throughout phase II. This variation in pore fluid pressure relates to the dynamics and evolution of the debris flow, where the clasts in the central part of the flow were supported by the excess pore pressure due to the compression of the debris flow as the flow head decelerated. Although pore fluid pressure plays a critical role in the dynamics of debris flows, there was no previous methodology to quantify both the stress fields and pore fluid pressures in large debris flows and their resultant MTDs. Our results implemented for outcrop studies imply that meso-scale faults in MTDs can provide clues to better understand these paleoflow mechanisms.

Demonstration of Thrust Vector Control by Hydrogen Peroxide Injection in Hybrid Rockets

A liquid injection thrust vector control (LITVC) system was designed for a hybrid rocket that uses 95 wt % hydrogen peroxide, and the system was demonstrated by using the hydrogen peroxide as the injectant. The influence of the chamber pressure, injectant flow rate, and injection location on the LITVC performance was parametrically investigated. The investigations revealed that the chamber pressure had a significant influence on the LITVC performance. As the chamber pressure increased from 20 to 40 bar, the side specific impulse improved from 71.7 to 157.3 s under injectant flow rates equal to 9% of the primary gas flow rates and at the injection location of (where is the distance from the throat to the injection location and is the length of the nozzle diverging section). To examine the effects of injection location on the LITVC performance, side specific impulses were measured at , 0.47, and 0.72 under the chamber pressure condition of 40 bar. Among all injection locations, provided the highest side specific impulses under all injectant flow rate conditions. Furthermore, the radial spreading caused by increasing the injectant flow rates degraded the LITVC efficiency.

Ret and Substrate-Derived TGF-β Maverick Regulate Space-Filling Dendrite Growth in Drosophila Sensory Neurons

Dendrite morphogenesis is a highly regulated process that gives rise to stereotyped receptive fields, which are required for proper neuronal connectivity and function. Specific classes of neurons, including Drosophila class IV dendritic arborization (C4da) neurons, also feature complete space-filling growth of dendrites. In this system, we have identified the substrate-derived TGF-β ligand maverick (mav) as a developmental signal promoting space-filling growth through the neuronal Ret receptor. Both are necessary for radial spreading of C4da neuron dendrites, and Ret is required for neuronal uptake of Mav. Moreover, local changes in Mav levels result in directed dendritic growth toward regions with higher ligand availability. Our results suggest that Mav acts as a substrate-derived secreted signal promoting dendrite growth within not-yet-covered areas of the receptive field to ensure space-filling dendritic growth.

Modeling Soot Formation in Turbulent Jet Flames at Atmospheric and High-Pressure Conditions

Simulations of soot in an atmospheric turbulent jet flame and in high-pressure turbulent diesel jets are presented. A kinetic soot model and a semiempirical soot model are employed for predicting soot in the atmospheric jet flame. Consistent with results published in the literature, this work shows that the kinetic model predicts the location of the maximum soot volume fraction to lie considerably upstream of the measured maximum soot volume fraction. Furthermore, the radial spreading and axial penetration are lesser than in the measurements. The semiempirical model is able to predict the location of the maximum within 20%, but the lower radial spreading and axial penetration persist suggesting potential deficiencies in predicted soot oxidation. The semiempirical model is applied to simulate soot in diesel jets and shown to predict the measured location of the soot and effect of changes in operating conditions well.

Axisymmetric three-dimensional gravity currents generated by lock exchange

Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial–buoyancy equilibrium regime and a viscous–buoyancy equilibrium regime. The viscous–buoyancy phase is in good agreement with the model of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), while the inertial phase is consistent with the experiments of Britter (Atmos. Environ., vol. 13, 1979, pp. 1241–1247), conducted for purely axially symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert & Simpson (J. Fluid Mech., vol. 99 (04), 1980, pp. 785–799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. As expected, the slumping phase is governed by the Froude number at the lock’s gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial–buoyancy regime in the presence of hydrodynamic shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant-volume and planar gravity currents, despite their own environmental relevance.

Insights into the kinematics and dynamics of the Luanshibao rock avalanche (Tibetan Plateau, China) based on its complex surface landforms

Complex topographic features on the surfaces of rock avalanche deposits have been regarded as important indicators for understanding avalanche kinematics and dynamics. Based on a combination of remote sensing data and in-situ observations of surface landforms, including toreva blocks, transverse and longitudinal ridges, ridges separated by conjugate troughs, and hummocks, a giant Holocene rock avalanche on the Tibetan Plateau is recognized. This work aims to understand the kinematics of this event. In planview, the tongue-shaped rock avalanche exhibits a clear sequential distribution of various landforms. The translation zone (II) is characterised by toreva blocks originating from extension. In subzone III-1 of the accumulation zone (III), compression-related transverse ridges are well developed. Longitudinal ridges resulting from lateral velocity differences due to radial spreading are present in the front part of subzone III-1. Farther down, ridges separated by conjugate troughs (generated by a combination of compression and radial spreading) are common in subzone III-2. Subzone III-3 is characterised by abundant scattered hummocks with circular to oval shapes. Based on the distributions of these landforms, this rock avalanche is proposed to have mainly experienced a motion featuring laminar flow with radial spreading in its distal and marginal parts. During transport, three distinct processes appear to have occurred in the avalanche mass from the proximal to the distal zones: extension-dominated sliding in zone II, compression-dominated sliding in subzones III-1 and III-2, and rapid radial spreading in subzone III-3.

Impact of bootstrap current and Landau-fluid closure on ELM crashes and transport

Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and collisionless Landau resonance closures make a little difference on linear growth rate spectra which are quite close to the results with the flux limited Spitzer-Härm parallel flux. Both linear and nonlinear simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total pressure and current, as the pedestal current decreases due to the bootstrap current which becomes smaller when the density (collisionality) increases, the operational point is shifted downwards vertically in the Jped – α diagram, resulting in threshold changes of different modes. The bootstrap current can slightly increase radial turbulence spreading range and enhance the energy and particle transports by increasing the perturbed amplitude and broadening cross-phase frequency distribution.

Modeling the dynamics of remobilized CO2 within the geologic subsurface

Long after CO2 is injected into a brine aquifer, most reservoir-scale fluid dynamic simulations predict large fractions of the original plume will become immobilized via capillary trapping and dispersed throughout the formation. We begin our analysis with a reservoir in this state and consider the effects caused by a depressurization of the domain (e.g. from a nearby production well or newly formed fracture between neighboring reservoirs) and predict the fraction of CO2 that will be remobilized as a result. We then model the dynamics of this remobilized CO2 in two distinct steps: (1) vertical rise within the reservoir, followed by (2) spreading of mobile CO2 into the far-field of the domain and justify this approach from a scaling analysis of the governing equations. We show that a model of relative permeability that takes account of insights from percolation theory near the minimum CO2 saturation leads to much more rapid rise and subsequent radial spreading of remobilized CO2 than a traditional empirical correlation such as the Brooks-Corey model. Furthermore, we find that over a broad range of remobilized CO2 mass fraction and Bond number, the radial extent of the mobile plume does not exceed a factor of 1.8 times the radius of the original immobilized CO2 region.

Investigating the radial spreading behavior of superimposed liquid drops

While the spreading behavior of a drop of liquid on a spinning surface is well-understood, a new study looks at what happens with superimposed drops, where one liquid drop is enclosed by another.

Preoperative ultrasound to identify distribution of the lateral femoral cutaneous nerve in total hip arthroplasty using the direct anterior approach.

Introduction: Recently, the branching pattern of the lateral femoral cutaneous nerve (LFCN) named Fan type has been reported that LFCN injury cannot be avoided in surgical dissections that use the direct anterior approach to the hip joint in the cadaveric study. We hypothesized that the Fan type can be identified by ultrasound The aim of this study was to investigate whether LFCN injury occurs in DAA-THA in cases identified as the Fan type based on preoperative ultrasound of the proximal femur.Methods: Ultrasonography of the proximal femur on the surgical side was performed before surgery and the LFCN distribution was judged as the Fan type or Non-Fan type. A self-reported questionnaire was sent to the patients at two months after surgery, and the presence or absence of LFCN injury was prospectively surveyed.Results: After application of exclusion criteria, 45 hips were included. LFCN injury was observed after surgery in 9 of the 10 patients judged as the Fan type based on the ultrasound of the proximal femur (positive predictive value: 90%), and no LFCN disorder was actually observed in 25 of the 26 patients judged as Non-Fan type (specificity: 96.2%).Conclusions: To prevent injury of the LFCN in patients judged as the Fan type on the ultrasound test before surgery, the risk of direct injury of the LFCN may be reduced through the approach in which an incision is made in the fascia which is opposite to the radial spreading, i.e., between the sartorius and tensor fasciae latae muscles or slightly medial from it.

Roles of interfacial heat transfer and relative solder height on segregated growth behavior of intermetallic compounds in Sn/Cu joints during furnace cooling

Pure Sn solder balls of initial diameter of 2 mm, having been reflow soldered on Cu substrate at 573.15 K for 1, 2 and 5 min, were subjected to furnace cooling. Upon the start of reflow, the initially spherical solder balls underwent a rapid radial spreading and wetting on Cu substrate and thus attained non-spherical geometry with a maximum height at the center whereas a minimum one at the periphery. The wetting or interfacial reaction, that would produce an even scalloped intermetallic compounds (IMCs) during isothermal reflow, resulted in the growth of dense prismatic IMC rods at the central region during cooling whereas the peripheral scalloped IMCs were not overriden by the faceted or prismatic rods during the temperature reduction procedure. Reduced interfacial heat transfer at the central interface, existence of radial isotherms and lowered supply of Cu precipitates at the peripheral interface owing to the compromised solder height have been discussed as the factors responsible for the segregated IMC morphology. The abundant precipitation of Cu and the presence of thermal gradient, sustain a screw dislocation based growth of hexagonal IMC whiskers. The increase in reflow duration is associated with the enhanced tubularity of the rods. Finite element method has been utilized to accomplish numerical simulations for heat and mass transfer in solder phase as well as for anisotropic thermal conduction at the dislocation in evolving IMC.

Quantitative comparison of the spreading and invasion of radial growth phase and metastatic melanoma cells in a three-dimensional human skin equivalent model.

BackgroundStandard two-dimensional (2D) cell migration assays do not provide information about vertical invasion processes, which are critical for melanoma progression. We provide information about three-dimensional (3D) melanoma cell migration, proliferation and invasion in a 3D melanoma skin equivalent (MSE) model. In particular, we pay careful attention to compare the structure of the tissues in the MSE with similarly-prepared 3D human skin equivalent (HSE) models. The HSE model is identically prepared to the MSE model except that melanoma cells are omitted. Using the MSE model, we examine melanoma migration, proliferation and invasion from two different human melanoma cell lines. One cell line, WM35, is associated with the early phase of the disease where spreading is thought to be confined to the epidermis. The other cell line, SK-MEL-28, is associated with the later phase of the disease where spreading into the dermis is expected.Methods3D MSE and HSE models are constructed using human de-epidermised dermis (DED) prepared from skin tissue. Primary fibroblasts and primary keratinocytes are used in the MSE and HSE models to ensure the formation of a stratified epidermis, with a well-defined basement membrane. Radial spreading of cells across the surface of the HSE and MSE models is observed. Vertical invasion of melanoma cells downward through the skin is observed and measured using immunohistochemistry. All measurements of invasion are made at day 0, 9, 15 and 20, providing detailed time course data.ResultsBoth HSE and MSE models are similar to native skin in vivo, with a well-defined stratification of the epidermis that is separated from the dermis by a basement membrane. In the HSE and MSE we find fibroblast cells confined to the dermis, and differentiated keratinocytes in the epidermis. In the MSE, melanoma cells form colonies in the epidermis during the early part of the experiment. In the later stage of the experiment, the melanoma cells in the MSE invade deeper into the tissues. Interestingly, both the WM35 and SK-MEL-28 melanoma cells lead to a breakdown of the basement membrane and eventually enter the dermis. However, these two cell lines invade at different rates, with the SK-MEL-28 melanoma cells invading faster than the WM35 cells.DiscussionThe MSE and HSE models are a reliable platform for studying melanoma invasion in a 3D tissue that is similar to native human skin. Interestingly, we find that the WM35 cell line, that is thought to be associated with radial spreading only, is able to invade into the dermis. The vertical invasion of melanoma cells into the dermal region appears to be associated with a localised disruption of the basement membrane. Presenting our results in terms of time course data, along with images and quantitative measurements of the depth of invasion extends previous 3D work that has often been reported without these details.

Sheet intrusions and deformation of Piton des Neiges, and their implication for the volcano-tectonics of La Réunion

To understand the volcano-tectonic history of Piton des Neiges (the dormant volcano of La Réunion), we measured in the field the orientation of sheeted intrusions and deformation structures, and interpreted the two datasets separately with a paleostress inversion. Results show that the multiple proposed rift zones may be simplified into three trends: (1) a N30°E, 5km wide linear rift zone running to the south of the edifice, active in the shield building (≥2.48–0.43Ma) and terminal stages (190–22ka); (2) a curved N110 to N160°E rift zone, widening from 5km to 10km toward the NW flank, essentially active during the early emerged shield building (≥1.3Ma); and (3) two sill zones, ≤1km thick in total, in the most internal parts of the volcano, active in the shield building and terminal stages.In parallel, deformation structures reveal that the tectonics of the edifice consisted in three end-member stress regimes sharing common stress axes: (1) NW-SE extension affecting in priority the south of the edifice near the N30°E rift zone; (2) NNE-SSW extension on the northern half of the volcano near the N110-160°E rift zone; (3) compression occurring near the sill zones, with a NE-SW or NW-SE maximum principal stress. These three stress regimes are spatially correlated and mechanically compatible with the injection trends.Combined together, our data show that the emerged Piton des Neiges underwent sector spreading delimited by perpendicular rift zones, as observed on Piton de la Fournaise (the active volcano of La Réunion). Analogue experiments attribute such sector spreading to brittle edifices built on a weaker substratum. We therefore conclude that La Réunion volcanoes are both brittle, as opposed to Hawaiian volcanoes or Mount Etna whose radial spreading is usually attributed to a ductile body within the edifices.

The empty primordial asteroid belt.

The asteroid belt contains less than a thousandth of Earth's mass and is radially segregated, with S-types dominating the inner belt and C-types the outer belt. It is generally assumed that the belt formed with far more mass and was later strongly depleted. We show that the present-day asteroid belt is consistent with having formed empty, without any planetesimals between Mars and Jupiter's present-day orbits. This is consistent with models in which drifting dust is concentrated into an isolated annulus of terrestrial planetesimals. Gravitational scattering during terrestrial planet formation causes radial spreading, transporting planetesimals from inside 1 to 1.5 astronomical units out to the belt. Several times the total current mass in S-types is implanted, with a preference for the inner main belt. C-types are implanted from the outside, as the giant planets' gas accretion destabilizes nearby planetesimals and injects a fraction into the asteroid belt, preferentially in the outer main belt. These implantation mechanisms are simple by-products of terrestrial and giant planet formation. The asteroid belt may thus represent a repository for planetary leftovers that accreted across the solar system but not in the belt itself.

Intra-salt deformation: Implications for the evolution of the Messinian evaporites in the Levant Basin, eastern Mediterranean

We present new evidence of deformation features supporting a multiple deformation phase mechanism of the Messinian evaporites, through the interpretation of Pre-Stack Depth Migration (PSDM) seismic data including all intra-salt, base of salt (BS) and top of salt (TS) reflectors. The mechanism presented here involves a syn-depositional deformation event caused by a NW basin tilting during the last stage of the Messinian Salinity Crisis (MSC). This was followed by post-depositional differential sediment loading through radial spreading of the Nile Cone after the MSC. Inside the evaporite sequence, the upper intra-salt units may reside in a brittle domain with predominant thrust faults while the lower units in a ductile deformation domain with folds instead. A NW-flowing channel system is for the first time observed on the TS horizon, suggesting a northwestward basin depocenter during the TS formation. The observed NNW-NNE flow of the water bottom (WB) channels indicates the direction of the current basin depocenter, which suggests a dramatic clockwise shift during post-Messinian. A model of the Messinian evaporite evolution in the Levant Basin during the MSC has been established. The model is based on our observations and the detailed intra-salt interpretation, and is divided into four stages: a) the horizontal deposition of all the intra-salt units excluding the uppermost unit, b) the deposition of the uppermost unit and basin NW tilting occurred coevally or sequentially, c) the TS erosion and the development of NW trending TS channels and d) the deposition of post-Messinian sediments over the evaporite sequence.

Exponential estimates of perturbations of rigid-plastic spreading-sink of an annulus

The time evolution of the plane picture of small perturbations imposed on the radial spreading or sink of an annulus made of incompressible ideally rigid-plastic material obeying the Mises–Hencky plasticity criterion is studied. The adhesion conditions are posed on the extending (contracting) boundaries of the annulus in both the ground and perturbed processes. The method of integral relations, which is based on variational inequalities in the corresponding complex Hilbert space, is used to reduce the linearized problem in perturbations to a single relation for quadratic functionals, which permits deriving new exponential upper bounds for the growth or decay of kinematic perturbations. It is shown that the evolution of angular harmonics with distinct numbers is qualitatively distinct.

Entrapment of air during imbibition of agglomerated powder beds

Complete wetting is crucial for efficient recombination of powders. On the powder bed scale, wetting is governed solely by capillary forces and the resistance to flow, i.e. spontaneous imbibition. Slow or incomplete imbibition of the powder bed may lead to gelling of the liquid front, which will stop the recombination process and cause the formation of lumps, which is usually undesirable.In this study, the spontaneous imbibition of powder beds consisting of spray-dried dairy powders with diverse morphologies has been investigated. Uniform radial spreading of the imbibition front was seen in all the beds, but a large amount of air was trapped in the inter-particle free space in the imbibed volume. A positive correlation was found between bed porosity and the fraction of air trapped in the bed after imbibition. Since the amount of trapped air was calculated as a fraction of the porosity of the dry bed, this relation was unexpected.The large fraction of air trapped in the bed and the uniform radial spreading of the imbibition front indicate considerable heterogeneity of bed on the microscopic scale, but a homogenous structure on the macroscopic scale. Possible explanations of the large fraction of trapped air are the presence of local dead-end structures in the bed and film flow of the imbibing liquid.