Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0110081

Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation

Jens Eggers·Todd F. Dupont
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jens Eggers, Todd F. Dupont. 2001-10-28. Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation. https://doi.org/10.1017/s0022112094000480

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Similarity Scaling of Fully Developed Mass Transport and Pressure Drop in Oriented Spacer-Filled Channels in Spiral-Wound Membrane Modules

Feed spacers in reverse osmosis membrane modules enhance mass transport but simultaneously increase flow resistance. The quantitative dependence of both on spacer orientation remains poorly understood despite its importance for optimal module design. This work introduces an analytic least-square method for deriving scaling laws governing Sherwood number ($Sh$) and friction factor ($f$) as functions of spacer orientation and Reynolds number ($Re$) through high-resolution computational fluid dynamics simulations. The analytical least-square fitting method provides a systematic approach for extracting transport coefficients. Physical similarity analyses on industrial spacers reveal that mass transport follows $Sh = 3.595(1 + 0.244 \sin(2α)) Re^{1/2}$ while pressure drop scales as $f = 11.63(1 + 0.19 \sin(2α)) Re^{-1/2}$, enabling quantification of orientation-dependent transport efficiency across the full operating range. A novel RO performance analysis scheme shows that the trade-off between water flux and pressure drop crucially depends on the spacer orientation. $45^\circ$-oriented spacers improve the water flux marginally, while increasing the pressure drop significantly, compared to $0^\circ$-oriented spacers.

physics.flu-dyn↗
arXiv2026

Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments

Rapid urbanization demands efficient monitoring of turbulent wind and pollutant dispersion, yet existing reconstruction and sensor placement strategies fail under realistic sparsity constraints. Here, we introduce Diff--SPORT, a diffusion-based framework that combines a generative diffusion prior with maximum a posteriori inference and Shapley-value attribution for high-fidelity flow reconstruction and optimal sensor placement. By training a diffusion prior model once over a domain, Diff--SPORT enables non-linear optimal sensor placement and near-real-time flow reconstruction from sparse measurements orders of magnitude faster than RANS or LES simulations, consistently outperforming state-of-the-art methods. The framework also extends, without algorithmic modification, to experimental passive scalar concentration dataset, a direct proxy for pollutant dispersion, measured in a 1:2400 scale water-flume model of the Beijing Haidian neighbourhood under realistic urban flow conditions. Shapley-guided sensor placement achieves up to 57\% lower reconstruction error than randomly placed sensors at extreme sparsity, identifying compact and physically interpretable configurations. These results establish Diff--SPORT as a modular foundation offering a zero-shot alternative to retraining-intensive downstream strategies, supporting scalable urban flow monitoring for air quality management and resilient city design.

physics.flu-dyn↗
arXiv2026

Vertical motion of a periodically driven floating disc

We present the results of a combined theoretical and experimental investigation into the vertical dynamics of floating discs subjected to an imposed time-periodic forcing. The axisymmetric and inviscid wavefield is governed by a linear elliptic boundary value problem with mixed boundary conditions, wherein the no-penetration boundary condition is satisfied under the disc while the free surface boundary conditions are enforced away from it. The problem is solved by recasting the system of partial differential equations as a second-kind Fredholm integral equation which is then solved numerically. The solution furnishes a prediction for the dependence of the disc's oscillation amplitude on the forcing frequency, which exhibits good agreement with experiments. We interpret our results physically by computing the added mass, wave damping and effective spring coefficients of the disc, both numerically for a range of forcing frequencies and analytically in the low-frequency limit.

physics.flu-dyn↗