skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Time-dependent motion of a confined bubble in a tube: transition between two steady states
When a confined bubble translates steadily in a cylindrical capillary tube, without the consideration of gravity effects, a uniform thin film of liquid separates the bubble surface and the tube wall. In this work, we investigate how this steady state is established by considering the transitional motion of the bubble as it adjusts its film thickness profile between two steady states, characterized by two different bubble speeds. During the transition, two uniform film regions coexist, separated by a step-like transitional region. The transitional motion also requires modification of the film solution near the rear of the bubble, which depends on the ratio of the two capillary numbers. These theoretical results are verified by experiments and numerical simulations.  more » « less
Award ID(s):
1804863
PAR ID:
10093238
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
857
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Journal of Fluid Mechanics)
    null (Ed.)
    We study bubble motion in a vertical capillary tube under an external flow. Bretherton ( J. Fluid Mech. , vol. 10, issue 2, 1961, pp. 166–188) has shown that, without external flow, a bubble can spontaneously rise when the Bond number ( $${Bo} \equiv \rho g R^2 / \gamma$$ ) is above the critical value $${Bo}_{cr}=0.842$$ , where $$\rho$$ is the liquid density, $$g$$ the gravitational acceleration, $$R$$ the tube radius and $$\gamma$$ the surface tension. It was then shown by Magnini et al. ( Phys. Rev. Fluids , vol. 4, issue 2, 2019, 023601) that the presence of an imposed liquid flow, in the same (upward) direction as buoyancy, accelerates the bubble and thickens the liquid film around it. In this work we carry out a systematic study of the bubble motion under a wide range of upward and downward external flows, focusing on the inertialess regime with Bond numbers above the critical value. We show that a rich variety of bubble dynamics occurs when an external downward flow is applied, opposing the buoyancy-driven rise of the bubble. We reveal the existence of a critical capillary number of the external downward flow ( $${Ca}_l \equiv \mu U_l/\gamma$$ , where $$\mu$$ is the fluid viscosity and $$U_l$$ is the mean liquid speed) at which the bubble arrests and changes its translational direction. Depending on the relative direction of gravity and the external flow, the thickness of the film separating the bubble surface and the tube inner wall follows two distinct solution branches. The results from theory, experiments and numerical simulations confirm the existence of the two solution branches and reveal that the two branches overlap over a finite range of $${Ca}_l$$ , thus suggesting non-unique, history-dependent solutions for the steady-state film thickness under the same external flow conditions. Furthermore, inertialess symmetry-breaking shape profiles at steady state are found as the bubble transits near the tipping points of the solution branches, which are shown in both experiments and three-dimensional numerical simulations. 
    more » « less
  2. ; (, American Society of Mechanical Engineers)
    Abstract Helical blood flow, characterized by its spiral motion, is a crucial physiological phenomenon observed in various circulatory structures, including the heart, aorta, vessel bifurcations, umbilical cord, and respiratory system. Despite its importance, a comprehensive understanding of helical flow dynamics is limited. This study aims to investigate the transition from laminar to turbulent flow in helical tubes under both steady and pulsatile conditions. An experimental setup was developed, featuring a closed-loop system with a pulsatile flow generator and steady pump, producing sinusoidal waveforms with adjustable frequencies and amplitudes. Five helical tube models, varying in curvature radius and torsion, were fabricated with a fixed inner diameter of 15 mm. High-frequency pressure transducers, ultrasonic flow sensors, and Laser Doppler Velocimetry (LDV) were employed to visualize flow fields and measure turbulence kinetic energy (TKE). Results indicate that helical tube geometry significantly impacts turbulence transitions. Specifically, larger curvature radii stabilize the flow and reduce turbulence downstream, while smaller radii lead to earlier transitions to turbulence. Under steady flow conditions, the critical Reynolds number (Re) for turbulence onset was found to be around 2300 upstream, similar to straight pipes, but significantly higher turbulence levels were observed downstream. Pulsatile flow with high pulsatility indices (PI > 3) near transitional Re markedly increases turbulence, particularly downstream, with large bursts of turbulence occurring during the deceleration phase. These findings enhance the understanding of helical flow dynamics and have implications for biomedical device design, diagnostics, and treatments for circulatory disorders. 
    more » « less
  3. ; ; ; ; (, Physics of Fluids)
    Swimming at the microscale has recently garnered substantial attention due to the fundamental biological significance of swimming microorganisms and the wide range of biomedical applications for artificial microswimmers. These microswimmers invariably find themselves surrounded by different confining boundaries, which can impact their locomotion in significant and diverse ways. In this work, we employ a widely used three-sphere swimmer model to investigate the effect of confinement on swimming at low Reynolds numbers. We conduct theoretical analysis via the point-particle approximation and numerical simulations based on the finite element method to examine the motion of the swimmer along the centerline in a capillary tube. The axisymmetric configuration reduces the motion to one-dimensional movement, which allows us to quantify how the degree of confinement affects the propulsion speed in a simple manner. Our results show that the confinement does not significantly affect the propulsion speed until the ratio of the radius of the tube to the radius of the sphere is in the range of O(1)−O(10), where the swimmer undergoes substantial reduction in its propulsion speed as the radius of the tube decreases. We provide some physical insights into how reduced hydrodynamic interactions between moving spheres under confinement may hinder the propulsion of the three-sphere swimmer. We also remark that the reduced propulsion performance stands in stark contrast to the enhanced helical propulsion observed in a capillary tube, highlighting how the manifestation of confinement effects can vary qualitatively depending on the propulsion mechanisms employed by the swimmers. 
    more » « less
  4. ; ; ; (, Soft Matter)
    The displacement of a suspension of particles by an immiscible fluid in a capillary tube or in porous media is a canonical configuration that finds application in a large number of natural and industrial applications, including water purification, dispersion of colloids and microplastics, coating and functionalization of tubings. The influence of particles dispersed in the fluid on the interfacial dynamics and on the properties of the liquid film left behind remain poorly understood. Here, we study the deposition of a coating film on the walls of a capillary tube induced by the translation of a suspension plug pushed by air. We identify the different deposition regimes as a function of the translation speed of the plug, the particle size, and the volume fraction of the suspension. The thickness of the coating film is characterized, and we show that similarly to dip coating, three coating regimes are observed, liquid only, heterogeneous, and thick films. We also show that, at first order, the thickness of films thicker than the particle diameter can be predicted using the effective viscosity of the suspension. Nevertheless, we also report that for large particles and concentrated suspensions, a shear-induced migration mechanism leads to local variations in volume fraction and modifies the deposited film thickness and composition. 
    more » « less
  5. ; (, Journal of Fluid Mechanics)
    We present an experimental study of bubble coalescence at an air–water interface and characterize the evolution of both the underwater neck and the surface bridge. We explore a wide range of Bond number, $Bo$ , which compares gravity and capillary forces and is a dimensionless measure of the free surface's effect on bubble geometry. The nearly spherical $$Bo\ll 1$$ bubbles exhibit the same inertial–capillary growth of the classic underwater dynamics, with limited upper surface displacement. For $Bo>1$ , the bubbles are non-spherical – residing predominantly above the free surface – and, while an inertial–capillary scaling for the underwater neck growth is still observed, the controlling length scale is defined by the curvature of the bubbles near their contact region. With it, an inertial–capillary scaling collapses the neck contours across all Bond numbers to a universal shape. Finally, we characterize the upper surface with a simple oscillatory model which balances capillary forces and the inertia of liquid trapped at the centre of the liquid-film surface. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email