Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface

The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

Experimental study and mathematical modelling of self-oscillation at the electrode-magnetic fluid interface in an electric field

The article describes a mathematical model of self-oscillation in the form of a boundary value problem for a nonlinear system of partial differential equations, with a numerical solution. The numerical results were compared to the experimental data to confirm the adequacy of the model. The model uses the classical system of differential equations of material balance, Nernst-Planck and Poisson equations without simplifications or fitting parameters. The aim of the article was to study the parameters of concentration self-oscillation in a layer of the dispersed phase particles of magnetic fluid at the interface with an electrode in an electric field. For this purpose, we developed a mathematical model, the consistency of which wasconfirmed by the corresponding physical mechanism.As a result of numerical experiments, we found the critical value of the potential jump after which self-oscillation began. We also determined the oscillation growth period and other characteristics of the process. We developed software called AutoWave01 with an intuitive user interface and advanced functionality for the study of self-oscillation in a thin layer of magnetic colloid.

Continuum and Molecular Dynamics Studies of the Hydrodynamics of Colloids Straddling a Fluid Interface

Colloid-sized particles (10 nm–10 μm in characteristic size) adsorb onto fluid interfaces, where they minimize their interfacial energy by straddling the surface, immersing themselves partly in each phase bounding the interface. The energy minimum achieved by relocation to the surface can be orders of magnitude greater than the thermal energy, effectively trapping the particles into monolayers, allowing them freedom only to translate and rotate along the surface. Particles adsorbed at interfaces are models for the understanding of the dynamics and assembly of particles in two dimensions and have broad technological applications, importantly in foam and emulsion science and in the bottom-up fabrication of new materials based on their monolayer assemblies. In this review, the hydrodynamics of the colloid motion along the surface is examined from both continuum and molecular dynamics frameworks. The interfacial energies of adsorbed particles is discussed first, followed by the hydrodynamics, starting with isolated particles followed by pairwise and multiple particle interactions. The effect of particle shape is emphasized, and the role played by the immersion depth and the surface rheology is discussed; experiments illustrating the applicability of the hydrodynamic studies are also examined. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

A mini-module with embedded spacers for high-throughput ultrafiltration

Ultrafiltration membrane modules suffer from performance losses that arise during filtration from concentration polarization and fouling. Such performance losses are frequently mitigated by controlling the hydrodynamic conditions at the membrane/fluid interface. For instance, the hydrodynamic conditions are manipulated using mesh spacers that act as a static mixer. The design of such spacers is rarely optimized to effectively maintain mass transport through the membrane. Also, the spacer is an additional part added to the feed channel of the membrane module, improving mass transport in general, yet accepting less transport in dead zones.Here, we present a mini module with spacers embedded in the module housing of a flat-sheet ultrafiltration membrane to attain high permeation rates. The performance of two new embedded spacer geometries – staggered herringbone and sinusoidal corrugation – prove experimentally that indeed a CFD-simulated flux increase can be realized during bovine serum albumin (BSA) filtration. The flow characteristics inside the mini module are further investigated using magnetic resonance velocity imaging. The new embedded sinusoidal corrugation spacers outper- form conventional mesh spacer inlays. The fabrication of such module-embedded spacers has been conceptually implemented through an in-silico design and a 3D-printing production process. The latter can be easily realized using injection molding processes, as is now done for the Sartorius ambra(R) crossflow product line.