A cut finite element method for coupled bulk-surface problems on time-dependent domains

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh

A level-set model for two-phase flow with variable surface tension: thermocapillary and surfactants

An unstructured conservative level-set method for two-phase flow with variable surface tension is introduced. Surface tension is a function of temperature or surfactant concentration on the interface. Consequently, the called Marangoni stresses induced by temperature gradients or surfactant concentration gradients on the interface lead to a coupling of momentum transport equation with thermal energy transport equation or interface surfactant transport equation. The finite-volume method discretizes transport equations on 3D collocated unstructured meshes. The unstructured conservative level-set method is employed for interface capturing, whereas the multiple marker approach avoids the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters are proposed to discretize the convective term of transport equations. A central difference scheme discretizes diffusive terms. Gradients are evaluated by the weighted least-squares method. Verifications and validations are reportedThe main author, N. Balcazar-Arciniega, as a Serra-Húnter Fellow (UPC-LE8027), acknowledges the Catalan Government for the financial support through this programme. Simulations were executed using computing time granted by the RES (IM-2021-1-0013, IM-2020-2-0002) and PRACE 14th Call (2016153612) on the supercomputer MareNostrum IV based in Barcelona, Spain. The authors acknowledge the financial support of the MINECO, Spain (PID2020-115837RB-100).Peer ReviewedPostprint (published version

Effect of the surfactant on complex multi-phase annular flows

In the modern world, the scale of industrial production within all sectors has reached unprecedented levels due to ever-growing demand and consumption of various products. A vast majority of industrial processes exploits the benefits brought by the multiphase flows whose complex dynamics are governed by the concoction of fundamental physics. Probing the details of such flows, experimentally and/or theoretically provides an ability to develop and optimise the needs of industrial applications. Yet, this progression is gradual as it depends on the advancement of measurement technologies that enable the investigation of the complex behaviour and topologies of many different possible combinations of phases utilised in industry. Use of the novel optical diagnostic techniques coupled with bespoke capacitance probes in the present study enables us to explore uncharted territory of two-phase gas-liquid annular flows in vertically orientated pipes. In the present study, a recently developed variant of laser-induced fluorescence (LIF) technique, termed structured-planar laser-induced fluorescence (S-PLIF), is used which allows us to eliminate biases commonly encountered during film-thickness measurements of gas-liquid flows due to refraction and reflection of the light at the interface. In parallel, a bespoke capacitance probe is also employed which permits us to conduct film thickness measurements with high temporal resolution along the perimeter of the pipe. Simultaneous application of these two measurement techniques provides an opportunity to study the subtle differences found in thin annular film structures caused not only by the function of liquid and gas flow rates, but also by the surface-active agents which are widely known to cause drastic changes in flow behaviour due to surface tension gradients. The flow characteristics are studied in terms of mean film thickness, roughness, probability density functions, time-scales of the flows, and gas entrainment in the liquid film. The analysis of the data reveals important changes in the flow characteristics due to the presence of soluble surfactant. Firstly, it is observed that surfactant promotes thinning of annular films at nearly all flow conditions investigated herein, hinting at its influence on the turbulence within the bulk flow. The behaviour of interfacial waves was also found to be notably altered by the surfactant where the film roughness and the time-scale of the waves increase in gas-sheared film flows with low to moderate turbulence and low gas entrainment. This corresponds to flows not in the `regular wave' regime. A decrease in both characteristics then follows upon an increase in turbulence to a sufficiently high level of the two phases. The high gas-shear rate not only limits the highest attainable wave amplitude downstream, but also results in high agitation of air and water phases, and thus, high gas and liquid entrainment. Ultimately, this smooths the base film populated with small-amplitude waves and substantially reduces the amplitude of large interfacial waves. Generally, good agreement with relevant literature correlations is found. The estimated time-scales of the wave dynamics and Marangoni flow showed that the surfactant plays an increasingly important role on waves with lower amplitudes. The sizes of the bubbles entrained in the surfactant-free liquid film are found to exhibit log-normal distributions that become flatter with a decrease in the gas Reynolds number, while this distribution is maintained for surfactant-laden flows. On the other hand, wider distributions in the bubble sizes are found for the surfactant-laden flows at the highest gas-shear rate for all liquid Reynolds numbers. The normalised location of the bubbles (quantified as the relative entrainment depth, i.e., distance of the bubble from the local air-water film height in the wall-normal direction divided by the local film thickness) follows a Gaussian distribution, where the majority of the bubbles accumulate in the middle of the thin film. Understanding the need for further development of the multiphase flows that involves the use of surfactants, motivated us to develop a method to prepare water soluble fluorescent surfactant, which is described in the present work. Furthermore, a detailed characterisation of the fluorescent surfactant is also provided, which may encourage further experimental and modelling investigations of the relevant surfactant-laden multiphase dynamics found in small- and large-industrial scale applications.Open Acces

Effect of surfactants during drop formation in a microfluidic channel: a combined experimental and computational fluid dynamics approach

The effect of surfactants on the flow characteristics during rapid drop formation in a microchannel is investigated using high-speed imaging, micro-particle image velocimetry and numerical simulations; the latter are performed using a three- dimensional multiphase solver that accounts for the transport of soluble surfactants in the bulk and at the interface. Drops are generated in a flow-focusing microchannel, using silicone oil ( 4.6 mPa s) as the continuous phase and a 52 % w/w glycerol solution as the dispersed phase. A non-ionic surfactant (Triton X-100) is dissolved in the dispersed phase at concentrations below and above the critical micelle concentration. Good agreement is found between experimental and numerical data for the drop size, drop formation time and circulation patterns. The results reveal strong circulation patterns in the forming drop in the absence of surfactants, whose intensity decreases with increasing surfactant concentration. The surfactant concentration profiles in the bulk and at the interface are shown for all stages of drop formation. The surfactant interfacial concentration is large at the front and the back of the forming drop, while the neck region is almost surfactant free. Marangoni stresses develop away from the neck, contributing to changes in the velocity profile inside the drop

Ambit of Multiphase CFD in Modelling Transport Processes Related to Oil Spill Scenario and Microfluidics

During the ‘Deepwater Horizon’ accident in the deep sea in 2010, about 4.9 million barrels of oil was released into the Gulf of Mexico, making the spill one of the worst ocean spills in recent times. To mitigate the ill effects of the event on the environment, subsea injection of dispersants was carried out. Dispersant addition lowers the interfacial tension at oil/water interface and presence of local turbulence enhances the droplet disintegration process. The oil droplets contain a plethora of hydrocarbons which are soluble in water. In deep spill scenarios, droplets spend large amounts of time in water column; hence, the dissolution process of soluble hydrocarbons becomes important. In this study, our focus is to exploit the capabilities of multiphase CFD in developing an integrated numerical model which accounts for various transport processes and hence would effectively guide us in predicting the fate of oil mass. In the initial stages, studies were conducted to understand these transport processes at a very fundamental level where the effect of surfactant, on the dynamics of crude oil, droplet rising in a stagnant column, was investigated. To capture the subsurface dissolution of hydrocarbons from oil droplet, a unique experiment was devised wherein a binary organic mixture, representing a pseudo oil droplet comprising of volatile and non-volatile hydrocarbons, was employed to study the effect of unsteady mass transport on the overall dynamics of the droplet. In the next phase of project, we developed a numerical model, by integrating traditional multiphase CFD models and turbulence models, with a population balance (PB) approach, for predicting the droplet size distribution resulting from the interaction of turbulent oil jets with the surrounding quiescent environment. Apart from the simulations specific to oil spill related situations, the multiphase CFD was also employed to study the fluid flow in micro-channels. The mass transfer mechanisms in micro-channels for immiscible fluids in squeezing and dripping regimes were studied by employing the numerical model, which couples the features of the traditional Volume of fluid method and the Continuous Species transport approach for evaluating the concentration fields inside dispersed and continuous phase

Effect of surfactant-laden droplets on turbulent flow topology

In this work, we investigate flow topology modifications produced by a swarm of large surfactant-laden droplets released in a turbulent channel flow. Droplets have same density and viscosity of the carrier fluid, so that only surface tension effects are considered. We run one single-phase flow simulation at $Re_\tau=\rho u_\tau h / \mu = 300$, and ten droplet-laden simulations at the same $Re_\tau$ with a constant volume fraction equal to $\Phi \simeq5.4\%$. For each simulation, we vary the Weber number ($We$, ratio between inertial and surface tension forces) and the elasticity number ($\beta_s$, parameter that quantifies the surface tension reduction). We use direct numerical simulations of turbulence coupled with a phase field method to investigate the role of capillary forces (normal to the interface) and Marangoni forces (tangential to the interface) on turbulence (inside and outside the droplets). As expected, due to the low volume fraction of droplets, we observe minor modifications in the macroscopic flow statistics. However, we observe major modifications of the vorticity at the interface and important changes in the local flow topology. We highlight the role of Marangoni forces in promoting an elongational type of flow in the dispersed phase and at the interface. We provide detailed statistical quantification of these local changes as a function of the Weber number and elasticity number, which may be useful for simplified models