scholarly journals A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field

2016 ◽  
Vol 798 ◽  
pp. 955-969 ◽  
Author(s):  
Lailai Zhu ◽  
François Gallaire
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Symmetric Pair ◽  
Lubrication Film ◽  
Stagnation Points ◽  
Interior Flow ◽  
Hele Shaw Cell

We adopt a boundary integral method to study the dynamics of a translating droplet confined in a Hele-Shaw cell in the Stokes regime. The droplet is driven by the motion of the ambient fluid with the same viscosity. We characterize the three-dimensional (3D) nature of the droplet interface and of the flow field. The interface develops an arc-shaped ridge near the rear-half rim with a protrusion in the rear and a laterally symmetric pair of higher peaks; this pair of protrusions has been identified by recent experiments (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501) and predicted asymptotically (Burgess & Foster, Phys. Fluids A, vol. 2 (7), 1990, pp. 1105–1117). The mean film thickness is well predicted by the extended Bretherton model (Klaseboer et al., Phys. Fluids, vol. 26 (3), 2014, 032107) with fitting parameters. The flow in the streamwise wall-normal middle plane is featured with recirculating zones, which are partitioned by stagnation points closely resembling those of a two-dimensional droplet in a channel. Recirculation is absent in the wall-parallel, unconfined planes, in sharp contrast to the interior flow inside a moving droplet in free space. The preferred orientation of the recirculation results from the anisotropic confinement of the Hele-Shaw cell. On these planes, we identify a dipolar disturbance flow field induced by the travelling droplet and its $1/r^{2}$ spatial decay is confirmed numerically. We pinpoint counter-rotating streamwise vortex structures near the lateral interface of the droplet, further highlighting the complex 3D flow pattern.

scholarly journals A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

2017 ◽  
Vol 836 ◽  
pp. 952-997 ◽  
Author(s):  
Achim Guckenberger ◽  
Stephan Gekle
Keyword(s):  
Drug Delivery ◽  
Integral Equation ◽  
Boundary Integral Equation ◽  
Integral Method ◽  
Three Dimensional ◽  
Formal Proof ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Drug Uptake ◽  
Periodic Domains

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

Energy dissipation and the contact-line region of a spreading bridge

2012 ◽  
Vol 703 ◽  
pp. 111-141 ◽  
Author(s):  
H. B. van Lengerich ◽  
P. H. Steen
Keyword(s):  
Energy Dissipation ◽  
Flow Field ◽  
Contact Line ◽  
Sliding Friction ◽  
Slip Length ◽  
Cox Model ◽  
Hydrophobic Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Line Region

AbstractA drop on a circular support spontaneously spreads upon contact with a substrate. The motion is driven by a loss of surface energy. The loss of recoverable energy can be expressed alternatively as work done at the liquid–gas interface or dissipation through viscosity and sliding friction. In this paper we require consistency with the energy lost by dissipation in order to infer details of the contact-line region through simulations. Simulations with the boundary integral method are used to compute the flow field of a corresponding experiment where polydimethylsiloxane spreads on a relatively hydrophobic surface. The flow field is used to calculate the energy dissipation, from which slip lengths for local slip and Navier slip boundary conditions are found. Velocities, shear rates and pressures along the interface as well as interface shapes in the microscopic region of the contact line are also reported. Angles, slip length and viscous bending length scale allow a test of the Voinov–Hocking–Cox model without free parameters.

Sign in / Sign up

Export Citation Format

Share Document