Liquid Rivulet Research Articles

An experimental investigation of shear-driven rivulets on a flat plate by using a two-perspective view

Shear-driven liquid rivulet flow on a horizontal plate is experimentally investigated. In contrast to publications found in the literature, a two-side view on the rivulet is used to simultaneously capture the side and top view. This enables more accurate measurements of the rivulet dimensions and the subsequent calculation of derived quantities. Throughout the experimental test campaign, the ambient gas velocity and the liquid mass flux are altered. In a first qualitative analysis, the occurring rivulet flow regimes are classified and mapped depending on the gas Reynolds number ReG and the rivulet Weber number We. Furthermore, the goal is to quantify the correlation between characteristic rivulet dimensions and the ambient conditions, with a focus on straight and surging rivulets. The quantitative analysis results in an implicit correlation for the rivulet width and height depending solely on the ambient gas velocity and the rivulet mass flow. The investigation of the rivulet wavelength reveals an analogous dependence on the ambient gas velocity. However, the dependence on the rivulet mass flow changes depending on the rivulet flow regimes.

Two-Phase Flow Phenomena in Gas Turbine Compressors with a Focus on Experimental Investigation of Trailing Edge Disintegration

Two-phase flow in gas turbine compressors occurs, for example, at heavy rain flight condition or at high-fogging in stationary gas turbines. The liquid dynamic processes are independent of the application. An overview on the processes and their approach in literature is given. The focus of this study lies on the experimental investigation of the trailing edge disintegration. In the experiments, shadowgraphy is used to observe the disintegration of a single liquid rivulet with constant liquid mass flow rate at the edge of a thin plate at different air flow velocities. A two side view enables calculating droplet characteristics with high accuracy. The results show the asymptotic behavior of the ejected mean droplet diameters and the disintegration period. Furthermore, it gives a detailed insight into the droplet diameter distribution and the spreading of the droplets perpendicular to the air flow.

Inclined impact of drops

Here we extend the results in Gordillo et al. (J. Fluid Mech., vol. 866, 2019, pp. 298–315), where the spreading of drops impacting perpendicularly a solid wall was analysed, to predict the time-varying flow field and the thickness of the liquid film created when a spherical drop of a low viscosity fluid, like water or ethanol, spreads over a smooth dry surface at arbitrary values of the angle formed between the drop impact direction and the substrate. Our theoretical results accurately predict the time evolving asymmetric shape of the border of the thin liquid film extending over the substrate during the initial instants of the drop spreading process. In addition, the particularization of the ordinary differential equations governing the unsteady flow when the rim velocity vanishes provides an algebraic equation for the asymmetric final shapes of the liquid stains remaining after the impact, valid for low values of the inclination angle. For larger values of the inclination angle, the final shape of the drop can be approximated by an ellipse whose major and minor semiaxes can also be calculated by making use of the present theory. The predicted final shapes agree with the observed remaining stains, excluding the fact that a liquid rivulet develops from the bottom part of the drop. The limitations of the present theory to describe the emergence of the rivulet are also discussed.

Movement of liquid rivulet in a microchannel with a co-current gas flow

The joint steady-state motion of a rivulet of incompressible liquid and a gas flow in a microchannel was studied taking into account the action of gravity forces, tangential stress at the gas-liquid interface, and Van der Waals forces. The values of contact angle are calculated for various values of liquid and gas flow rates. It is shown that for a constant liquid flow rate, an increase in gas velocity leads to a decrease in the height of rivulet, and the surface of rivulet becomes flatter. A significant deforming effect of rivulet on the velocity distribution in gas is found.

Breakup of a liquid rivulet falling over an inclined plate: Identification of a critical Weber number

We have numerically investigated the breakup of a rivulet falling over a smooth inclined plate using the volume of fluid method. Rivulet breakup is a complex phenomenon dictated by many factors, such as physical properties (viscosity and surface tension), contact angle, inertia, and plate inclination. An extensive simulation was conducted wherein these factors were systematically investigated. Regimes for a stable rivulet and an unstable rivulet that leads to breakup are examined in terms of a critical value of the Weber number (Wecr) that delineates these regimes. A higher Wecr implies that a higher flow rate is required to maintain a stable rivulet. The impact of liquid properties is characterized by the Kapitza number (Ka). Variation of Wecr with Ka shows two trends depending on the Ka value of the liquid. Liquids with lower Ka values, corresponding to high viscosities and/or low surface tensions, show linear variation and smaller value of the critical Weber number. In other words, the lower the liquid Ka value, the more stable the rivulet will tend to be with changes in liquid inertia. A liquid having higher Ka value exhibits larger value of Wecr and quadratic variation of Wecr with Ka. This behavior is more pronounced with increasing contact angle (γ). Higher contact angles promote rivulet breakup so that inertia must be higher to suppress breakup, consequently Wecr increases with increasing γ. The effect of plate inclination on breakup shows that Wecr decreases with increased inclination angle (θ) owing to higher effective liquid inertia. However, the effect is negligible beyond θ> 60°. The effect of the inlet size reveals that Wecr decreases with inlet cross-sectional area, but the corresponding solvent flow rate for rivulet breakup remains unchanged. A phenomenological scaling for the critical Weber number with the Kapitza number and contact angle is presented, which may offer insight into rivulet breakup.

Coupled Level-Set Volume of Fluid Simulations of Water Flowing Over a Simplified Drainage Channel With and Without Air Coflow

The motivation for this paper is to predict the flow of water over exterior surfaces of road vehicles. We present simulations of liquid flows on solid surfaces under the influence of gravity with and without the addition of aerodynamic forces on the liquid. This is done using an implementation of a Coupled Level Set Volume of Fluid method (CLSVOF) multiphase approach implemented in the open source OpenFOAM CFD code. This is a high fidelity interface-resolving method that solves for the velocity field in both phases without restrictions on the flow regime. In the current paper the suitability of the approach to Exterior Water Management (EWM) is demonstrated using the representative test cases of a continuous liquid rivulet flowing along an inclined surface with a channel located downstream perpendicular to the oncoming flow. Experimental work has been carried out to record the motion of the rivulet in this case and also to measure the contact angle of the liquid with the solid surface. The measurements of the liquid/solid characteristics such as equilibrium and dynamic contact angles are described along with the analytical expression for contact angle vs. capillary number used in the CFD code. The results from the simulations are compared to experimental measurements. The simulations are carried out with air co-flows of 0, 0.5 and 10 m/s. The simulations are seen to reproduce physical phenomena such as the liquid pinning at sharp corners and the longitudinal stretching of the rivulet with higher air velocity.

Liquid rivulet moved by a gas flow in a minichannel

The mathematical model of steady-state flow of incompressible and nonisothermal liquid rivulet moved by a gas in an inclined minichannel was developed. Action of van der Waals and capillary forces, as well as gravity and tangential stress at the gas-liquid interface are taking into account. Numerically it is found out that rivulet formation gives a significant disturbing effect on the gas velocity distribution. It is shown that at the rivulet profile clearly visible three-phase contact line and region with practically constant inclination could be seen near the thin liquid film areas. The angle of this inclination could be considered as a contact angle. Region with practically constant derivative of the function h(y) with respect to y, near the contact line confirms this statement.

Stability of a rivulet flowing in a microchannel

A novel microfluidic technique has been recently proposed to produce quasi-monodisperse collections of microbubbles with a controlled size. In this technique, a gaseous stream is injected through a T-junction into a microchannel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a quasi-monodisperse collection of microbubbles. Motivated by this application, we here analyze the stability of both gas and liquid rivulets coflowing with a current in a quadrangular microfluidic channel. The results essentially differ from those of cylindrical jets because the contact-line-anchorage condition affects fundamentally the rivulet’s instability nature. The temporal stability analysis shows that the rivulet becomes unstable not only for (unperturbed) contact angles larger than 90° (as can be expected) but also for values smaller than that angle. Interestingly enough, the maximum growth factor exhibits a non-monotonic dependence with respect to the Reynolds number (i.e., the viscosities). In fact, there are intervals of that parameter where the fluid system becomes unstable, while all the perturbations are damped outside that interval. The gaseous rivulet does not stabilize as the Reynolds number decreases, which means that it can be unstable even in the Stokes limit and for contact angles less than 90°. In addition, the stability of a flowing liquid rivulet is not determined by its contact angle exclusively (as occurs in the static case), but by the Reynolds number as well. Liquid rivulets with contact angles less than 90° can be unstable for sufficiently high Reynolds numbers.

Flow Transition Behavior between the Liquid Film Flow and the Liquid Rivulet Flow on an Inclined Plate

Flow Transition Behavior between the Liquid Film Flow and the Liquid Rivulet Flow on an Inclined Plate

The role of wetting heterogeneities in the meandering instability of a partial wetting rivulet

Rivers are subject to a meandering instability caused by sediment transport. A liquid rivulet on an inclined plate in partial wetting conditions exhibits a similar instability at sufficiently high flow rates. It takes a sinuous shape: curves become bigger and bigger, growing by inertia from contact line defects. Meanders are eventually stationary because of the pinning force. The way the initial rivulet is created has consequences on the contact line's shape. We run experiments to study how the critical flow rate depends on initial conditions. We measure a strong dependence, in particular by modifying the initial state from which meanders are growing: it shows that the pinning force plays the main role in the meandering instability. This is in contrast with the previous approach in which only a balance is considered between inertia and a line tension of capillary origin. Because of wetting hysteresis, rivulets have the capacity to deform without any movement of the contact line. We show that the rivulet deforms in response to the centrifugal force. This deformation also helps us to understand how the critical flow rate depends on the initial rivulet shape.

Instability of a transverse liquid rivulet on an inclined plane

This work concentrates on the stability of a viscous liquid rivulet positioned across an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slip model. Both normal and parallel components of gravity are considered. We find the stability regions for given area of the cross section of the rivulet, A, plane inclination angle, α, and static contact angle, θ0, characterizing the wettability of the substrate. For α’s smaller than some critical angle, α*, a static solution exists. This solution is characterized by rear/front contact angles given by θ0 ± δ. The linear stability analysis of this solution is performed using an efficient pseudo-spectral Chebyshev method. We analyze the effects of A, θ0, and α on the predictions of the model, such as the dominant wavelength, the maximum growth rate, and the behavior of the most unstable perturbation mode. To verify them, we also carry out experiments with silicone oils spreading on a coated glass substrate for several different fluid volumes and inclination angles. We find very good agreement between the wavelength of maximum growth rate given by the theory and the average distance between the drops after rivulet breakup. An analysis of finite size effects shows that the inclusion of normal gravity effects leads to a better agreement between theoretical and experimental results.

G050072 傾斜板上での液膜流と液柱流の遷移現象に関する実験

G050072 傾斜板上での液膜流と液柱流の遷移現象に関する実験

Effect of substrate wettability in liquid dielectrophoresis (LDEP) based droplet generation: Theoretical analysis and experimental confirmation

The generation of droplets for biological reactions at the microscale can be achieved by many techniques, among which the so-called liquid dielectrophoresis technique (LDEP). This is not a new process, but the parameters influencing actuation voltage still need further insight: size and geometry (electrodes width and gap, dielectric thickness), materials (dielectric constant), liquids (surface tension, dielectric constant, conductivity), working conditions (voltage, frequency) and substrate wettability (contact angle). This large experimental space is firstly reduced using non dimensional numbers and then studied in a systematic way thanks to the design of experiments. The contact angle influence is explained thanks to a new analytical model. To summarize, this paper recalls analytical models used to predict the voltage threshold required to develop a liquid rivulet from a mother drop, taking the contact angle into account and providing a large set of experimental results.

Effect of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel

The objective of this paper is to investigate the effects of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel. The test section consists of a bottom silicon substrate bonded with a top glass cover. Three consecutive parts of an inlet fluid plenum, a central microchannel and an outlet fluid plenum were etched in the silicon substrate. The central microchannel had a width of 800 µm and a depth of 30 µm. Acetone liquid was used as the working fluid. High outlet vapor qualities were dealt with here. The flow pattern consists of a fluid triangle (shrinkage of the liquid films) and a connected long liquid rivulet, which is generated in the central microchannel in the timescale of milliseconds. The peculiar flow pattern is formed due to the following reasons: (1) the liquid rivulet tends to have a large contact area with the top hydrophilic channel surface of the glass cover, but a smaller contact area with the bottom silicon hydrophobic surface. (2) The temperature gradient in the chip width direction at the top channel surface of the glass cover not only causes the shrinkage of the liquid films in the central microchannel upstream, but also attracts the liquid rivulet populated near the microchannel centerline. (3) The zigzag pattern is formed due to the competition between the evaporation momentum forces at the vapor–liquid interfaces and the force due to the Marangoni effect. The former causes the rivulet to deviate from the channel centerline and the latter draws the rivulet toward the channel centerline. (4) The temperature gradient along the flow direction in the central microchannel downstream causes the breakup of the rivulet to form isolated droplets there. (5) Liquid stripes inside the upstream fluid triangle were caused by the small capillary number of the liquid film, at which the large surface tension force relative to the viscous force tends to populate the liquid film locally on the top glass cover surface.

The Use of the VOF‐Model to Study the Wetting of Solid Surfaces

AbstractThe laminar liquid rivulet flow on an inclined flat metal plate and wavy metal plate is taken as a test case to validate the CFD‐simulation results using the VOF (Volume of Fluid) multiphase flow model. The local rivulet thickness was measured using an optically assisted mechanical sensor and compared with the simulation results. The circular shape of the rivulet profile has been proven for an inclined plate. Glycerin water mixtures with different concentrations were used in the experiments. Two theoretical models to describe this laminar rivulet flow in comparison to the experimental and CFD results are discussed.

Small‐Scale Features of Gravity‐Driven Flow in Unsaturated Fractures

Liquid flow through unsaturated fractures often proceeds as fingers or preferential flow paths. During the invasion of liquid fingers into an initially dry, nonhorizontal fracture, fingers may drain, forming a narrow thread of liquid called a rivulet that connects to a wider portion of liquid at the advancing front, defined as a blob. Experimental studies using idealized fractures were performed to investigate the effects of wettability, surface roughness, and aperture size on several important features of gravity‐driven flow in fractures: liquid drainage, blob migration, and rivulet flow. The experiments demonstrate that the critical length of the blob before drainage occurred was significantly longer on surfaces with intermediate wettability and on surfaces with roughness on the order of 100 μm than on a smooth, flat water‐wetting surface. However, drainage did not occur on surfaces with smaller‐scale roughness on the order of 10 μm. Blob velocities were also measured and were always less than the saturated gravity‐driven flow velocity, even when a liquid with a static contact angle of zero was used. This reduction in velocity was attributed to contact angle hysteresis. Rivulet widths measured as a function of flow rate between glass and acrylic parallel plates were generally larger on the acrylic plates than the glass plates for a particular flow rate, demonstrating the sensitivity of rivulet flow to wettability. In addition, the cubic law overpredicted the measured rivulet widths, except for the widths measured between the acrylic plates at 20°. The effect of aperture variability on rivulet flow was also examined. At a critical aperture ranging between 0.25 and 0.37 mm, the liquid in the rivulet did not completely span the aperture, forming two streamlets of liquid on either side of the fracture.

Small-Scale Features of Gravity-Driven Flow in Unsaturated Fractures

Liquid flow through unsaturated fractures often proceeds as fingers or preferential flow paths. During the invasion of liquid fingers into an initially dry, nonhorizontal fracture, fingers may drain, forming a narrow thread of liquid called a rivulet that connects to a wider portion of liquid at the advancing front, defined as a blob. Experimental studies using idealized fractures were performed to investigate the effects of wettability, surface roughness, and aperture size on several important features of gravity-driven flow in fractures: liquid drainage, blob migration, and rivulet flow. The experiments demonstrate that the critical length of the blob before drainage occurred was significantly longer on surfaces with intermediate wettability and on surfaces with roughness on the order of 100 μm than on a smooth, flat water-wetting surface. However, drainage did not occur on surfaces with smaller-scale roughness on the order of 10 μm. Blob velocities were also measured and were always less than the saturated gravity-driven flow velocity, even when a liquid with a static contact angle of zero was used. This reduction in velocity was attributed to contact angle hysteresis. Rivulet widths measured as a function of flow rate between glass and acrylic parallel plates were generally larger on the acrylic plates than the glass plates for a particular flow rate, demonstrating the sensitivity of rivulet flow to wettability. In addition, the cubic law overpredicted the measured rivulet widths, except for the widths measured between the acrylic plates at 20°. The effect of aperture variability on rivulet flow was also examined. At a critical aperture ranging between 0.25 and 0.37 mm, the liquid in the rivulet did not completely span the aperture, forming two streamlets of liquid on either side of the fracture.

A stochastic approach to cable dynamics with moving rivulets

This article constructs a stochastic model for the response of stay cables of cable-stayed bridges to the combined effect of wind and rain. It describes a spring-mounted section model of a stay cable in a steady wind where aerodynamic forces are modified by the dynamics of a mobile liquid rivulet. The motion of the rivulet is described by a simple stochastic process that, together with aerodynamic forces, models the complex fluid–structure interaction. Based on measured data for drag and lift coefficients and a static rivulet location, an analysis of the model suggests a new stochastic excitation mechanism for the rain–wind induced vibrations of stay cables.

An Investigation of the Breakup of an Evaporating Liquid Film, Falling Down a Vertical, Uniformly Heated Wall

The breakup of an evaporating, thin liquid film falling down a vertical, uniformly heated wall is of interest in many applications. Analytical expressions are developed for predicting the thickness of an evaporating liquid film and the corresponding wetting rate at breakup, which are in good agreement with experimental data for water. These expressions, derived from minimizing the total energy of a stable liquid rivulet forming immediately following the film breakup, required solving for the rivulet profile and the two-dimensional velocity field in the rivulet. The total energy of the rivulet is the sum of the kinetics energy of the liquid, the surface energies at the liquid-vapor and the solid-liquid interfaces, and those due to evaporation and the thermocapillary force along the liquid-vapor interface. The liquid film thickness at breakup is a function of Marangoni number, vapor Reynolds number, liquid and vapor properties, equilibrium contact angle of the liquid with underlying wall material, and the wall thermal conductance <3×104 W/m2K. For a wall conductance <3×104 W/m2K, the film thickness at breakup, when the wall is heated uniformly at its inner surface, is higher than when the wall is heated at its outer surface, but both are identical when the wall conductance ⩾3×104 W/m2K. The contribution of the equilibrium contact angle diminishes, but the thickness of the liquid film at breakup increases, as the wall heat flux increases.

Predicting liquid flow profile in randomly packed beds from computer simulation

AbstractOur previous work on the simulation of packing processes was extended to study the liquid trickle flow down randomly packed beds. An algorithmic procedure with detailed geometrical description of packing elements was developed for tracking the liquid flow and holdup distributions in packed beds. Unlike the conventional continuum‐based models such as the diffusion model, it goes into the subparticle scale to capture the geometrical characteristics of the packed bed. Three mechanisms of the trickle flow—film flow, dripping flow, and splash—were observed in packed beds, and the first two were captured in the model. At each point within a packed bed, liquid flow is simplified to two possible directions: vertically down and horizontally in the direction of the negative gradient of the packing surface. The 3‐D geometric model constructed with the packing process simulation was used to determine the direction of the horizontal flow and fraction of the flow rate in each direction. By assuming that the liquid flow is uniform free surface flow, the Manning formula was used to predict the liquid holdup with the width of the liquid rivulet on a packing surface calculated by the Shi and Mersmann correlation. Metal Pall rings and metal Raschig rings were simulated with water as the fluid. Results of liquid flow distributions and average liquid holdup were validated against experimental data and semiempirical correlation from Billet et al.