arXiv subjects

David Halpern

Publications and source records attributed to David Halpern.

6 recordsLinked to original sources

arXiv2026

Stability and nonlinear dynamics of three-layer viscous films inside a vertical cylindrical tube

We investigate the dynamics and stability of three immiscible viscous liquid layers coating the interior of a vertical cylindrical tube, a configuration relevant to stratified core--annular transport processes. A long-wave asymptotic analysis yields a coupled system of nonlinear evolution equations governing the motion of the three interfaces. Linear stability analysis predicts a persistent long-wave instability, the capillary (Rayleigh--Plateau) instability of the air--core interface, together with secondary finite-wavenumber instability bands that emerge from interfacial coupling in certain parameter regimes. These stability characteristics depend sensitively on the layer thicknesses, viscosity ratios, and surface tension parameters, and include mode-switching associated with competing maxima in the dispersion relation. Nonlinear simulations reveal three distinct dynamical outcomes: saturation to finite-amplitude travelling waves, air-core closure through plug formation, and rupture of the intermediate liquid layer while the air core remains open. The intermediate-layer rupture mechanism is unique to the three-layer configuration which has no analogue in one- or two-interface cylindrical film flows. Numerical continuation is used to compute branches of travelling-wave solutions and their associated limit points. Comparison with time-dependent simulations shows that travelling-wave branches successfully predict the transition from saturated waves to plug formation, but do not capture the distinct rupture mechanism associated with collapse of the intermediate layer.

physics.flu-dyn↗

arXiv2025

Moving contact lines of power-law fluids: How nonlinear fluid rheology drastically alters stress singularity and dynamic wetting behavior

Power-law fluids can strongly affect the degree of the contact line stress singularity and hence the nature of moving contact lines. We develop a framework beyond the classical paradigm for power-law fluids, providing a unified account for the distinct behaviors of the advancing contact lines. We show that the apparent dynamic contact angle $\theta_d$ can depend on the extent of the characteristic dissipation length $h^* \propto U_n/(n-1)$, altering its dependence on the contact line speed $U$. For shear-thinning fluids, we find $\theta_d \sim (h/h^*)^{(1-n)/3}$, with contact line motion being dissipated within $h^*$ extending beyond the local wedge height $h$ without requiring a cutoff. In drop spreading problems, $\theta_d$ varies with the spreading radius $R$, leading to $\theta_d \propto U^{3n/(2n+7)}$ consistent with the spreading law $R \propto t^{n/(3n+7)}$ derived from a self-similar solution, where $R$ is the spreading radius and $t$ is time. For shear-thickening fluids, the apparent contact line motion is characterized by $\theta_d \sim (h^*/h_m)^{(1-n)/3}$, where dissipation is concentrated within $h^*$ which is smaller than the microscopic liquid height $h_m$ near the contact line. In fact, the dynamic contact angle relationship in this case can be expressed as the Cox-Voinov law $\theta_d \sim Ca_{eff}^{1/3}$ in terms of a capillary number $Ca_{eff} =\eta_f U/\gamma$ where $\gamma$ is the surface tension and $\eta_f \propto (U/ h_m)^{n-1}$ is the viscosity based on the local shear rate $U/h_m$ across $h_m$. We also show that a precursor film induced by molecular forces ahead of the wedge leads to $h_m \propto U^{-n/(4-n)}$ and hence $\theta_d \propto U^{3n/(4-n)}$, making the spreading behavior highly sensitive to the contact line microstructure. Our predictions show good agreement with experimental results.

physics.flu-dyn↗

arXiv2021

Convergence of a Human-in-the-Loop Policy-Gradient Algorithm With Eligibility Trace Under Reward, Policy, and Advantage Feedback

Fluid human-agent communication is essential for the future of human-in-the-loop reinforcement learning. An agent must respond appropriately to feedback from its human trainer even before they have significant experience working together. Therefore, it is important that learning agents respond well to various feedback schemes human trainers are likely to provide. This work analyzes the COnvergent Actor-Critic by Humans (COACH) algorithm under three different types of feedback-policy feedback, reward feedback, and advantage feedback. For these three feedback types, we find that COACH can behave sub-optimally. We propose a variant of COACH, episodic COACH (E-COACH), which we prove converges for all three types. We compare our COACH variant with two other reinforcement-learning algorithms: Q-learning and TAMER.

cs.LG↗

arXiv2018

Surfactant and gravity dependent instability of two-layer channel flows: Linear theory covering all wave lengths

A linear stability analysis of a two-layer plane Couette flow of two immiscible fluid layers with different densities, viscosities and thicknesses, bounded by two infinite parallel plates moving at a constant relative velocity to each other, with an insoluble surfactant along the interface and in the presence of gravity is carried out. The normal modes approach is applied to the equations governing flow disturbances. These equations, together with boundary conditions at the plates and the interface, yield a linear eigenvalue problem. When inertia is neglected velocity amplitudes are linear combinations of hyperbolic functions, and a quadratic dispersion equation for the complex growth rate is obtained where coefficients depend on the aspect ratio, the viscosity ratio, the basic velocity shear, the Marangoni number Ma that measures the effects of surfactant, and the Bond number Bo that measures the influence of gravity. An extensive investigation is carried out that examines the stabilizing or destabilizing influences of these parameters. There are two continuous branches of the normal modes: a robust branch that exists even with no surfactant, and a surfactant branch that vanishes when Ma $\downarrow 0$. Due to the availability of the explicit forms for the growth rates, in many instances the numerical results are corroborated with analytical asymptotics. For the less unstable branch, a mid-wave interval of unstable wavenumbers (Halpern and Frenkel (2003)) sometimes co-exists with a long-wave one. We study the instability landscape, determined by the threshold curve of the long-wave instability and the critical curve of the mid-wave instability in the (Ma, Bo)-plane. The changes of the extremal points of the critical curves with the variation of the other parameters, such as the viscosity ratio, and the extrema bifurcation points are investigated.

nlin.AO↗

arXiv2016

Surfactant and gravity dependent inertialess instability of two-layer Couette flows and its nonlinear saturation

A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily strong gravity cannot completely stabilize the flow. The correlations of vorticity-thickness phase differences with instability, present when the gravitational effects are neglected, are found to break down when gravity is important. The physical mechanisms of instability for the two modes are explained with vorticity playing no role in them. Unlike the semi-infinite case that we previously studied, a small-amplitude nonlinear saturation of the surfactant instability is possible in the absence of gravity. For certain parametric ranges, the interface deflection is governed by a decoupled Kuramoto-Sivashinsky equation, which provides a source term for a linear convection-diffusion equation governing the surfactant concentration. The full numerics confirm the prediction that, along with the interface, the surfactant wave is chaotic, but the ratio of the two chaotic waves is constant.

nlin.AO↗

arXiv2006

Strongly nonlinear nature of interfacial-surfactant instability of Couette flow

Nonlinear stages of the recently uncovered instability due to insoluble surfactant at the interface between two fluids are investigated for the case of a creeping plane Couette flow with one of the fluids a thin film and the other one a much thicker layer. Numerical simulation of strongly nonlinear longwave evolution equations which couple the film thickness and the surfactant concentration reveals that in contrast to all similar instabilities of surfactant-free flows, no amount of the interfacial shear rate can lead to a small-amplitude saturation of the instability. Thus, the flow is stable when the shear is zero, but with non-zero shear rates, no matter how small or large (while remaining below an upper limit set by the assumption of creeping flow), it will reach large deviations from the base values-- of the order of the latter or larger. It is conjectured that the time this evolution takes grows to infinity as the interfacial shear approaches zero. It is verified that the absence of small-amplitude saturation is not a singularity of the zero surface diffusivity of the interfacial surfactant.

nlin.CD↗