Showing papers on "Pipe flow published in 2011"
TL;DR: In this article, the authors investigated the macro-to-microscale transition during flow boiling in small scale channels of three different sizes with three different refrigerants over a range of saturation conditions to investigate the effects of channel confinement on two-phase flow patterns and liquid film stratification.
280 citations
TL;DR: In this paper, two new correlations of single-phase friction factor for turbulent flow are proposed, one for smooth pipes and the other for both smooth and rough pipes, which is an idea replacement of the correlations of Blasius and Filonenko.
206 citations
TL;DR: In this paper, large-eddy simulations of isothermal round jets at a Mach number of 09 and a diameter-based Reynolds number ReD of 105 originating from a pipe are performed using low-dissipation schemes in combination with relaxation filtering.
Abstract: Large-eddy simulations (LESs) of isothermal round jets at a Mach number of 09 and a diameter-based Reynolds number ReD of 105 originating from a pipe are performed using low-dissipation schemes in combination with relaxation filtering The aim is to carefully examine the capability of LES to compute the flow and acoustic fields of initially nominally turbulent jets As in experiments on laboratory-scale jets, the boundary layers inside the pipe are tripped in order to obtain laminar mean exit velocity profiles with high perturbation levels At the pipe outlet, their momentum thickness is δθ(0)=0018 times the jet radius, yielding a Reynolds number Reθ=900, and peak turbulence intensities are around 9% of the jet velocity Two methods of boundary-layer tripping and five grids are considered The results are found to vary negligibly with the tripping procedure but appreciably with the grid resolution Based on analyses of the LES quality and on comparisons with measurements at high Reynolds numbers, fine d
186 citations
TL;DR: In this paper, the interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction is analysed, and the optimal rib size is collapsed best by the square root of the groove cross-section, lg+=Ag+1/2.
Abstract: The interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction are analysed. The ‘viscous regime’ of vanishing riblet spacing, in which the drag reduction produced by the riblets is proportional to their size, is reasonably well understood, but this paper focuses on the behaviour for spacings s+ ≃ 10–20, expressed in wall units, where the viscous regime breaks down and the reduction eventually becomes an increase. Experimental evidence suggests that the two regimes are largely independent, and, based on a re-evaluation of existing data, it is shown that the optimal rib size is collapsed best by the square root of the groove cross-section, lg+=Ag+1/2. The mechanism of the breakdown is investigated by systematic DNSs with increasing riblet sizes. It is found that the breakdown is caused by the appearance of long spanwise rollers below y+ ≈ 20, with typical streamwise wavelengths λx+ ≈ 150, that develop from a two-dimensional Kelvin–Helmholtz-like instability of the mean streamwise flow, similar to those over plant canopies and porous surfaces. They account for the drag breakdown, both qualitatively and quantitatively. It is shown that a simplified linear instability model explains the scaling of the breakdown spacing with lg+.
185 citations
TL;DR: The question of why the fluid motion along a pipe changes from a laminar to a turbulent state at modest flow rates remains an enigma as all theoretical and numerical evidence suggests that the base state of fully developed flow, Hagen-Poiseuille flow, is linearly stable.
Abstract: In his landmark paper of 1883, Reynolds addressed the question of why the fluid motion along a pipe changes from a laminar to a turbulent state at modest flow rates. His discoveries have remained a focus of hydrodynamic stability for the intervening 125 years, and the central puzzle of why the transition takes place at all remains unresolved. It is an enigma as all theoretical and numerical evidence suggests that the base state of fully developed flow, Hagen-Poiseuille flow, is linearly stable. The transition to turbulence is abrupt, mysterious, and largely dependent on the quality of the facility used in any experimental investigation. It is therefore not an example of transition via a sequence of instabilities or bifurcations in which considerable success has been achieved over the same period. Despite wide-ranging research activity that has uncovered many important pieces of the jigsaw, the central puzzle remains unresolved. The purpose of this review is to bring together the available experimental evidence and attempt to extract a set of accepted facts about this important problem.
180 citations
TL;DR: In this article, the convective heat transfer of SiO2/water colloidal suspensions was investigated experimentally in a flow loop with a horizontal tube test section whose wall temperature was imposed.
156 citations
TL;DR: A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability, and a discrete model reproduces almost all large-scale features of transitional pipe flow.
Abstract: Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, which additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular, it captures metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction toward uniform, featureless turbulence.
140 citations
TL;DR: In this article, a simulation of stable stratified, turbulent channel flow at low to moderate Reynolds number has been performed using large computational boxes and considering a wide range of stratification levels.
Abstract: Direct numerical simulations of stably stratified, turbulent channel flow at low to moderate Reynolds number have been performed using large computational boxes and considering a wide range of stratification levels. For weak stratification or high Reynolds number, the turbulence is affected by buoyancy in the core of the channel, but the near-wall region differs little from the neutral case. With strong stratification, large laminar patches appear in the near-wall region and turbulent momentum and buoyancy fluxes vanish in the core of the channel. With increasing stratification, the near-wall streaks remain essentially unmodified, while large-scale global modes are damped. In the central region, internal gravity waves are dominant. In addition, there is an intermediate outer layer where the dynamics of the turbulent structures is governed by local fluxes. In this region, energy spectra collapse when using local Obukhov scaling.
135 citations
TL;DR: In this article, the performance of heat transfer and the associated higher pressure drop for liquid flow in rectangular micochannels with longitudinal vortex generators (LVGs) were determined experimentally for the Reynolds numbers of 170-1200 with hydraulic diameter of 187.5μm and aspect ratio of 0.067 for LVGs with different number of pairs and angles of attack.
123 citations
TL;DR: In this article, the authors examined flow structure and turbulence in a rough-wall channel flow for Reτ in the 3520-5360 range using an optically index-matched facility and high-resolution particle image velocimetry measurements.
Abstract: Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Reτ in the 3520–5360 range. The scales of pyramidal roughness elements satisfy the ‘well-characterized’ flow conditions, with h/k ≈ 50 and k+ = 60 ~ 100, where h is half height of the channel and k is the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined to y < 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly at y < k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding to k − 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.
121 citations
TL;DR: Two-dimensional flow over periodically arranged hills was investigated experimentally in a water channel as mentioned in this paper, where point-by-point 1D laser Doppler anemometry (LDA) measurements were undertaken at four Reynolds numbers.
Abstract: Two-dimensional flow over periodically arranged hills was investigated experimentally in a water channel. Two-dimensional particle image velocimetry (PIV) and one-dimensional laser Doppler anemometry (LDA) measurements were undertaken at four Reynolds numbers (
$$\text{5,600} \le Re \le \text{37,000}$$
). Two-dimensional PIV field measurements were thoroughly validated by means of point-by-point 1D LDA measurements at certain positions of the flow. A detailed study of the periodicity and the homogeneity was undertaken, which demonstrates that the flow can be regarded as two-dimensional and periodic for $$Re \ge \text{10,000}$$
. We found a decreasing reattachment length with increasing Reynolds number. This is connected to a higher momentum in the near-wall zone close to flow separation which comes from the velocity speed up above the obstacle. This leads to a velocity overshoot directly above the hill crest which increases with Reynolds number as the inner layer depth decreases. The flow speed up above that layer is independent of the Reynolds number which supports the assumption of inviscid flow disturbance in the outer layer usually made in asymptotic theory for flow over small hills.
TL;DR: In this article, a semi-theoretical model is used to estimate the effect of backward erosion piping by underseepage in a dike by computing the critical head, which accounts for the groundwater flow through subsoil, pipe flow through the erosion channel and a limited particle equilibrium at the bottom of the channel.
Abstract: A semi-theoretical model is available to estimate the effect of backward erosion piping by underseepage in a dike by computing the critical head. The model accounts for the groundwater flow through the subsoil, pipe flow through the erosion channel and a limited particle equilibrium at the bottom of the channel. This model is extended and updated with the results of a wide range of tests presented in the paper of (Van Beek et al., 2011). The small- scale tests are analyzed by means of a multivariate regression in order to identify the level of influence of each variable. The regression outcome for the permeability corresponds precisely with the outcome of the prediction rule. The effect of relative density, uniformity and particle roundness is empirically dealt with. The role of the particle size is adapted in the new empirical formulation.
TL;DR: It is concluded that the reason behind the observed enhancement in the rate of fluid flow through carbon nanotubes could be the nonlinear variation of viscosity.
Abstract: Molecular dynamics simulations are carried out to study the pressure driven fluid flow of water through single walled carbon nanotubes. A method for the calculation of viscosity of the confined fluid based on the Eyring theory of reaction rates is proposed. The method involves the calculation of the activation energy directly from the molecular dynamics trajectory information. Computations are performed using this method to study the effect of surface curvature on the confined fluid viscosity. The results indicate that the viscosity varies nonlinearly with the carbon nanotube diameter. It is concluded that the reason behind the observed enhancement in the rate of fluid flow through carbon nanotubes could be the nonlinear variation of viscosity.
TL;DR: In this article, the effects of inlet flow condition, tube diameter, header size, area ratio, flow directions (Z and U-type), as well as the gravity are investigated.
TL;DR: In this article, the results of fluid flow experiments carried out for air flow through a fractured granite sample under various pressures of confinement are presented, showing that the cubic law appears to be applicable for flow cases that return a Forcheimer number for non-Darcian flow cases where inertial effects were modest.
TL;DR: In this article, the cross-stream inertial migration of neutrally buoyant deformable particles in a pressure-driven channel flow is studied using three-dimensional computer simulations, where the particles are modeled as elastic shells filled with a viscous fluid.
Abstract: Using three-dimensional computer simulations, we study the cross-stream inertial migration of neutrally buoyant deformable particles in a pressure-driven channel flow. The particles are modeled as elastic shells filled with a viscous fluid. We show that the particles equilibrate in a channel flow at off-center positions that depend on particle size, shell compliance, and the viscosity of encapsulated fluid. These equilibrium positions, however, are practically independent of the magnitude of channel Reynolds number in the range between 1 and 100. The results of our studies can be useful for sorting, focusing, and separation of micrometer-sized synthetic particles and biological cells.
TL;DR: In this paper, the structure of the very large-scale motions (VLSMs) in fully developed turbulent pipe flow is visualized using snapshot proper orthogonal decomposition, and it is shown that the structures can be reconstructed using a small number of the most energetic modes.
Abstract: Time-resolved stereoscopic particle image velocimetry is used to investigate the structure of the very-large-scale motions (VLSMs) in fully developed turbulent pipe flow. The motions are visualized using snapshot proper orthogonal decomposition. It is shown that the structures can be reconstructed using a small number of the most energetic modes. The results strongly suggest a possible connection between the origin of the VLSM and linear stability analysis. The structures are seen to be highly three-dimensional, meandering azimuthally and radially. At this Reynolds number (ReD=12 500), they occasionally extend from the near-wall region to the wake region of the pipe.
TL;DR: In this article, the role of pipeflow in ephemeral gully erosion is not well understood, and experiments were conducted on continuous soil pipes to better understand the role internal erosion of soil pipes and its relation to ephemerale gully development.
Abstract: The role of soil pipeflow in ephemeral gully erosion is not well understood. Experiments were conducted on continuous soil pipes to better understand the role of internal erosion of soil pipes and its relation to ephemeral gully development. Soil beds of 140 cm length, 100 cm width and 20 cm depth had a single soil pipe of different initial sizes (2, 4, 6, 8, and 10 mm diameter) extend from a water reservoir to the outlet. Experiments were run on Providence silt loam and Smithdale loam soils under a constant head of 15 cm established for 30 min. Either the tunnel collapsed or the head could not be maintained. Soil pipes that were initially 2 and 4 mm clogged instantaneously at their mouth and did not exhibit flow, whereas, pipes initially ≥ 6 mm enlarged by 268, 397, and 699% on average for the 6, 8, and 10 mm diameters, respectively. Critical shear stress values were found to be essentially zero, and erodibility values gave erosion indexes that were extremely high. The rapid internal erosion resulted in erratic flow and sediment concentrations with periods of no flow as pipes were temporarily clogged followed by surges of high flow and high sediment concentrations. Tensiometers within 6 cm of the soil pipes did not exhibit pressure increases typically associated with pipe clogging. Flow through 10 mm diameter soil pipes exhibited tunnel collapse for both soils tested. Tunnel collapse typically occurred within minutes of flow establishment suggesting that ephemeral gullies could be misinterpreted as being caused by convergent surface flow if observations were made after the runoff event instead of when flow is first established through soil pipes. Copyright © 2011 John Wiley & Sons, Ltd.
TL;DR: In this paper, a variational problem was proposed to find the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows, which is the nonlinear analogue of the well-studied (linear) transient growth optimal.
Abstract: We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. This seems at least approximately true for our choice of energy growth functional and the pipe flow geometry chosen here.
TL;DR: In the large eddy simulation (LES) approach, large-scale energy-containing structures are resolved, smaller structures are filtered out, and unresolved subgrid effects are modeled as discussed by the authors.
Abstract: In the large eddy simulation (LES) approach, large-scale energy-containing structures are resolved, smaller structures are filtered out, and unresolved subgrid effects are modeled. Extensive recent work has demonstrated that predictive under-resolved simulations of the velocity fields in turbulent flows are possible without resorting to explicit subgrid models when using a class of physics-capturing high-resolution finite-volume numerical algorithms. This strategy is denoted as implicit LES (ILES). Tests in fundamental applications ranging from canonical to complex flows indicate that ILES is competitive with conventional LES in the LES realm proper—flows driven by large-scale features. The performance of ILES in the substantially more difficult problem of under-resolved material mixing driven by under-resolved velocity fields and initial conditions is a focus of the present work. Progress in addressing relevant resolution issues in studies of mixing driven by Richtmyer–Meshkov instabilities in planar sho...
TL;DR: In this paper, the simulation results were averaged to obtain the liquid and gas mean velocity distributions, the local void fractions as well as the local turbulent kinetic energy and dissipation rate of the liquid phase.
TL;DR: In this paper, the heat transfer analysis with thermal radiation on the two-dimensional magnetohydrodynamic (MHD) flow in a channel with porous walls is described, where the upper-convected Maxwell (UCM) fluid fills the porous space between the channel walls.
TL;DR: In this paper, an internal ribbed cooling channel including a 180 deg bend with a 2:1 inlet and a 1:1 aspect ratio outlet channel was validated against experimental results in terms of spatially resolved heat transfer distributions, pressure losses, and velocity distributions.
Abstract: Numerical results for an internal ribbed cooling channel including a 180 deg bend with a 2:1 inlet and a 1:1 aspect ratio outlet channel were validated against experimental results in terms of spatially resolved heat transfer distributions, pressure losses, and velocity distributions. The numerical domain consisted of one rib segment in the inlet channel and three ribs segments in the outlet chcannel to reduce the overall numerical effort and allow for an extensive parametric study. The results showed good agreement for both heat transfer magnitudes and spatial distributions, and the numerical results captured the predominate flow physics resulting from the 180 deg bend. The production of Dean vortices and acceleration of the flow in the bend produced strongly increased heat transfer on both the ribbed and unribbed walls in the outlet channel in addition to increases due to the ribs. Numerical simulations were performed for a wide range of divider wall-to-tip wall distances, which influenced the position of the highest heat transfer levels on the outlet walls and changed the shape of the heat transfer distribution on the tip wall. Analysis of section averages of heat transfer in the bend and outlet channel showed a strong influence of the tip wall distance, while no effect was seen upstream of the bend. A similarly large effect on pressure losses in the bend was observed with varying tip wall position. Trends in averaged heat transfer varied linearly with tip wall distance, while pressure losses followed a nonlinear trend, resulting in an optimum tip wall distance with respect to heat transfer efficiency.
TL;DR: In this article, a nano-scale thermal anemometry probe (NSTAP) was developed using a novel procedure based on deep reactive ion etching, which was then used to measure the streamwise velocity component of fully developed turbulent pipe flow, and the results were compared with data obtained using conventional hot-wire probes.
Abstract: A new nano-scale thermal anemometry probe (NSTAP) has been developed using a novel procedure based on deep reactive ion etching. The performance of the new probe is shown to be superior to that of the previous design by Bailey (J Fluid Mech 663:160–179, 2010). It is then used to measure the streamwise velocity component of fully developed turbulent pipe flow, and the results are compared with data obtained using conventional hot-wire probes. The NSTAP agrees well with the hot-wire at low Reynolds numbers, but it is shown that it has better spatial resolution and frequency response. The data demonstrate that significant spatial filtering effects can be seen in the hot-wire data for probes as small as 7 viscous units in length.
TL;DR: In this article, the development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied and the results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.
TL;DR: In this paper, the performance of hydrodynamically and thermally developing single-phase flow in an array of rectangular mini-channels has been experimentally and numerically investigated.
TL;DR: In this paper, single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Reτ ≤ 3,000.
Abstract: Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Reτ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l+ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l+ = 22 and \(l/d \gtrsim 200\), the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l+ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l+ and l/d were systematically varied reveal that l+ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.
TL;DR: The statistical properties of the generated fluctuations indicate that this turbulentlike flow is different from previously studied flows displaying elastic turbulence and shows a direct cascade of energy to small scales with practically no intermittency.
Abstract: The flow of polymer solutions is examined in a flow geometry where a jet is used to inject the viscoelastic solution into a cylindrical tube. We show that this geometry allows for the generation of a "turbulentlike" flow at very low Reynolds numbers with a fluctuation level which can be as high as 30%. The fluctuations increase with an increase in solution polymer concentration and flow velocity. The turbulent fluctuations decay downstream for small flow velocities but persist for high velocities. The statistical properties of the generated fluctuations indicate that this turbulentlike flow is different from previously studied flows displaying elastic turbulence and shows a direct cascade of energy to small scales with practically no intermittency.
TL;DR: In this article, a numerical methodology that combines incompressible flow simulations with vortex sound theory is proposed to estimate the acoustic source power in periodic systems, which successfully predicts the Strouhal number ranges of acoustic energy production/absorption and the nonlinear saturation mechanism responsible for the stabilization of the limit cycle oscillation.
Abstract: Whistling behaviour of two geometrically periodic systems, namely corrugated pipes and multiple side branch systems, is investigated both experimentally and numerically. Tests are performed on corrugated pipes with various lengths and cavity geometries. Experiments show that the peak-whistling Strouhal number, where the maximum amplitude in pressure fluctuations is registered, is independent of the pipe length. Experimentally, a decrease of the peak-whistling Strouhal number by a factor of two is observed with increasing confinement ratio, i.e. the ratio of pipe diameter to cavity width. A numerical methodology that combines incompressible flow simulations with vortex sound theory is proposed to estimate the acoustic source power in periodic systems. The methodology successfully predicts the Strouhal number ranges of acoustic energy production/absorption and the nonlinear saturation mechanism responsible for the stabilization of the limit cycle oscillation. The methodology predicts peak-whistling Strouhal numbers in agreement with experiments and explains the dependence of the peak-whistling Strouhal number on the confinement ratio. Combined with an energy balance, the proposed methodology is used to estimate the acoustic fluctuation amplitudes.
TL;DR: In this article, numerical simulations of wicking through micropores of two types of geometries, axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation are presented.
Abstract: We report numerical simulations of wicking through micropores of two types of geometries, axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation. The aim is to gain a detailed understanding of the interfacial dynamics in these geometries, with an emphasis on the motion of the three-phase contact line. We adopt a diffuse-interface formalism and use Cahn-Hilliard diffusion to model the moving contact line. The Stokes and Cahn-Hilliard equations are solved by finite elements with adaptive meshing. The results show that the liquid meniscus undergoes complex deformation during its passage through contraction and expansion. Pinning of the interface at protruding corners limits the angle of expansion into which wicking is allowed. For sufficiently strong contractions, the interface negotiates the concave corners, thanks to its diffusive nature. Capillary competition between branches downstream of a Y-shaped bifurcation may result in arrest of wicking in the wider branch. Spatial variation of wettability in one branch may lead to flow reversal in the other.