Fluid Drop Research Articles

Dynamics of self-rewetting drop on an inclined uniformly heated substrate

The dynamics of a self-rewetting drop on a uniformly heated, inclined substrate are considered. Based on the lubrication theory and Navier slip condition, an evolution equation for the drop thickness of a two-dimensional drop is established. The migration characteristics of the drop are investigated when the interfacial tension is positive and negative and in a quadratic functional relationship with temperature under the same wetting scenario. The effects of the inclination angle, capillary number, Bond number, and thermocapillary force on the drop migration are examined when the interfacial tension has a nonmonotonic dependence on temperature. Numerical results indicate that the direction of interfacial tension has a significant influence on drop spreading. When the conventional pure fluid drop and self-rewetting fluid drop have the same wettability, the self-rewetting drop spreads more rapidly and the fluid is more evenly distributed on the inclined substrate. The effect of gravity parallel to the wall is enhanced by the increase in the inclination angle, resulting in faster drop sliding velocity. The increase in Ca results in a delay of the contact line pinning state and prolonged pinning time; however, the increase in Bo leads to an advanced pinning state of the contact line and reduced pinning time. The thermocapillary force is important to the deformation of the drop. When the enhancement in the thermocapillary force overcomes the effect of the other forces, less fluid is driven to flow down the wall, resulting in a relatively uniform distribution of the fluid on the substrate.

Unilateral rhinorrhoea associated with cerebrospinal fluid leak

A 56-year-old postmenopausal obese woman presented with a 6-month history of right-sided rhinorrhoea. There was no history of head trauma or surgery. On clinical examination drops of clear fluid were...

Boundary Element Simulation of Axisymmetric Viscous Creeping Flows under Gravity in Free Surface Domains

An indirect boundary element method is proposed for the numerical solution of the Stokes equations in the axisymmetric case with Dirichlet and Neumann boundary conditions, which correspond to the velocity given on a part of the boundary and to the traction given on the other part. The method is described as applied to quasi-steady viscous creeping flows under gravity in regions bounded by a free surface and solid walls. A viscous fluid drop spreading over a hydrophobic horizontal surface is considered as an example. It is shown that the use of no-slip conditions ensure that the results have approximation convergence and satisfy the mass and energy conservation laws.

Heat transfer enhancement due to internal circulation within a rising fluid drop

Motion of drops and bubbles plays a critical role in the efficiency of industrial operations such as extraction. As the drop moves in the continuous phase, the tangential shear stress induced by the continuous fluid at the drop interface results in internal circulation, which may enhance transport of components and energy between the dispersed phase (drop) phase and the continuous phase. In the present study, computational fluid dynamics (CFD) simulations have been used to study this aspect in detail. Coupled calculations for the two phases have been carried out for fluid flow over a spherical, non-deformable drop of a given diameter. The predicted internal circulation is validated by comparing with analytical results for very low Reynolds numbers and experimental data at higher Re. The calculation framework is then used to study the convective-diffusive heat transfer to the drop for various combinations of Re and Pr. The heat transfer within the drop is found to comprise of three regimes, two diffusion controlled heat transfer regimes (initial and final) connected by an intermediate convection controlled heat transfer regime. The heat transfer enhancement by convection has been deduced and is found to depend both on Re and Pr. A dimensionless correlation has been developed to predict the convective heat transfer enhancement.

An assessment of the PTT model on the impacting drop problem

This work presents a numerical method and simulations of axisymmetric free-surface flows of a polymeric fluid using the Phan–Thien–Tanner (PTT) constitutive relationship. The governing equations are solved by finite differences on a staggered grid that employs accurate boundary conditions on the free surface together with bounded, monotone, high-order upwinding approximation of the convection terms. The numerical method is partially verified by solving fully developed flow in a tube and comparing it to a known analytic solution. The problem of a drop impacting on a rigid plate is considered. The effect of varying the five parameters, characterizing the PTT model, is studied extensively, and the results are interpreted physically. The expansion–contraction phenomenon of the viscoelastic drop that occurs when it hits a flat surface is tracked, and the time evolution of the normal and shear components of the extra-stress tensor is analyzed. To further verify the code, the impacting drop of an Oldroyd-B fluid is simulated and the time evolution of the drop width is compared to that of other authors.

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

SummaryIn this paper, a three‐dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three‐dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT‐based pressure solver, with the evolution equation for non‐Newtonian (including EVP) stresses. In this flexible computational framework, the fluid can be modeled by either Oldroyd‐B, neo‐Hookean, FENE‐P, or Saramito EVP models, and the additional equations for the non‐Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid, whereas the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an immersed boundary method with a computationally efficient direct forcing method, allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level‐set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single‐phase and two‐phase EVP flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy‐driven drop in an EVP fluid.

Progress in pressure drop of fluid in microchannels

Progress in pressure drop of fluid in microchannels

A porous viscoelastic model for the cell cytoskeleton

The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid. doi:10.1017/S1446181118000081

The motion of long drops in rectangular microchannels at low capillary numbers

Drop flow in rectangular microchannels has been utilized extensively in microfluidics. However, the pressure-gradient versus flow-rate relation is still not well understood. We study the motion of a long drop in a rectangular microchannel in the limit the capillary number $Ca\rightarrow 0$ ($Ca=\unicode[STIX]{x1D707}U/\unicode[STIX]{x1D70E}$, where $U$ is the constant drop velocity, $\unicode[STIX]{x1D707}$ is the viscosity of the carrier liquid and $\unicode[STIX]{x1D70E}$ is the interfacial tension). In this limit, the moving drop looks like the static drop and has two end caps connected by a long column, which is surrounded by thin films on the microchannel wall and by menisci along the microchannel corners. Integral axial force balances on the drop fluid and on the carrier liquid surrounding the drop relate the carrier-liquid pressure gradient to the drop-fluid pressure gradient and the contact-line drag. The contact-line drag is argued to be the same as that for a long bubble (which has been determined by Wong et al. (J. Fluid Mech., vol. 292, 1995b, pp. 95–110)) if the viscosity ratio $\unicode[STIX]{x1D706}\ll Ca^{-1/3}$ and $\unicode[STIX]{x1D706}\ll L$, where $\unicode[STIX]{x1D706}=\bar{\unicode[STIX]{x1D707}}/\unicode[STIX]{x1D707}$, $\bar{\unicode[STIX]{x1D707}}$ is the drop viscosity and $L~(\gg 1)$ is the dimensionless drop length. Thus, the force balances yield one equation relating the two pressure gradients. The two pressure gradients also drive unidirectional flows in the drop and in the corner channels along the long middle column. These coupled flows are solved by a finite-element method to yield another equation relating the two pressure gradients. From the two equations, we determine the pressure gradients and thus the unidirectional velocity fields inside and outside the drop for $\unicode[STIX]{x1D706}=0$–100 and various microchannel aspect ratios. We find that in the limit $LCa^{1/3}\rightarrow 0$, the contact-line drag dominates and the carrier liquid bypasses the drop through the corner channels alongside the drop. For $LCa^{1/3}\gg 1$, the contact-line drag is negligible and the corner fluid is stationary. Thus, the drop moves as a leaky piston. We extend our model to a train of long drops, and compare our model predictions with published experiments.

Many-body dissipative particle dynamics (MDPD) simulation of a pseudoplastic yield-stress fluid with surface tension in some flow processes

The dynamics of Newtonian and pseudoplastic yield-stress fluid drops impacting on solid surfaces are studied numerically by the many body dissipative particle dynamics (MDPD) method. The pseudoplastic yield stress fluid is modelled by two groups of different MDPD particles, in which the parameters are tuned so that the overall fluid behaves in a similar manner to the Herschel–Bulkley pseudoplastic material in simple shear flow. The droplet characteristics are measured by its central drop diameter and its height, and an effective unyielded region is observed in the drop impacting process. The MDPD simulation results compare well with previous drop impact experiments and simplified theoretical studies on the slump test, serving to demonstrate the capability of the MDPD method to explore yield-stress fluid drop’s flow processes.

Collecting Ni-Sulfate Compound from Electroless Plating Waste by Magnetic Separation Technique with Use of HTS Bulk Magnets

The authors have developed a useful technique for extracting the Ni-sulfate compound from the “processed waste/fluid” of the electroless Ni-plating processes. After forming the fine NiHPO3 precipitate from the waste, the coarse NiSO4 crystals were synthesized through the reaction with the concentrated sulfuric acid. In the experiment, the open-gradient magnetic separation was employed to collect the NiSO4 crystals from the muddy mixture composed of these compounds. The experiments were practically conducted with use of the Gd123-based HTS bulk magnets generating up to 3.99 T, which were activated by the field cooling magnetizing method operated at 35 K. Intense magnetic field emitted from the bulk magnet attracted the paramagnetic fluid and coarse NiSO4 crystals on the bottom of the water channel, forming a giant drop of NiSO4-saturated clear fluid and the slurry of nickel sulfate hexahydrate. This preferential collection suggests a feasible recycling process of Ni resource as a raw material in the plating processes.

Instabilities triggered in different conducting fluid geometries due to slowly time-dependent magnetic fields.

The main objective of this work is the study and analysis of non-linearities forced through oscillating magnetic fields in a conducting fluid where the instabilities are triggered due to magnetohydrodynamic forces. Different geometries have been studied and different surface patterns that break the symmetries have been observed. First, an InGaSn drop of fluid where the system breaks the azimuthal and radial symmetries depending on the volume is observed. Second, we extend the study to an InGaSn annular configuration where the presence of patterns opens the door to discuss the possibility to extend these results to other configurations as biological systems, where the conducting fluid is an electrolyte. This configuration has an added interest, as it has been proposed that the vertigoes triggered on patients in an MRI test could be generated by the interaction of the magnetic field with the electrolyte present in the inner ear.

Single and Two Phase Pressure Drop in Fluid

Single and Two Phase Pressure Drop in Fluid

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field.

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a^{*}), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation.

Numerical Investigation of Heat Transfer Enhancement Inside the Pipes Filled With Radial Pore-Size Gradient Porous Materials

The gradient porous materials (GPMs)-filled pipe structure has been proved to be effective in improving the heat transfer ability and reducing pressure drop of fluid. A GPMs-filled pipe structure in which radial pore-size gradient increased nonlinearly has been proposed. The field synergy theory and tradeoff analysis on the efficiency of integrated heat transfer has been accomplished based on performance evaluation criteria (PEC). It was found that the ability of heat transfer was enhanced considerably, based on the pipe structure, in which the pore-size of porous materials increased as a parabolic opening up. The flow resistance was the lowest and the integrated heat transfer performance was the highest when radial pore-size gradient increasing as a parabolic opening down.

Fast liquid sheet and filament dynamics in the fluid splitting process

We consider the fluid splitting dynamics of a small fluid drop entrapped between two parallel solid plates, which are rapidly pulled apart such that a free liquid sheet is formed between them for a few milliseconds. Velocities, time scales and shear rates correspond to the lift-off of a printing cylinder from the substrate in an industrial printing process.The formation and collapse of the liquid sheets, and the filaments forming at their rim are studied. Driven by the surface tension of the liquid sheet, the filaments are accelerated towards each other, and finally collide and decay. We show that surface waves that travel on the liquid sheet have a critical impact on this collision, which may either result in a smooth unification or in a highly dynamical collapse, ending in a random emission of fluid drops. Furthermore, we discuss the relevance of the Laplace number on the propagation of these waves.We also consider the liquid sheet decay by capillarity-driven expansion of spontaneously forming holes and discuss how sheet thickness and its local variation can be detected by an anisotropic hole expansion rate measurement.

Drop of viscous magnetic fluid in a non-stationary magnetic field

Drop of viscous magnetic fluid in a non-stationary magnetic field

The form of the magnetic fluid drop in a uniform harmonic electric field with the concentration of surface charge transportations

The form of the magnetic fluid drop in a uniform harmonic electric field with the concentration of surface charge transportations

Spinning superfluidHe4nanodroplets

We have studied spinning superfluid $^4$He nanodroplets at zero temperature using Density Functional theory. Due to the irrotational character of the superfluid flow, the shapes of the spinning nanodroplets are very different from those of a viscous normal fluid drop in steady rotation. We show that when vortices are nucleated inside the superfluid droplets, their morphology, which evolves from axisymmetric oblate to triaxial prolate to two-lobed shapes, is in good agreement with experiments. The presence of vortex arrays confers to the superfluid droplets the rigid-body behavior of a normal fluid in steady rotation, and this is the ultimate reason of the surprising good agreement between recent experiments and the classical models used for their description.

Universal Rim Thickness in Unsteady Sheet Fragmentation.

Unsteady fragmentation of a fluid bulk into droplets is important for epidemiology as it governs the transport of pathogens from sneezes and coughs, or from contaminated crops in agriculture. It is also ubiquitous in industrial processes such as paint, coating, and combustion. Unsteady fragmentation is distinct from steady fragmentation on which most theoretical efforts have been focused thus far. We address this gap by studying a canonical unsteady fragmentation process: the breakup from a drop impact on a finite surface where the drop fluid is transferred to a free expanding sheet of time-varying properties and bounded by a rim of time-varying thickness. The continuous rim destabilization selects the final spray droplets, yet this process remains poorly understood. We combine theory with advanced image analysis to study the unsteady rim destabilization. We show that, at all times, the rim thickness is governed by a local instantaneous Bond number equal to unity, defined with the instantaneous, local, unsteady rim acceleration. This criterion is found to be robust and universal for a family of unsteady inviscid fluid sheet fragmentation phenomena, from impacts of drops on various surface geometries to impacts on films. We discuss under which viscous and viscoelastic conditions the criterion continues to govern the unsteady rim thickness.