Axisymmetric Spreading Research Articles

Axisymmetric Spreading of Petroleum Products on the Ice Cover

Axisymmetric Spreading of Petroleum Products on the Ice Cover

One-Dimensional Spreading of Petroleum Products on the Surface of the Water

The process of quasi-one-dimensional spreading of oil product spots on the water surface has been experimentally and theoretically investigated. The theoretical model is based on an approximate equation obtained using the laws of conservation of the mass of the decomposed product and the total energy of the system. Approximate solutions of this equation and the results of experimental studies on the spreading of machine oil and crude oil in a narrow extended container are presented, and their good compliance with the theory is shown. A comparison is made with the process of two-dimensional axisymmetric spreading of a spot of the same petroleum products.

Maximum spreading of an impacting drop

The maximum diameter of a drop impacting on a flat solid surface is studied theoretically assuming axi-symmetric spreading without splashing. The energy balance between the initial state of the drop (sphere diameter d0) and that a maximum spread (contact diameter dm) is closed by two novel concepts. For the gas-liquid surface area, an approximate spherical cap model is proposed. Energy loss by viscous dissipation is related to the total energy dissipation when the drop has come to rest. The fractional dissipation upon maximum spread is modelled as a function of an impact parameter (P) that combines the power laws of the capillary and viscous regimes depending on a regime discrimination parameter (A). Exponents of the Weber (We) and Reynolds (Re) numbers in P=WeRe−2/5 are determined by asymptotic analysis. The parameter A is determined from experimental data as a function of the advancing contact angle (θa). In this way, an explicit model for the maximum spread factor (βm=dm/d0) is proposed which includes the scaling laws βm∼We1/2, βm∼We1/4 and βm∼Re1/5 and is in good agreement with experimental data for wide ranges of We, Re and θa.

DYNAMICS OF ONE-DIMENSIONAL WATER SPILLS OIL PRODUCT STAINS

The process of quasi-one-dimensional spreading of oil product spots on the water surface has been experimentally and theoretically investigated. The theoretical model is based on an approximate equation obtained using the laws of conservation of the mass of the decomposed product and the total energy of the system. Approximate solutions of this equation and the results of experimental studies on the spreading of machine oil and crude oil in a narrow extended container are presented, and their good compliance with the theory is shown. A comparison is made with the process of two-dimensional axisymmetric spreading of a spot of the same petroleum products.

Droplet orthogonal impact on nonuniform wettability surfaces

AbstractThe vast majority of prior studies on droplet impact have focused on collisions of liquid droplets with spatially homogeneous (i.e., uniform‐wettability) surfaces. But in recent years, there has been growing interest on droplet impact on nonuniform wettability surfaces, which are more relevant in practice. This paper presents first an experimental study of axisymmetric droplet impact on wettability‐patterned surfaces. The experiments feature millimeter‐sized water droplets impacting centrally with on a flat surface that has a circular region of wettability (Area 1) surrounded by a region of wettability (Area 2), where (i.e., outer domain is less wettable than the inner one). Depending upon the droplet momentum at impact, the experiments reveal the existence of three possible regimes of axisymmetric spreading, namely (I) interior (only within Area 1) spreading, (II) contact‐line entrapment at the periphery of Area 1, and (III) exterior (extending into Area 2) spreading. We present an analysis based on energetic principles for , and further extend it for cases where (i.e., the outer domain is more wettable than the inner one). The experimental observations are consistent with the scaling and predictions of the analytical model, thus outlining a strategy for predicting droplet impact behavior for more complex wettability patterns.

On axisymmetric dynamic spin coating with a single drop of ethanol

We carried out experimental and numerical investigations on the axisymmetric spreading evolution of dynamic spin coating with a single drop of ethanol. The results show that the dynamic spreading process consists of two stages: inertial spreading stage and centrifugal thinning stage. These two stages are connected by a transient state in between characterized by the minimum contact line moving velocity. The Weber number determines the spreading in the first stage, similar to the case of the impact of a drop on a static substrate. The rotational Bond number has a marginal effect on the inertia spreading and the radius at the transient state. In the centrifugal thinning stage, the rotational Bond number dominates the flow while the effect of the Weber number is negligible.

Lubricated axisymmetric gravity currents of power-law fluids

The motion of glaciers over their bedrock or drops of fluid along a solid surface can become unstable when these substrates are lubricated. Previous studies modelled such systems as coupled gravity currents (GCs), consisting of one fluid that lubricates the flow of another fluid, and having two propagating fronts. When both fluids are Newtonian and discharged at constant flux, global similarity solutions were found. However, when the top fluid is strain-rate softening, experiments have shown that each fluid front evolved with a different exponent. Here, we explore theoretically and numerically such lubricated GCs consisting of axisymmetric spreading of a power-law fluid on top of a Newtonian fluid, where each fluid volume grows in time like$t^{\alpha }$. We find that the structure imposed by the non-Newtonian flow precludes general self-similarity, unlike purely Newtonian GCs. Consequently, we identify outstripping solutions in which the inner fluid front outstrips the outer fluid front. Despite the absence of a general global similarity solution, we find similarity solutions in several asymptotic limits. These include the purely Newtonian limit for any$\alpha$, the case of$\alpha =5$for a general power-law fluid, asymptotic limits in the viscosity ratio, and in the vicinity of the fluid fronts. Many of our theoretical predictions are found to be consistent with recent laboratory experiments. Discrepancies suggest the presence of hydrofracturing or wall slip near the fronts, and potentially, a progressive significance of extensional stresses as front outstripping is approached.

The impact of vent geometry on the growth of lava domes

SUMMARY Thick lava flows that are a feature of many volcanic fields on the Earth and Venus vary from sheet-like to nearly perfect axisymmetric domes. Here, we investigate how these geometrical characteristics depend on the shape of the feeder vent. We study the gravitational spreading of viscous lava erupting from elliptical vents onto a flat surface using 3-D numerical models. The aspect ratio of the vent, defined to be the major to minor axes ratio, varies between 1 and 25. In the limit of an aspect ratio of one, the vent is circular and spreading is axisymmetric. In the limit where the ratio is large, the vent behaves as a fissure. The numerical models rely on an isoviscous lava rheology and a constant volumetric eruption rate. In all cases, the initial phase of the dome’s evolution is in a lava-discharge dominated regime such that spreading is insignificant and the height of the dome increases at a constant rate over the vent area. For vent aspect ratios greater than five, three successive regimes of spreading are identified: 2-D spreading in the direction perpendicular to the major axis of the vent, a transient phase such that the dome shape evolves towards that of a circular dome and a late axisymmetric spreading phase that does not depend on the vent shape. These regimes are delimited by the times required for the flow thickness above the vent to reach a given height and for the flow to spread axisymmetrically up to a length equal to the semi-major axis of the vent. Numerical results for the flow height and runout length tend towards the similarity solutions in the 2-D and axisymmetric regimes. Two main implications for highly viscous (rhyolitic) fissure eruptions can be drawn. First, the fissure length determines the flow regimes. The longer the vent fissure length, the longer the early lava discharge regime and 2-D spreading perpendicular to the length of the fissure. Second, the aspect ratio of fissure-fed lava flows can be used as an indicator of the fissure length and the duration of lava discharge. The ellipticity of some terrestrial fissure-fed flows provides evidence for viscous gravity-driven spreading terminated before the onset of the axisymmetric regime. On the other hand, the circular domes on Venus appear to be the result of fissure-fed eruptions sustained enough for the spreading to reach the axisymmetric regime. We propose relationships providing estimates of the fissure length and the duration of lava discharge based on fossil dome dimensions.

Draining and spreading along geometries that cause converging flows: Viscous gravity currents on a downward-pointing cone and a bowl-shaped hemisphere

We report experiments observing the gravitational axisymmetric spreading of a viscous liquid with a fixed volume on inclined geometries that cause converging flows, for example, on a funnel and a bowl. The spreading of the liquid on these geometries is different from that on typical geometries such as an inclined plate: the thickness of the spreading front first decreases in time and then increases. These geometries also induce different new thresholds of fingering instabilities.

On the modelling of joint formation in dissolutive brazing processes

In this paper, earlier dissolutive wetting models describing the dynamics of an axisymmetric alloy drop spreading on pure metal substrate are extended to describe reactive wetting and subsequent joint formation in brazing processes. A two-dimensional time-dependent problem is formulated, and the model equations are nondimensionalized, revealing the possibilities for asymptotic model reduction. Whilst the numerical solution of the time-dependent problem, which contains two moving contact lines and would not in general be amenable to lubrication theory, is relegated to future work, the steady-state problem is analyzed in detail. The analysis offers an arguably more transparent alternative to an earlier energy minimization approach for finding the location of the meniscus, which ultimately constitutes the joint. The results of the present model are found to compare favourably to those of earlier experimental and theoretical work.

AFFF spread over liquid surface under external radiation conditions

Aqueous film forming foam (AFFF) is effective in extinguishing oil fires. The extinguishing effect generally depends on the foam spread process and its coverage area. In this study, the foam spread process under external thermal radiation is investigated. Firstly, based on the axisymmetric foam spread model, the relationship of radiation and foam thickness is discussed. Then foam spreading experiments under pool fire condition were carried out, to simulate the actual extinguishing process of AFFF. Finally, the foam spread model considering the external radiation flux is developed which may provide theoretical guidance for fire suppression using AFFF.

Broadband modulated absorption/emission technique to probe sooting flames: Implementation, validation, and limitations

A new optical setup and its associated post-processing have been designed in an effort to map soot related quantities in an axisymmetric flame spreading over solid samples in microgravity environment where setup compactness constraints are stringent. Extending the well-established spectral modulated absorption/emission (S-MAE) technique that uses lasers as light sources together with a sophisticated optical arrangement, LEDs have been associated with broadband optics to enable the broadband modulated absorption/emission (B-MAE) technique. The design and the cautious assessment of the original B-MAE setup are reported in the present paper. Algorithms that need to be reformulated for broadband integration are first validated retrieving both two-dimensional soot temperature and volume fraction fields produced by numerical simulations. Then, these fields are measured with both B-MAE and S-MAE techniques in a largely documented steady laminar non-premixed coflow ethylene/air flame established at normal gravity. Thus, outputs delivered by the B-MAE technique can be compared with those obtained with the S-MAE setup. Both soot temperature and volume fraction are shown to be decently measured by the B-MAE technique. As the spread of the non-buoyant flames to be investigated in the near future is especially driven by radiative heat transfer, the discrepancies between both techniques outputs are commented in the light of the fields of local radiative loss computed from the fields measured by both techniques. As a result, the fields delivered by the B-MAE technique are expected to provide ground-breaking insights into the control of flame spread in the absence of buoyancy, therefore manned spacecraft fire safety.

Experimental and theoretical study on near-floor flame spread along a thin solid

This paper presents experimental observations and a theory of near-floor flame spread along a thin solid. Experiments were conducted by igniting at the center of a thin circular paper sheet that was held at a given height h from the bottom floor. It was observed that the flame front was corrugated and often broke into separated structures when h was small, and highly disturbed burned areas were obtained for h=2 mm; flame spread was not possible at h=1 mm. When h was larger than about 5 mm, on the other hand, nearly axisymmetric spread was observed, and the spread velocity was found to increase with h. Since the front structure showed a similarity with smoldering combustion, an analysis was conducted based on a theory of smoldering spread, in which oxidizer flow velocity and the degree of heat loss are two important parameters. Boundary-layer consideration and PIV measurement showed that the oxidizer flow velocity did not significantly vary under the conditions studied, thereby suggesting the importance of heat loss to the bottom floor. An equation that describes the front normal velocity was then derived, which was numerically solved. Since the tangential velocity does not alter the shape of a curve, it was adjusted such that the grid-point spacing would be asymptotically uniform. Theoretically predicted front-shape evolution for different values of h agreed reasonably well with the experimental observations, validating the theory at least qualitatively.

Viscous drops on a layer of the same fluid: from sinking, wedging and spreading to their long-time evolution

We study the axisymmetric spreading of drops deposited on a pre-existing horizontal layer of the same viscous fluid. Using a combination of experiments, numerical modelling based on the axisymmetric free-surface Navier–Stokes equations and scaling analyses, we explore the drops’ behaviour in a regime where the flow is driven by gravitational and/or capillary forces while inertial effects are small. We find that during the early stages of the drops’ evolution there are three distinct spreading behaviours depending on the thickness of the liquid layer. For thin layers the fluid ahead of a clearly defined spreading front is at rest and the overall behaviour resembles that of a drop spreading on a dry substrate. For thicker films, the spreading is characterised by an advancing wedge which is sustained by fluid flow from the drop into the layer. Finally, for thick layers the drop sinks into the layer, accompanied by significant flow within the layer. As the drop keeps spreading, the evolution of its shape becomes self-similar, with a power-law behaviour for its radius and its excess height above the undisturbed fluid layer. We employ lubrication theory to analyse the drop’s ultimate long-term behaviour and show that all drops ultimately enter an asymptotic regime which is reached when their excess height falls below the thickness of the undisturbed layer.

Axisymmetric spreading of surfactant from a point source

Guided by computation, we theoretically calculate the steady flow driven by the Marangoni stress due to a surfactant introduced on a fluid interface at a constant rate. Two separate extreme cases, where the surfactant dynamics is dominated by the adsorbed phase or the dissolved phase, are considered. We focus on the case where the size of the surfactant source is much smaller than the size of the fluid domain, and the resulting Marangoni stress overwhelms the viscous forces so that the flow is strongest in a boundary layer close to the interface. We derive the resulting flow in a region much larger than the surfactant source but smaller than the domain size by approximating it with a self-similar profile. The radially outward component of fluid velocity decays with the radial distance $r$ as $r^{-3/5}$ when the surfactant spreads in an adsorbed phase, and as $r^{-1}$ when it spreads in a dissolved phase. Universal flow profiles that are independent of the system parameters emerge in both the cases. Three hydrodynamic signatures are identified to distinguish between the two cases and verify the applicability of our analysis with successive stringent tests.

Near Axisymmetric Partial Wetting Using Interface-Localized Liquid Dielectrophoresis.

The wetting of solid surfaces can be modified by altering the surface free energy balance between the solid, liquid, and vapor phases. Liquid dielectrophoresis (L-DEP) can produce wetting on normally nonwetting surfaces, without modification of the surface topography or chemistry. L-DEP is a bulk force acting on the dipoles of a dielectric liquid and is not normally considered to be a localized effect acting at the interface between the liquid and a solid or other fluid. However, if this force is induced by a nonuniform electric field across a solid-liquid interface, it can be used to enhance and control the wetting of a dielectric liquid. Recently, it was reported theoretically and experimentally that this approach can cause a droplet of oil to spread along parallel interdigitated electrodes thus forming a stripe of liquid. Here we show that by using spiral-shaped electrodes actuated with four 90° successive phase-shifted signals, a near axisymmetric spreading of droplets can be achieved. Experimental observations show that the induced wetting can achieve film formation, an effect not possible with electrowetting. We show that the spreading is reversible thus enabling a wide range of partial wetting droplet states to be achieved in a controllable manner. Furthermore, we find that the cosine of the contact angle has a quadratic dependence on applied voltage during spreading and deduce a scaling law for the dependence of the strength of the effect on the electrode size.

Elastomeric PDMS Planoconvex Lenses Fabricated by a Confined Sessile Drop Technique.

The ubiquity of high quality smartphones at affordable prices not only accelerated the social penetration in the global population but also promoted nontraditional usage of smartphones as point-of-care medical diagnostic devices, sensors, and portable digital microscopes. This paper reveals a simple, rapid, cost-effective, and template-free technique for mass-scale production of an elastomeric PDMS (ePDMS) planoconvex lens capable of converting a smartphone into a portable digital microscope. By taking advantage of the resistance to spreading of liquid by a sharp edge, highly stable spherical cap of viscous liquid PDMS (lPDMS) on a smooth PMMA circular disk was fabricated. The axisymmetric spreading of lPDMS under the gravitational force and interfacial tension force enable the formation of spherical cap with a certain radius of curvature. A thermal treatment at 80 °C for 30 min cured the spherical cap lPDMS into a bubble-free ePDMS planoconvex lens. Lenses with focal lengths of 55.2-3.4 mm could be reproducibly fabricated by adjusting the volume of dispensed lPDMSs and diameter of PMMA disks. High-resolution panoramic microscope images without a distortion of small cylindrical object could be constructed on-the-fly using the imbedded smartphone app. Applications of the smartphone digital microscope equipped with an ePDMS planoconvex lens for imaging of micro printings, gun shot residues, cylindrical objects, and bullet toolmarks were explored.

Diffuse interface simulation of ternary fluids in contact with solid

In this article we developed a geometrical wetting condition for diffuse-interface simulation of ternary fluid flows with moving contact lines. The wettability of the substrate in the presence of ternary fluid flows is represented by multiple contact angles, corresponding to the different material properties between the respective fluid and the substrate. Displacement of ternary fluid flows on the substrate leads to the occurrence of moving contact point, at which three moving contact lines meet. We proposed a weighted contact angle model, to replace the jump in contact angle at the contact point by a relatively smooth transition of contact angle over a region of 'diffuse contact point' of finite size. Based on this model, we extended the geometrical formulation of wetting condition for two-phase flows with moving contact lines to ternary flows with moving contact lines. Combining this wetting condition, a Navier-Stokes solver and a ternary-fluid model, we simulated two-dimensional spreading of a compound droplet on a substrate, and validated the numerical results of the drop shape at equilibrium by comparing against the analytical solution. We also checked the convergence rate of the simulation by investigating the axisymmetric drop spreading in a capillary tube. Finally, we applied the model to a variety of applications of practical importance, including impact of a circular cylinder into a pool of two layers of different fluids and sliding of a three-dimensional compound droplet in shear flows.

Droplet spreading and absorption on rough, permeable substrates

Wetting of permeable substrates by liquids is an important phenomenon in many natural and industrial processes. Substrate heterogeneities may significantly alter liquid spreading and interface shapes, which in turn may alter liquid imbibition. A new lubrication-theory-based model for droplet spreading on permeable substrates that incorporates surface roughness is developed in this work. The substrate is assumed to be saturated with liquid, and the contact-line region is described by including a precursor film and disjoining pressure. A novel boundary condition for liquid imbibition is applied that eliminates the need for a droplet-thickness-dependent substrate permeability that has been employed in previous models. A nonlinear evolution equation describing droplet height as a function of time and the radial coordinate is derived and then numerically solved to characterize the influence of substrate permeability and roughness on axisymmetric droplet spreading. Because it incorporates surface roughness, the new model is able to describe the contact-line pinning that has been observed in experiments but not captured by previous models.

Surfactant spreading on a thin liquid film: reconciling models and experiments

The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg [J Fluid Mech 235:399–414, 1992] describing the spreading of a single layer of insoluble surfactant has become widely accepted, and several experiments on axisymmetric spreading have confirmed its predictions for both the height profile of the free surface and the spreading exponent (the radius of the circular area covered by surfactant grows as $$t^{1/4}$$ ). However, these prior experiments utilized primarily surfactant quantities exceeding (sometimes far exceeding) a monolayer. In this paper, we report that this regime is characterized by a mismatch between the timescales of the experiment and model and, additionally, find that the spatial distribution of surfactant molecules differs substantially from the model prediction. For experiments performed in the monolayer regime for which the model was developed, the surfactant layer is observed to have a spreading exponent of less than $$1/10$$ , far below the predicted value, and the surfactant distribution is also in disagreement. These findings suggest that the model is inadequate for describing the spreading of insoluble surfactants on thin fluid layers.