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Gustav Amberg

Publications and source records attributed to Gustav Amberg.

16 recordsLinked to original sources
arXiv2026

Solid adsorption: the missing mechanism for surfactant contact lines -- a phase-field approach

We develop a thermodynamically consistent phase-field model for soluble surfactants in two-phase flows, incorporating both interfacial and solid surface adsorption. The model is derived via variational principles consistent with the second law of thermodynamics, resulting in modified free energies and boundary conditions that capture surfactant transport, adsorption, and wetting dynamics. A key contribution of this work is the inclusion of surfactant adsorption on solid walls, which leads to qualitative agreement with experimental observations: unlike prior numerical studies that predicted hydrophilic surfaces becoming more hydrophilic and hydrophobic surfaces more hydrophobic, our model shows a shift toward increased hydrophilicity across all contact angles-consistent with experimental trends. Our results establish that solid adsorption provides the missing mechanism required for predictive modelling of surfactant-laden contact line dynamics.

cond-mat.soft↗
arXiv2026

Cahn-Hilliard Phase Field modelling captures nanoscale contact line dynamics on high-friction surfaces

Incorporating molecular-scale effects in the description of contact line motion is essential for accurately capturing all sources of energy dissipation in wetting dynamics. This holds particularly true in the cases where contact line friction dominates, and hydrodynamics models struggle to achieve regularisation due to the negligible Navier slip. We perform Molecular Dynamics simulations of water/hexane biphasic systems in a two-phase Couette flow configuration. Wetting occurs over a silica-like surface with controllable wettability. The simulation results are reproduced by a Phase Field model (Cahn-Hilliard Navier-Stokes equations), which includes localised contact line slip and contact angle dynamics. The continuous equations are directly parametrized from Molecular Dynamics simulation results, under the numerical sharp interface limit. We demonstrate that the Phase Field model can quantitatively reproduce Molecular Dynamics through a systematic calibration protocol. Critically, we show that contact line friction is the primary physical parameter requiring empirical calibration based on Molecular Dynamics data. Once extracted by matching contact angle dynamics, quantitative agreement across multiple observables is obtained, including interface curvature, steady contact line displacement, and the structure of streamlines. All other model parameters are determined a posteriori, according to the calculation of independent observables and under numerical constraints. The results presented in this article indicate that Phase Field modelling can capture the net effect of molecular processes on the mobility of contact lines and that the careful calibration of contact line friction based on the reconstruction of contact angle dynamics and interface bending is key to fully reconcile continuous models with Molecular Dynamics.

physics.flu-dyn↗
arXiv2025

Mass diffusion and bending in dynamic wetting by phase-field and sharp-interface models

Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring empirical fitting for the slip length. On the other hand, this paradox does not appear in phase-field models as the contact line moves through diffusive mass transport. In this work, we present a toy model that accounts for mass diffusion at the contact line within a sharp-interface framework. This model is based on a theoretical relation derived from the Cahn-Hilliard equations, which links the total diffusive mass transport to the curvature at the wall. From an estimate of the chemical potential on a curved interface, we obtain an expression for the width of the highly curved region $\delta$ and the apparent angle. In the sharp-interface model, we then introduce a fictitious boundary, displaced by a distance $\delta$ into the domain, where a Navier boundary condition is applied along a dynamic apparent contact angle that accounts for the local interface bending. The robustness of the model is assessed by comparing the toy model results with standard phase-field ones on two cases: the steady state profiles of a liquid bridge between two plates moving in opposite directions and the transient behaviors of a drop spreading on a solid with a prescribed equilibrium angle. This offers a practical and efficient alternative to solve contact line problems at lower cost in a sharp-interface framework with input parameters from phase-field models.

physics.flu-dyn↗
arXiv2024

Dynamic hysteresis of an oscillatory contact line

During oscillatory wetting, a phase retardation emerges between contact angle variation and contact line velocity, presenting as a hysteresis loop in their correlation -- an effect we term dynamic hysteresis. This phenomenon is found to be tunable by modifying the surface with different molecular layers. A comparative analysis of dynamic hysteresis, static hysteresis, and contact line friction coefficients across diverse substrates reveals that dynamic hysteresis is not a result of dissipative effects but is instead proportionally linked to the flexibility of the grafted layer on the surface. In the quest for appropriate conditions to model oscillatory contact line motion, we identify the generalized Hocking's linear law and modified Generalized Navier Boundary Condition (GNBC) as alternative options for predicting realistic dynamic hysteresis.

physics.flu-dyn↗
arXiv2022

Rapid wetting of shear-thinning fluids

Using experiments and numerical simulations, we investigate the spontaneous spreading of droplets of aqueous glycerol (Newtonian) and aqueous polymer (shear-thinning) solutions on smooth surfaces. We find that in the first millisecond the spreading of the shear-thinning solutions is identical to the spreading of water, regardless of the polymer concentration. In contrast, aqueous glycerol solutions show a different behavior, namely, significantly slower spreading rate than water. In the initial rapid spreading phase, the dominating forces that can resist the wetting are inertial forces and contact-line friction. For the glycerol solutions, an increase in glycerol concentration effectively increases the contact-line friction, resulting in increased resistance to wetting. For the polymeric solutions, however, an increase in polymer concentration does not modify contact-line friction. As a consequence, the energy dissipation at the contact line can not be controlled by varying the amount of additives for shear-thinning fluids. The reduction of the spreading rate of shear-thinning fluids on smooth surfaces in the rapid wetting regime can only be achieved by increasing solvent viscosity. Our results have implications for phase-change applications where the control of the rapid spreading rate is central, such as anti-icing and soldering

physics.flu-dyn↗
arXiv2022

Nanoscale sheared droplet: Volume-of-Fluid, phase-field and no-slip molecular dynamics

The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular phenomena close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics (MD) simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended (SPC/E) water model with particle-mesh Ewald electrostatics treatment. This model provides a very small slip and a more realistic representation of the molecular physics than Lennards-Jones models. The Cahn-Hilliard phase-field model and the Volume-of-Fluid model are calibrated against the drop displacement from MD reference data. It is demonstrated that the calibrated continuum models can accurately capture droplet displacement and droplet breakup for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behavior, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight of the line friction experienced by the advancing and receding contact lines and evidence of large-scale temporal "stick-slip" like oscillations. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics.

physics.flu-dyn↗
arXiv2022

Droplet impact on asymmetric hydrophobic microstructures

Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and anti-icing. However, droplet impact on such surfaces is not fully understood. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be a useful for designing structured surfaces for controlling droplet mobility.

physics.flu-dyn↗
arXiv2021

Droplet impact on surfaces with asymmetric microscopic features

The impact of liquid drops on a rigid surface is central in cleaning, cooling and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drop impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We define the line-friction capillary number $Ca_f={μ_f V_0}/σ$ (where $μ_f$, $V_0$ and $σ$ are the line friction, impact velocity and surface tension, respectively) as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when $Ca_f \ll 1$, the contact line speed in the direction against the inclination of the ridges is set by line-friction, whereas in the direction with inclination the contact line is pinned at acute corners of the ridge. When $Ca_f \sim 1$, the pinning is only temporary until the liquid-vapor interface reaches to the next ridge where a new contact line is formed. Finally, when $Ca_f\gg 1$, the geometric details of non-smooth surfaces play little role.

physics.flu-dyn↗
arXiv2020

Steady moving contact line of water over a no-slip substrate

The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn-Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models can reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase field mobility parameter and the local slip length in accurately modelling the moving contact line.

physics.flu-dyn↗
arXiv2019

Droplet leaping governs microstructured surface wetting

Microstructured surfaces that control the direction of liquid transport are not only ubiquitous in nature, but they are also central to technological processes such as fog/water harvesting, oil-water separation, and surface lubrication. However, a fundamental understanding of the initial wetting dynamics of liquids spreading on such surfaces is lacking. Here, we show that three regimes govern microstructured surface wetting on short time scales: spread, stick, and contact line leaping. The latter involves establishing a new contact line downstream of the wetting front as the liquid leaps over specific sections of the solid surface. Experimental and numerical investigations reveal how different regimes emerge in different flow directions during wetting of periodic asymmetrically microstructured surfaces. These insights improve our understanding of rapid wetting in droplet impact, splashing, and wetting of vibrating surfaces and may contribute to advances in designing structured surfaces for the mentioned applications.

physics.flu-dyn↗
arXiv2016

Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates

A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius $β_\mathrm{max}$. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter $μ_f$. Moreover, our analysis shows that at low and intermediate impact speeds dissipation at the contact line limits the dynamics and we describe $β_\mathrm{max}$ by the scaling law $β_\mathrm{max} \sim (Re μ_\mathrm{l}/μ_f)^{1/2}$ that is a function of the droplet viscosity ($μ_\mathrm{l}$) and its Reynolds number ($Re$).

physics.flu-dyn↗
arXiv2014

Surface structure determines dynamic wetting

Liquid wetting of a surface is omnipresent in nature and the advance of micro-fabrication and assembly techniques in recent years offers increasing ability to control this phenomenon. Here, we identify how surface roughness influences the initial dynamic spreading of a partially wetting droplet by studying the spreading on a solid substrate patterned with microstructures just a few micrometers in size. We reveal that the roughness influence can be quantified in terms of a line friction coefficient for the energy dissipation rate at the contact line, and that this can be described in a simple formula in terms of the geometrical parameters of the roughness and the line-friction coefficient of the planar surface. We further identify a criterion to predict if the spreading will be controlled by this surface roughness or by liquid inertia. Our results point to the possibility of selectively controlling the wetting behavior by engineering the surface structure.

physics.flu-dyn↗
arXiv2012

Universality in dynamic wetting dominated by contact line friction

We report experiments on the rapid contact line motion present in the early stages of capillary driven spreading of drops on dry solid substrates. The spreading data fails to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact line friction ($μ_f$), which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact line friction is shown to yield a universal curve for the evolution of the contact line radius as a function of time, for a range of fluid viscosities, drop sizes and surface wettabilities.

physics.flu-dyn↗
arXiv2011

On diffuse interface modeling and simulation of surfactants in two-phase fluid flow

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

math.NA↗
arXiv2007

Electrothermal flow in Dielectrophoresis of Single-Walled Carbon Nanotubes

We theoretically investigate the impact of the electrothermal flow on the dielectrophoretic separation of single-walled carbon nanotubes (SWNT). The electrothermal flow is observed to control the motions of semiconducting SWNTs in a sizeable domain near the electrodes under typical experimental conditions, therefore helping the dielectrophoretic force to attract semiconducting SWNTs in a broader range. Moreover, with the increase of the surfactant concentration, the electrothermal flow is enhanced, and with the change of frequency, the pattern of the electrothermal flow changes. It is shown that under some typical experimental conditions of dielectrophoresis separation of SWNTs, the electrothermal flow is a dominating factor in determining the motion of SWNTs.

cond-mat.mtrl-sci↗