arXiv subjects

Radu Cimpeanu

Publications and source records attributed to Radu Cimpeanu.

At least 19 recordsLinked to original sources

arXiv2026

Bouncing or Merging in Drop-Bath Impacts

When a liquid drop impacts a liquid surface, it deforms the surface, trapping a thin layer of air between drop and bath. The drop then either bounces off the bath or, if the gas film ruptures, merges with it. We present a model for drop-bath impacts that can accurately predict whether a drop will bounce or merge, and compare it to theory-driven experiments. The model incorporates a lubrication description of the deforming trapped gas film, which accounts for its significant curvature, within a finite-element framework. Capturing this outcome requires micro- and nano-scale physics: van der Waals-driven disjoining pressure and gas-kinetic effects that depend on the mean free path of the gas. Using only independently measured material parameters, we obtain the first quantitative agreement with experiment for the critical impact speed separating bounce from merge. We explore the behaviour of drop-bath impacts at low ambient air pressure, and then investigate the bounce-merge threshold for impacts onto shallow baths and thin films, finding a bounce-merge-bounce-merge transition as the bath depth decreases.

physics.flu-dyn↗

arXiv2026

Controlling three-dimensional falling liquid films: from weighted-residual models to direct numerical simulation

We consider the problem of controlling a three-dimensional falling liquid film using same-fluid blowing and suction through the substrate. Building upon recent results for the corresponding two-dimensional problem, we employ a reduced-dimensional weighted-residual model for the film height and downstream flux as the basis for controller design. Linear stability analysis is used to estimate the number of actuators required to stabilise the film, while a linear-quadratic regulator (LQR) framework is used to construct feedback controls for the linearised system. The resulting gain matrix is then combined with observations from direct numerical simulation (DNS) of the three-dimensional Navier-Stokes equations, allowing controls derived from the reduced-dimensional model to be applied directly to the full flow. Through systematic numerical tests, we demonstrate that these controls successfully stabilise the flat-film solution across a physically relevant range of Reynolds numbers and domain configurations. We further show that both the number and placement of actuators play a crucial role in control performance, with spanwise instabilities requiring additional actuator coverage in the cross-stream direction. Although the extension from two to three dimensions substantially increases the cost of controller construction, this cost is incurred entirely offline during the computation of the gain matrix, making the overall framework computationally tractable. Our results demonstrate that LQR feedback controls derived from a three-dimensional weighted-residual model retain predictive value when applied to fully resolved DNS, extending previous two-dimensional control methodologies and helping bridge the gap between theoretical control design and experimentally relevant falling-film flows.

physics.flu-dyn↗

arXiv2026

Liquid bridges between horizontal cylinders: effects of gravity and electric fields

Liquid bridges suspended between two parallel horizontal cylinders are studied using experiments, reduced-order mathematical modelling and numerical simulations. Both non-electrified and electrified configurations are considered, with the cylinders acting as electrodes between which a potential difference can be applied. The initial focus is on equilibrium bridge shapes, while the dynamics is examined only in the non-electrified case. In the experiments, transformer-oil bridges are investigated and modelled as perfect dielectrics. The electric field counteracts the gravitational effects and causes the bridges to rise and become flatter, with shapes that are well described by Young--Laplace-type equations containing non-local electric-field contributions evaluated using a boundary-element method. Bifurcation diagrams of these solutions are constructed by pseudo-arclength continuation to characterise the dependence of bridge shapes on liquid volume and electric-field strength. In the absence of an electric field, the transient relaxation to equilibrium is analysed using a reduced-order model developed using Onsager's variational principle, with comparison to direct numerical simulations. The steady states predicted by the reduced-order model agree closely with those of the full formulation over a wide parameter range, and the dynamics is well captured in the overdamped regime.

physics.flu-dyn↗

arXiv2026

Data-Driven Equation Discovery for Nonlinear Liquid Film Flows

Over the past decade data-driven equation discovery emerged as a powerful alternative to first principles-based methodologies traditionally used in mathematical modelling cycles. The approach provides a promising path towards deep, physical insight into systems that have previously evaded rigorous mathematical derivation procedures, often due to intractable complexity. The strengths of such techniques have been successfully established for many problem classes described by systems of ordinary differential equations and continue to be extended, with their reach into partial differential equation systems gaining momentum, though comparatively nascent. Herein we tackle such a frontier: elucidating the dynamics of liquid film flows, a problem space providing a rich backdrop in terms of asymptotic analytical building blocks. By leveraging expert knowledge and the ability to carefully curate data, we establish a best-case scenario for identifying the underlying governing equations. Even here, multi-collinearity, stemming from the choice of monomial basis functions in our multi-scale flow configuration, introduces complex identifiability issues. Early-time transients compound this further, as the most dynamically rich behaviour carries the largest residuals in training data. Pinpointing such vulnerabilities allows us to better define the boundaries of current discovery techniques and paves the way for the next generation of more resilient, numerically stable algorithms.

physics.flu-dyn↗

arXiv2026

Bouncing to coalescence transition for droplet impact onto moving liquid pools

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

physics.flu-dyn↗

arXiv2025

Fast droplet impact onto slowly moving deep pools

When a fast droplet impacts a pool, the resulting ejecta sheet dynamics determine the final impact outcome. At low Capillary numbers, the ejecta sheet remains separate from a deep static pool, whilst at higher viscosities it develops into a lamella. Here, we show that the common natural scenario of a slowly moving deep pool can change the upstream impact outcome, creating highly three-dimensional dynamics no longer characterised by a single descriptor. By considering how pool movement constrains the evolution of the ejecta sheet angle, we reach a length-scale invariant parameterisation for the upstream transition that holds for a wide range of fluids and impact conditions. Direct numerical simulations show similar dynamics for an equivalent oblique impact, indicating that the pool boundary layer does not play a decisive role for low pool-droplet speed ratios. Our results also provide insight into the physical mechanism that underpins pool impact outcomes more generally.

physics.flu-dyn↗

arXiv2025

Drop rebound at low Weber number

We study the rebound of drops impacting non-wetting substrates at low Weber number $We$ through experiment, direct numerical simulation, and reduced-order modeling. Submillimeter-sized drops are normally impacted onto glass slides coated with a thin viscous film that allows them to rebound without contact line formation. Experiments are performed with various drop viscosities, sizes, and impact velocities, and we directly measure metrics pertinent to spreading, retraction, and rebound using high-speed imaging. We complement experiments with direct numerical simulation and a fully predictive reduced-order model that applies natural geometric and kinematic constraints to simulate the drop shape and dynamics using a spectral method. At low $We$, drop rebound is characterized by a weaker dependence of the coefficient of restitution on $We$ than in the more commonly studied high-$We$ regime, with nearly $We$-independent rebound in the inertio-capillary limit, and an increasing contact time as $We$ decreases. Drops with higher viscosity or size interact with the substrate longer, have a lower coefficient of restitution, and stop bouncing sooner, in good quantitative agreement with our reduced-order model. In the inertio-capillary limit, low $We$ rebound has nearly symmetric spreading and retraction phases and a coefficient of restitution near unity. Increasing $We$ or viscosity breaks this symmetry, coinciding with a drop in the coefficient of restitution and an increased dependence on $We$. Lastly, the maximum drop deformation and spreading are related through energy arguments, providing a comprehensive framework for drop impact and rebound at low $We$.

physics.flu-dyn↗

arXiv2025

Non-linear estimators for the observation and stabilisation of falling liquid films

Falling liquid films are complex physical processes modelled by infinite-dimensional dynamical systems. The interfacial behaviour is characterised by the Reynolds number, a nondimensional parameter, and above a critical value the uniform film becomes unstable and travelling waves occur. By injecting and removing fluid from the base at discrete locations, we aim to stabilise otherwise unstable flat interfaces, with the additional limitation that observations of the state are restricted to finitely many measurements of the film height. Successful feedback control has recently been achieved in the case of full observations using linear-quadratic regulator controls coupled to asymptotic approximations of the Navier-Stokes equations, but restricted observations severely curtailed their performance. In this study we couple the well understood full-information feedback control strategy to a non-linear estimator. The dynamics of the estimator are designed to approximate those of the film, and we apply a forcing term chosen to ensure that measurements of the estimator match the available measurements of the film. Using this method, we restore the performance of the controls to a level approaching their full information counterparts, even at moderately large Reynolds numbers. We also briefly investigate the effects of the relative positioning of actuators and observers on the resulting dynamics.

math.OC↗

arXiv2025

Modelling two-dimensional droplet rebound off deep fluid baths

In order for a droplet to rebound rather than coalesce with a liquid bath, a layer of gas must persist throughout the impact. This gas, typically an air layer acts as a lubricant to the system and permits a pressure transfer between the two liquid bodies. Through considering separately the bath, air, and drop regions of fluid, we introduce a fully coupled reduced dynamic model of two-dimensional droplets (i.e. cylindrical geometry) rebounding off liquid baths, which incorporates an evolving lubricating air layer. Numerical solutions of the lubrication-mediated model are compared to dedicated direct numerical simulation of the Navier-Stokes equations. The reduced model captures rebounding dynamics well in the regime where it is most relevant: for low-speed impacts of small droplets, where capillary forces are important. Numerically, the reduced model is efficient, allowing for the computation of multiple rebounds and of long time dynamics of droplets rebounding on a vibrating bath. Furthermore, the lubrication-mediated model is able to provide detailed information within the air layer such as pressure and lubrication-layer geometry, which is usually omitted from reduced models.

physics.flu-dyn↗

arXiv2025

A simulation modeling framework for fluid motion and transport in a rocking bioreactor with application to cultivated meat production

Rocking or wave-mixed bioreactors have emerged as a promising innovation in the production of cultivated meat due to their disposable nature, low operating costs, and scalability. However, despite these advantages, the performance of rocking bioreactors is not well characterized in view of their relatively short history in the market and the wide range of geometrical and operating parameters. In the present study we develop a rigorous computational framework for this multiphase, multi-physics system to quantitatively evaluate mixing, oxygen transfer, and shear stress within a rectangular rocking bioreactor under various operating conditions. This framework is implemented using the Basilisk open-source platform. We use a second-order finite volume Navier-Stokes solver and a volume-of-fluid interface reconstruction scheme to accurately resolve the highly nonlinear fluid motion. By solving the advection-diffusion equation for a multi-fluid system, we examine mixing time and the oxygen mass transfer coefficient for different operating conditions, both of which show a strong relationship with steady streaming underlying the instantaneous laminar flow. We further highlight two critical hydrodynamic phenomena that significantly influence bioreactor performance. Firstly, we investigate the transitional regime from laminar to turbulent flow. Moreover, we identify specific operating conditions that trigger resonance within the bioreactor, enhancing mixing and oxygen transfer. We finally discuss the potential effects of shear stress and energy dissipation rate on cell survival. Our findings are expected to provide valuable insights and guidelines for designing optimized bioreactors to support the next-generation cultivated meat industry pipelines.

physics.flu-dyn↗

arXiv2024

Stabilisation of falling liquid films with restricted observations

We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling the flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applied to simulations of the full system.

math.OC↗

arXiv2023

A new flow-based design for double-lumen needles

Oocyte retrieval forms a crucial part of in vitro fertilisation treatment and its ultimate outcome. Standard double-lumen needles, which include a sequence of aspiration and flushing steps, are characterised by a similar success rate to single-lumen needles, despite their increased cost. A novel hydrodynamics-based needle called the OxIVF needle is proposed here, which is geared towards the generation of an internal flow field within the full follicular volume via laterally, rather than frontally, oriented flushing, leading to successful retrievals with no additional stress on the oocyte. A two-dimensional digital twin of the follicular environment is created and tested via multi-phase flow direct numerical simulation. Oocyte initial location within the follicle is varied, while quantities of interest such as velocity magnitude and vorticity are measured with a high level of precision. This provides insight into the overall fluid motion, as well as the trajectory and stresses experienced by the oocyte. A comparative benchmark set of tests indicated a higher success rate of the OxIVF needle of up to 100%, marking a significant improvement over the traditional double-lumen design whose success rate of no more than 75% was also highly dependent on the location of the needle tip inside the follicle. All forces measured during these tests showcase how the oocyte experiences stresses which are no larger than at the aspiration point, with the flow field providing a gentle steering effect towards the extraction region. Finally, the flow generation strategy maximises oocyte yield, unlocking new capabilities in both human and veterinary contexts.

physics.flu-dyn↗

arXiv2023

Linear quadratic regulation control for falling liquid films

We propose and analyse a new methodology based on linear-quadratic regulation (LQR) for stabilising falling liquid films via blowing and suction at the base. LQR methods enable rapidly responding feedback control by precomputing a gain matrix, but are only suitable for systems of linear ordinary differential equations (ODEs). By contrast, the Navier-Stokes equations that describe the dynamics of a thin liquid film flowing down an inclined plane are too complex to stabilise with standard control-theoretical techniques. To bridge this gap we use reduced-order models - the Benney equation and a weighted-residual integral boundary layer model - obtained via asymptotic analysis to derive a multi-level control framework. This framework consists of an LQR feedback control designed for a linearised and discretised system of ODEs approximating the reduced-order system, which is then applied to the full Navier-Stokes system. The control scheme is tested via direct numerical simulation (DNS), and compared to analytical predictions of linear stability thresholds and minimum required actuator numbers. Comparing the strategy between the two reduced-order models we show that in both cases we can successfully stabilise towards a uniform flat film across their respective ranges of valid parameters, with the more accurate weighted-residual model outperforming the Benney-derived controls. The weighted-residual controls are also found to work successfully far beyond their anticipated range of applicability. The proposed methodology increases the feasibility of transferring robust control techniques towards real-world systems, and is also generalisable to other forms of actuation.

math.OC↗

arXiv2023

Inertio-capillary rebound of a droplet impacting a fluid bath

The rebound of droplets impacting a deep fluid bath is studied both experimentally and theoretically. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. Measurements of the droplet trajectory and other rebound metrics are compared directly to the predictions of a linear quasi-potential model, as well as fully resolved direct numerical simulations (DNS) of the unsteady Navier-Stokes equations. Both models resolve the time-dependent bath and droplet shapes in addition to the droplet trajectory. In the quasi-potential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to two sets of coupled damped linear harmonic oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in our parameter regime of interest. Starting from the inertio-capillary limit in which both gravitational and viscous effects are negligible, increases in gravity or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. The inertio-capillary limit defines an upper bound on the possible coefficient of restitution for droplet-bath impact, depending only on the Weber number. The quasi-potential model is able to rationalize historical experimental measurements for the coefficient of restitution, first presented by Jayaratne and Mason (1964).

physics.flu-dyn↗

arXiv2022

Electrostatic control of the Navier-Stokes equations for thin films

A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate, which induces an electric field in the gas phase, and a resultant Maxwell stress at the liquid-gas interface. The imposed potential at the second electrode is derived using a model predictive control loop, together with optimal control of a high-fidelity reduced-dimensional model. In this implementation the interfacial shape of the fluid is successfully controlled; however, the algorithm is sufficiently general to control any other quantity of interest.

physics.flu-dyn↗

arXiv2021

Active control of liquid film flows: beyond reduced-order models

The ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex to tackle directly and reduced-order modelling is used in order to create viable representations of the target systems. The simplified setting allows for the development of rigorous control theoretical approaches, but the propagation of their effects back up the hierarchy and into real-world systems remains a significant challenge. Using the canonical setup of a liquid film falling down an inclined plane under the action of active feedback controls in the form of blowing and suction, we develop a multi-level modelling framework containing both analytical models and direct numerical simulations acting as an in silico experimental platform. Constructing strategies at the inexpensive lower levels in the hierarchy, we find that offline control transfer is not viable, however analytically-informed feedback strategies show excellent potential, even far beyond the anticipated range of applicability of the models. The detailed effects of the controls in terms of stability and treatment of nonlinearity are examined in detail in order to gain understanding of the information transfer inside the flows, which can aid transition towards other control-rich frameworks and applications.

physics.flu-dyn↗

arXiv2020

Capillary-scale solid rebounds: experiments, modelling and simulations

A millimetre-size superhydrophobic sphere impacting on the free surface of a quiescent bath can be propelled back into the air by capillary effects and dynamic fluid forces, whilst transferring part of its energy to the fluid. We report the findings of a thorough investigation of this phenomenon, involving different approaches. Over the range from minimum impact velocities required to produce rebounds to impact velocities that cause the sinking of the solid sphere, we focus on the dependence of the coefficient of restitution, contact time and maximum surface deflection on the different physical parameters of the problem. Experiments, simulations and asymptotic analysis reveal trends in the rebound metrics, uncover new phenomena at both ends of the Weber number spectrum, and collapse the data. Direct numerical simulations using a pseudo-solid sphere successfully reproduce experimental data whilst also providing insight into flow quantities that are challenging to determine from experiments. A model based on matching the motion of a perfectly hydrophobic impactor to a linearised fluid free surface is validated against direct numerical simulations and used in the low Weber number regime. The hierarchical and cross-validated models in this study allow us to explore the entirety of our target parameter space within a challenging multi-scale system.

physics.flu-dyn↗

arXiv2020

Droplet impact onto a spring-supported plate: analysis and simulations

The high-speed impact of a droplet onto a flexible substrate is a highly nonlinear process of practical importance which poses formidable modelling challenges in the context of fluid-structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed mathematical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot and stiffness of the spring have on the motion of the solid, which undergoes forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length- and time-scales.

physics.flu-dyn↗