The rapid absorption of water by paper towels is driven by their porous structure, where capillary forces, viscous resistance, and gravitational effects govern wicking dynamics. This study investigates the influence of inter-layer interactions in multi-ply configurations and the role of gravity in wicking behavior. Experiments are conducted on four paper towel brands–Bounty®, Tuff®, Sparkle®, and Georgia-Pacific®–in both vertical and horizontal orientations, representing conditions with and without gravitational influence, respectively. Near-infrared imaging is used to track the wetting front and the spatio-temporal evolution of moisture content (MC). Analysis of capillary rise length as a function of time reveals two distinct wicking regimes: an initial transitional phase followed by a later stable phase. MC contour analysis shows a decrease in water volume with elevation in vertical wicking, whereas in horizontal wicking, MC remains nearly uniform. These behaviors are attributed to the heterogeneous pore structure of paper towels, composed of interconnected pores of varying sizes. Larger pores facilitate faster flow and predominantly supply water to smaller pores, shaping overall wicking dynamics. This hierarchical distribution of flow explains the transition between wicking regimes and underscores the role of pore size variation in capillary-driven absorption.

Various methods exist to measure the areal density of particles resting on stationary surfaces. These techniques can be expensive, intrusive, or time-consuming, and in general cannot be used to measure particulate on a moving surface. We demonstrate an inexpensive oblique light measurement technique using a digital camera to measure the areal density of particles on a moving surface. This measurement technique is applicable for both bright and dark powders deposited on contrasting backgrounds and is insensitive to the precise orientation of particles on the surface. While the areal densities inferred from this technique have a 13-15 % median relative error compared to gravimetric measurements, this error is inflated because the gravimetric measurements themselves have uncertainties between 1 % and 10 %. The technique's utility is demonstrated by measuring the particle deposition on a surface moving at several meters per second, which is an application where other areal density measurements cannot be used.

A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits are studied in detail to interrogate the dynamics of levitation: an infinitely wide wheel and a relatively narrow one. In both cases the front and back of the fluid-filled gap are either straight or nearly so. To bridge the gap between these two asymptotic limits, wheels of finite width are considered, introducing a further simplying approximation: although the front and back are no longer expected to remain straight for a finite width, the footprint of the fluid-filled gap is still taken to be rectangular, with boundary conditions imposed at the front and back in a wheel-averaged sense. The Reynolds equation can then be solved by separation of variables. For wider wheels, with a large amount of incoming flux or a relatively heavy loading of the wheel, the system is prone to flooding by back flow with fluid unable to pass underneath. Otherwise steady planing states are achieved. Both lift-off and touch-down are explored for a wheel rolling over a film of finite length. Theoretical predictions are compared with a set of experimental data.

Paper products, like tissue paper, are composed of bonded wood fiber networks. Dry creping is an industrial process used in tissue manufacturing. In this process, a wet paper sheet (web) is adhered to a high-speed metal dryer (substrate). The dried sheet is then scraped off against a stationary metal blade, leading to web-substrate debonding, sheet folding, and damage caused by the rupture of interfiber bonds. This process creates a microfolded structure, leading to a nonlinear tensile response and high failure strain, while sheet-damage results in sheet de-densification (through thickness explosion). Based on the visualized creped structures, creped sheets are classified as shaped-bulk (folding-dominated) or explosive-bulk (damage-dominated). While factors affecting sheet-folding have been studied extensively, the effects of sheet-damage on structural and tensile properties have not been previously studied. Using a Discrete Element Method (DEM) to model low grammage fiber networks, we simulate creping with a bilinear elastoplastic fiber model. We demonstrate that altering sheet-substrate bond (adhesive) properties relative to interfiber bonds shifts creping from shaped-bulk to explosive-bulk. Signatures of the above two creping modes are identified. Shaped-bulk sheets exhibit fewer interfiber bond ruptures, a higher degree-of-folding (waviness), and less through-thickness explosion, while explosive-bulk sheets show the opposite traits. During tensile deformation, bending dominates initially, followed by an increased axial deformation near failure as unfolding occurs. The transition from shaped-bulk to explosive-bulk creping shows an initial increase in stiffness followed by a decline, and a gradual then rapid, decrease in tensile strength.

Paper machine press felts often contain seams that facilitate their manufacturing and replacement. However, in industrial practice, breaks in the paper sheet commonly initiate at these seam locations. This study examines how press felt seams affect the local wet strength of high grammage papers. A custom experimental setup was developed to dewater paper using either tensioned seamed felts or two uniform felts separated by a small gap ("gap seam"). The pressed paper was then subjected to tensile testing. The pressure distribution near real press felt seams were mapped with pressure-sensitive film. From this, an "effective gap" was defined as the region with reduced pressure. This effective gap increases linearly with felt tension. The wet strength of paper produced using a seamed felt with a given effective gap matched that of paper pressed with a gap seam of the same size. The tests were conducted under industrially relevant conditions for a cardstock-grade paper, including press felt tension, pressure, furnish, and moisture content. Results showed that paper wet strength near the seam decreases exponentially with increasing seam size. The characteristic length scale of this decay closely matches the average fiber length in the furnish.

We present a novel non-contact method for measuring the moisture content of paper. In the method, paper is illuminated obliquely by light from an IR LED, and the light reflected from the paper is imaged by a short-wave infrared (SWIR) camera. Owing to the high absorptivity of liquid water to light in the 1400–1500 nm wavelength range, the intensity of light reflected off the paper diminishes sharply with increasing moisture content. We show that for a variety of paper samples (Whatman paper, NBSK, NBHK, tissue paper) and moisture contents of up to 200

Non-woven cellulose fiber networks of low areal density are widely used in many industrial applications and consumer products. A discrete element method (DEM) modeling framework is advanced to simulate the formation of strongly anisotropic cellulose fiber network sheets in the dilute limit with simplified hydrodynamic and hydroelastic interactions. Our modeling accounts for in-plane fiber orientation and viscous drag indirectly by using theories developed by Niskanen (2018 Fundamentals of Papermaking, Trans. 9th Pulp and Paper Fundamental Research Symp. Cambridge, 1989 (FRC) pp 275-308) and Cox (1970 J. Fluid Mech. 44 791-810) respectively. Networks formed on a patterned and flat substrate are simulated for different fiber types, and their tensile response is used to assess the influence of the out-of-plane topographical pattern, specifically, on their stiffness and strength. Sheets with the same grammage and thickness, but composed with a higher fraction of softwood fiber (longer fibers with large diameter), have higher strength and higher strain to failure compared to sheets made from hardwood fibers (short fibers with small diameter). However, varying the fiber fraction produces only an insignificant variation in the initial sheet stiffness. The above simulation predictions are confirmed experimentally for sheets comprised of fibers with different ratios of Eucalyptus kraft and Northern Bleached Softwood Kraft fibers. Sheets with out-of-plane topography show an unsymmetric mass distribution, lower tensile stiffness, and lower tensile strength compared to those formed on a flat substrate. The additional fiber deformation modes activated by the out-of-plane topography, such as bending and twisting, explain these differences in the sheet mechanical characteristics.

Various methods exist to measure the areal density of particles resting on surfaces. Most of these techniques are expensive, intrusive, or time-consuming. We propose an inexpensive oblique light measurement technique using a digital camera to measure the areal density of a monolayer of particles on a moving surface. This measurement technique is applicable for both bright and dark powders deposited on contrasting backgrounds. A quantitative relationship between the relative luminosity of the surface and particle accumulation was developed and verified using a simple 2D luminosity model. We show an application of this method by measuring the deposition efficiency of electrostatically coated talc and polyurethane powders on a moving target surface. While the current process requires ex situ image processing, the approach can be automated to yield real time measurements of particle deposition on a surface.

Energy Recovery Ventilators (ERVs) using semi-permeable membranes are widely used in buildings to improve indoor air quality and reduce energy consumption. These membranes are pretensioned but can deflect under the influence of inlet and flow-induced pressure differences. We measure the impact of membrane deflection on pressure drop, flow distribution, and thermal performance of a commercial crossflow ERV. A modest applied pressure differential and the resulting membrane deflection can cause significant variations in pressure drop along each flow path. The membrane deflections can cause the pressure drop along the channels to vary by up to a factor of two, depending on the inlet pressure differential. The ERV's sensible effectiveness decreases from 70.4% to 67% as the inlet pressure differential increases from 0.85 to +0.85 in center dot H2O (+211.5 Pa). A numerical model is proposed to determine the deflection pattern in an ERV. The model is validated against experimental data and is consistent with experiments to within an RMS error of 0.15 and 0.08 in center dot H2O (37.3 and 19.9 Pa), which corresponds to approximately 15% and 8% of the pressure drop under typical working conditions of the exchanger. However, the model is not able to capture the change in thermal effectiveness, which may originate from the texturing of the deflected membrane, which is not included in the model.

Low density tissue papers are soft fiber networks with a folded internal microstructure-deliberately imparted during a widely used manufacturing process, called dry creping. The folded crepe structure enhances a tissue paper's specific volume, stretchability, and softness. The influence of the micron-scale crepe structure on nonlinear tensile response is studied using experiments and a discrete elasto-plastic model (DEM). First, 'Crepe Index (CI)' is defined to quantify the crepe structure. An optical method to obtain high resolution edge images is developed to measure the CI. The relationship between the CI and tensile failure strain and initial elastic stiffness is assessed: the failure strain is observed to be proportional to CI, while the dependence of initial stiffness on CI is unclear-presumably due to the damage induced through the de-densification of fiber layers during the manufacturing. The effect of CI on initial stiffness and failure strain is assessed using DEM by idealizing the creped paper as a segmented triangular wave-each segment governed by a bilinear elastoplastic constitutive law and a strength-based failure criterion. The model reveals that the initial stiffness of a creped sheet depends not only on the CI but also on sheet-thickness to crepe-wavelength ratio, and the stiffness of the uncreped sheet. The failure strain is found to be stretching dominated at low CI, and bending dominated at higher CI. Qualitative agreement is found between the DEM and experiments. The significance of both the material and the geometric non-linearity on the macroscale tensile response of a creped tissue paper emerges from this study.

Fiber networks are ubiquitous. The networks of interest to this study are distinguished from the widely studied planar random fiber networks (RFN) by their low areal density (grammage), preferential orientation, and fiber curl. Oriented networks are created through a high speed manufacturing process called forming in paper making. A dilute suspension of elastic fibers in water impinges on a moving wire to create a formed network. A discrete element method (DEM) based forming model is developed that incorporates the qualitative effects of fluid shear (preferred fiber orientation) and viscous drag during drainage (fiber conformation to the wire topography). Virtual tensile tests performed on thus formed networks reveal that the tensile response is initially softer due to non-affine deformation, and anisotropic due to preferential orientation. Consequently, an orientation dependent power law with a non-unique exponent emerges for the scaling of modulus and strength with the network density. Tensile test simulations reveal the re-alignment of fibers along the loading direction, and strong strain localization resulting in a few fibers (∼1%) carrying the imposed strain energy. Fiber curl and orientation are observed to govern the degree of non-affine response, stiffness, and strain localization, suggesting that controlling the degree of anisotropy and fiber curl offers the possibility to design networks for specific stiffness and specific strength.

Sufficient adhesion in a wheel-rail contact is one of the key requirements for safe and efficient railway operations.Low adhesion conditions significantly increase the risk of braking issues leading to extended braking distances, passing signals at danger, reduced acceleration rate, and damage to the wheels and rails.Sanding remains one of the most common methods to overcome low adhesion conditions.However, over application of electrically insulating sand may interfere with railway track circuits of some signalling systems leading to loss of train detection and therefore limits of application have been imposed.The development of alternative, novel adhesion enhancing materials with higher electrically conductivity may mitigate the risk of electrical insulation and allow for larger amounts of material to be applied to improve wheel/rail adhesion.As well as not interfering with track circuits, these new materials must demonstrate good deposition efficiency using conventional sanders as well as providing a significant increase in friction levels under low adhesion conditions.This work describes the testing of proprietary coatings which can be applied to sand and other particles to improve conductivity and deposition efficiency.Laboratory scale testing of the deposition efficiency, adhesion enhancing and electrical characteristics of these materials were carried out at the University of British Columbia and LB Foster facilities in Canada and field testing of the influence on track circuits was

The impingement of a liquid jet onto a moving wall can lead to deposition in which fluid spreads into a steady, U-shaped lamella. Experiments are conducted by impinging a jet from a nozzle onto a rotating disk to produce jet Reynolds numbers 15 Rej 6000 and wall-to-jet velocity ratios 0.04 uw/vj 14 under conditions where the effects of surface tension and gravity are relatively minor. Although experiments were conducted over a broad range of Rej, the steady, U-shaped lamella only forms for 15 Rej 400; at higher Rej the jet splashes. High-speed video is used to measure the geometry of the impinging jet. The experiments are complemented with numerical simulations, which reveal the anatomy of the lamella: The jet is diverted sideways by pressure gradients over an impact zone that has a radius of order the jet diameter. Viscous stresses play little role in the diversion of incoming fluid but act outside the impact region to turn the flow towards the direction of motion of the wall. A fraction of the viscously redirected fluid is thereby taken back underneath the jet, cushioning its impact. Eventually, the fluid enters a downstream region of almost uniform depth wherein all the fluid is conveyed with the wall. A simple model is proposed to rationalize the U shape of the lamella, fixing that footprint by arguing that this arises where the radially symmetric, viscously modified outflow from the jet matches the wall velocity. The simple model predicts the dimensions of the lamella (the length of the upstream heel and the width of the downstream lamella) and that the shape takes a universal form when scaled by one of these distances. These predictions agree well with the experiments and simulations, except when the heel becomes excessively small.

Current methods of concentration measurements, such as laser Doppler anemometry (LDA)/phase Doppler anemometry (PDA), and planar nephelometry provide accurate local measurements of concentration but are expensive and complicated to set up and operate. Our concentration measurement method involves the measurement of light extinction through a two-phase flow and is based on well-established methods. The proposed configuration is comparatively inexpensive and easy to operate. It can also provide global measurements of mean particle concentration for axisymmetric distributions of particles. We validate the method by comparing the extinction efficiency measured with this method for a given particle size with the known value (of somewhat less than two) for a non-ideal imaging setup. We also use the technique to measure the concentration distribution in a round jet, and show that the results are similar to those measured by previous researchers using different measurement methods. Finally, we apply the method to show how the concentration distribution in a particulate jet varies with particle charging.

Asymmetric composite membranes, consisting of a dense polymer layer coated on a porous substrate layer, are widely used in devices such as Energy Recovery Ventilators (ERVs). The permeability of membranes typically depends on water vapour concentration and temperature. Due to the asymmetry of the composite membrane, the orientation of the membrane (i.e., which layer of the membrane experiences a higher water vapour concentration) can also affect the permeability. In this study, the permeability of two asymmetric composite membranes (commercial names "T4 (MX4) " and "HP2 '') is measured at temperatures ranging from 5 ? to 50 ? and water vapour activities ranging from 0.2 to 0.95 and the orientation-dependent behaviour of permeability is investigated. Consistent with other studies, the permeability of the membranes increases with increasing water vapour concentration and decreases with increasing temperature. The permeability of the membrane is also a function of the membrane orientation and the sweep flow water vapour concentration as well as the feed flow water vapour concentration. However, the computed permeability is shown to be independent of orientation and sweep flow water vapour concentration when results are plotted against the water vapour concentration at the dense coating layer.

Using membrane energy exchangers (also referred to as energy recovery ventilators, or ERVs for short) in winter conditions, and extremely hot and humid summer conditions, can result in condensation of water vapor. Condensation will affect the performance of the exchanger, facilitate the growth of microorganisms and is a precursor to frost formation at lower temperatures. Developing models that predict the onset of condensation and the performance of the exchanger under condensation conditions is therefore essential for the design of ventilation systems and the selection of the proper exchanger. Membrane permeability typically depends on water concentration and temperature. In this study, a heat and mass transfer model that accounts for the variations in the permeability of the membrane due to temperature, concentration and condensation is developed to predict the occurrence of condensation in membrane energy exchangers. The model is validated against experiments and is then used to investigate the effect of variation in the permeability of the membrane on the occurrence of condensation and to determine the operating conditions resulting in condensation. It is shown that assuming a constant permeability for the membrane can result in errors of up to 25% in the prediction of the rate of condensation. (C) 2022 Elsevier B.V. All rights reserved.

An experimental study is performed on high-acceleration separation of Newtonian liquid films trapped between two parallel plates. The test apparatus is capable of accelerating one plate at up to 325 m/s2 relative to a stationary substrate. Plates with average roughness up to 86 µm were studied. High-speed laser induced fluorescence (LIF) is used to determine the instantaneous film thickness distribution during the separation process. Two flow regimes exist in the film. As the gap between the substrates increases, a viscous fingering regime occurs along the perimeter of the wetted area, where air fingers grow radially inward. If the growth rate of those fingers is slow relative to the growth rate of the gap, a second regime exists in the center of the wetted region, in which cavitation bubbles emerge and grow. Once the two substrates are sufficiently separated, the liquid bridges connecting the two substrates break. At high accelerations, the separation ratio (the relative amount of fluid remaining on the moving substrate) is a nonlinear function of the surface roughness, liquid viscosity, and separation acceleration, and varies in the range between 35 and 55

Tissue is a low-density paper product distinguished by a microscale crepe structure. We investigate the relationship between the macroscale tissue tensile response and crepe structure. We propose a parameter called the Crepe Index (CI) that can be measured from edge images of the creped sheet. Crepe Index correlates very well with the measured tensile failure strain (“stretch”), but its correlation with the measured initial elastic stiffness is unclear. A discrete elastoplastic model (DEM) is developed to explain the experimental results and understand the nonlinearity in the tensile curve. The model accounts for both material nonlinearity through a bilinear elastoplastic constitutive law for the sheet material, and the geometric nonlinearity arising from large deformations. The creped sheet is idealized as a triangular wave of prescribed wavelength and waveheight, with nonlinear bending and stretching effects. The model results show that the tensile response is governed by both the nonlinearity of the sheet material (fibre network) and crepe structure (geometry). The yielding in stretching and bending gives rise to an inflection in the tensile response. It is found that the initial stiffness depends not only on CI, but also on parameters such as sheet thickness to crepe-wavelength ratio, and stiffness of sheet material after creping. Thus, the variability in above parameters can be one of the reason for unclear correlation between measured initial stiffness and CI. For CI range of tested commercial tissues, both experiments and model show that stretch varies linearly with CI, with an almost unity slope and a positive intercept (i.e, stretch> CI). Thus, the overall stretch of creped tissue is a sum of CI and network stretching.

Experiments are conducted to explore the rolling of a cylinder over a pool of viscous fluid. The speed, width and loading of the cylinder are varied along with the initial depth and length of the viscous pool. Depending on the conditions, the cylinder will either ride on a lubrication film or remain in solid contact with the underlying substrate. For the former situation, a lubrication theory is presented that describes the pressure underneath the cylinder and the thickness of the film. The theory approximates the flow by the one-dimensional Reynolds equation with the addition of one term, with an adjustable parameter, to account for the flux of fluid to the cylinder sides. Once this parameter is calibrated against experiment, the theory predicts peak lubrication pressures, gap sizes and film thicknesses to within approximately ten per cent. For lubricated rolling, the film splits evenly between the cylinder and substrate downstream of the nip. The printer's instability arises during the splitting process, patterning the residual fluid films on the substrate and cylinder. If the pool length is less than the cylinder circumference, the fluid adhering to the cylinder is rotated back into contact with the substrate, and when there is sufficient adhered fluid a lubrication film forms that can again be modelled by the theory. Conversely, if there is insufficient adhered fluid, no contiguous lubrication film is formed; instead, the pattern from the printer's instability ‘prints’ from the cylinder to the substrate.

The von-Karman–Pohlhausen averaging technique is employed to build a reduced model for the flow of a shallow film from a sluice gate or impacting jet over a moving surface. The viscous drag exerted on the film by the moving wall acts to arrest flow counter to the direction of the wall's motion, and force an adjustment toward the wall speed. For a (normally) impacting jet, this results in a range of wall speeds for which a steady state is reached in which all the fluid is eventually recirculated to flow along the wall, with a distinctive “heel” forming upstream of the impact region. For wall speeds below this range, the flow counter to the wall cannot be arrested, and unsteady states result. For wall speeds above this range, a different steady state emerges in which fluid is immediately diverted through and downstream of the impact region, eliminating any heel. The steady, heeled flow states predicted by the reduced model are in qualitative agreement with numerical simulations of the full two-dimensional problem.