arXiv subjects

Fernando Temprano-Coleto

Publications and source records attributed to Fernando Temprano-Coleto.

9 recordsLinked to original sources

arXiv2026

Upper bounds on the colloid separation efficiency of diffusiophoresis

The separation of colloidal particles from fluids is essential to ensure a safe global supply of drinking water, yet in the case of microscopic particles, it remains a highly energy-intensive process when using traditional filtration methods. Water cleaning through diffusiophoresis, spontaneous colloid migration in chemical gradients, effectively circumvents the need for physical filters, representing a promising alternative. This separation process is typically realized in internal flows, where a cross-channel electrolyte gradient drives particle accumulation at walls, with colloid separation slowly increasing in the streamwise direction. However, the maximum separation efficiency, achieved sufficiently downstream as diffusiophoretic migration (driving particle accumulation) is balanced by Brownian motion (inducing diffusive spreading), has not yet been characterized. In this work, we develop an asymptotic theory to predict colloid separation in this limit, deriving expressions for the water recovery, defined as the fraction of clean water that can be obtained from the suspension. We find that the mechanism by which the chemical permeates in the channel and the reaction kinetics governing its dissociation into ions play key roles in the process. Moreover, we identify four distinct regimes in which separation is controlled by different scaling laws involving Damköhler and Péclet numbers, which measure the ratios of reaction kinetics to ion diffusion and diffusiophoresis to Brownian motion, respectively. We also confirm the scaling of one of these regimes using microfluidic experiments where separation is driven by CO2 gradients. Our results shed light on pathways toward new, more efficient separations and are also applicable to quantify colloidal accumulation in the presence of chemical gradients in more general situations.

cond-mat.soft↗

arXiv2025

Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers

Motivated by microfluidic applications, we investigate drag reduction in laminar pressure-driven flows in channels with streamwise-periodic superhydrophobic surfaces (SHSs) contaminated with soluble surfactant. We develop a model in the long-wave and weak-diffusion limit, where the streamwise SHS period is large compared to the channel height and the Péclet number is large. Using asymptotic and numerical techniques, we determine the influence of surfactant on drag reduction in terms of the relative strength of advection, diffusion, Marangoni effects and bulk-surface exchange. In scenarios with strong exchange, the drag reduction exhibits a complex dependence on the thickness of the bulk-concentration boundary layer and surfactant strength. Strong Marangoni effects immobilise the interface through a linear surfactant distribution, whereas weak Marangoni effects yield a quasi-stagnant cap. The quasi-stagnant cap has an intricate structure with an upstream slip region, followed by intermediate inner regions, and a quasi-stagnant region that is mediated by weak bulk diffusion. The quasi-stagnant region differs from the immobile region of a classical stagnant cap, observed for instance in surfactant-laden air bubbles in water, by displaying weak slip. As exchange weakens, the bulk and interface decouple: the surfactant distribution is linear when the surfactant is strong, whilst it forms a classical stagnant cap when the surfactant is weak. The asymptotic solutions offer closed-form predictions of drag reduction across much of the parameter space, providing practical utility and enhancing understanding of surfactant dynamics in flows over SHSs.

physics.flu-dyn↗

arXiv2024

On the self-similarity of unbounded viscous Marangoni flows

The Marangoni flow induced by an insoluble surfactant on a fluid-fluid interface is a fundamental problem investigated extensively due to its implications in colloid science, biology, the environment, and industrial applications. Here, we study the limit of a deep liquid subphase with negligible inertia (low Reynolds number, $Re\ll{1}$), where the two-dimensional problem has been shown to be described by the complex Burgers equation. We analyze the problem through a self-similar formulation, providing further insights into its structure and revealing its universal features. Six different similarity solutions are found. One of the solutions includes surfactant diffusion, whereas the other five, which are identified through a phase-plane formalism, hold only in the limit of negligible diffusion (high surface Péclet number $Pe_s\gg{1}$). Surfactant 'pulses', with a locally higher concentration that spreads outward, lead to two similarity solutions of the first kind with a similarity exponent $β=1/2$. On the other hand, distributions that are locally depleted and flow inwards lead to similarity of the second kind, with two different exponents that we obtain exactly using stability arguments. We distinguish between 'dimple' solutions, where the surfactant has a quadratic minimum and $β=2$, from 'hole' solutions, where the concentration profile is flatter than quadratic and $β=3/2$. Each of these two cases exhibits two similarity solutions, one earlier than a critical time $t_*$ when the derivative of the concentration is singular, and another one valid after $t_*$. We obtain all six solutions in closed form, and discuss predictions that can be extracted from these results.

physics.flu-dyn↗

arXiv2024

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels

Recognising that surfactants can impede the drag reduction resulting from superhydrophobic surfaces (SHSs), we investigate the impact of spatio-temporal fluctuations in surfactant concentration on the drag-reduction properties of SHSs. We model the unsteady transport of soluble surfactant in a channel flow bounded by two SHSs. The flow is laminar, pressure-driven, and the SHSs are periodic in the streamwise and spanwise directions. We assume that the channel length is much longer than the streamwise period, the streamwise period is much longer than the channel height and spanwise period, and bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. By combining long-wave and homogenisation theories, we derive an unsteady advection-diffusion equation for surfactant-flux transport over the length of the channel, which is coupled to a quasi-steady advection-diffusion equation for surfactant transport over individual plastrons. As diffusion over the length of the channel is typically small, the surfactant flux is governed by a nonlinear wave equation. In the fundamental case of the transport of a bolus of surfactant, we predict its propagation speed and describe its nonlinear evolution via interaction with the SHS. The propagation speed can fall below the average streamwise velocity as the surfactant adsorbs and rigidifies the plastrons. Smaller concentrations of surfactant are advected faster than larger ones, so that wave-steepening effects can lead to shock formation in the surfactant-flux distribution. Our asymptotic results reveal how unsteady surfactant transport can affect the spatio-temporal evolution of the slip velocity, drag reduction and effective slip length in SHS channels.

physics.flu-dyn↗

arXiv2023

Exogenous-endogenous surfactant interaction yields heterogeneous spreading in complex branching networks

Experiments have shown that surfactant introduced to a liquid-filled maze can find the solution path. We reveal how the maze-solving dynamics arise from interactions between the added surfactant and endogenous surfactant present at the liquid surface. We simulate the dynamics using a nonlinear model solved with a discrete mimetic scheme on a graph. Endogenous surfactant transforms local spreading into a non-local problem with an omniscient view of the maze geometry, key to the maze-solving dynamics. Our results offer insight into surfactant-driven transport in complex networks such as lung airways.

physics.flu-dyn↗

arXiv2023

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

While superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs on both walls. We assume that diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting a long-wave theory that accounts for a rapid transverse Marangoni-driven flow, we derive a one-dimensional model for surfactant evolution, which allows us to predict the drag reduction across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, advection and shear dispersion. We map out asymptotic regions in the high-dimensional parameter space, deriving approximations of the drag reduction in each region and comparing them to numerical simulations. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

physics.flu-dyn↗

arXiv2023

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Recent experimental and computational investigations have shown that trace amounts of surfactants, unavoidable in practice, can critically impair the drag reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses at the air-liquid interface. However, predictive models for realistic SHS geometries do not yet exist, which has limited the understanding and mitigation of these adverse surfactant effects. To address this issue, we derive a model for laminar, three-dimensional flow over SHS gratings as a function of geometry and soluble surfactant properties, which together encompass 10 dimensionless groups. We establish that the grating length $g$ is the key geometric parameter and predict that the ratio between actual and surfactant-free slip increases with $g^2$. Guided by our model, we perform synergistic numerical simulations and microfluidic experiments, finding good agreement with the theory as we vary surfactant type and SHS geometry. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. For SHSs, we show that surfactant effects can be predicted by a single parameter, representing the ratio between the grating length and the interface length scale beyond which the flow mobilizes the air-water interface. This mobilization length is more sensitive to the surfactant chemistry than to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface active. These findings advance the fundamental understanding of realistic interfacial flows and provide practical strategies to maximize superhydrophobic drag reduction.

physics.flu-dyn↗

arXiv2023

A model for slip and drag in turbulent flows over superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHSs) can reduce the friction drag in turbulent flows. In the laminar regime, it has been shown that trace amounts of surfactant can negate this drag reduction, at times rendering these surfaces no better than solid walls (Peaudecerf et al., Proc. Natl. Acad. Sci. USA 114(28), 7254-9, 2017). However, surfactant effects on the drag-reducing properties of SHSs have not yet been studied under turbulent flow conditions, where predicting the effects of surfactant in direct numerical simulations remains expensive by today's standards. We present a model for turbulent flow inclusive of surfactant, in either a channel or boundary-layer configuration, over long but finite-length streamwise ridges that are periodic in the spanwise direction, with period $P$ and gas fraction $φ$. We adopt a technique based on a shifted log law to acquire an expression for the drag reduction. The average streamwise and spanwise slip lengths are derived by introducing a local laminar model within the viscous sublayer, whereby the effect of surfactant is modelled by modifying the average streamwise and spanwise slip lengths. Our model agrees with available laboratory experimental data from the literature when conditions are clean (surfactant-free), or when there are low surfactant levels. However, we find an appreciable drag increase for larger background surfactant concentrations that are characteristic of turbulent flows over SHSs for marine applications.

physics.flu-dyn↗

arXiv2019

A theory for the slip and drag of superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.

physics.flu-dyn↗