A unifying Rayleigh-Plesset-type equation for bubbles in viscoelastic media.

Understanding the ultrasound pressure-driven dynamics of microbubbles confined in viscoelastic materials is relevant for multiple biomedical applications, ranging from contrast-enhanced ultrasound imaging to ultrasound-assisted drug delivery. The volumetric oscillations of spherical bubbles are analyzed using the Rayleigh-Plesset equation, which describes the conservation of mass and momentum in the surrounding medium. Several studies have considered an extension of the Rayleigh-Plesset equation for bubbles embedded into viscoelastic media, but these are restricted to a particular choice of constitutive model and/or to small deformations. Here, we derive a unifying equation applicable to bubbles in viscoelastic media with arbitrary complex moduli and that can account for large bubble deformations. To derive this equation, we borrow concepts from finite-strain theory. We validate our approach by comparing the result of our model to previously published results and extend it to show how microbubbles behave in arbitrary viscoelastic materials. In particular, we use our viscoelastic Rayleigh-Plesset model to compute the bubble dynamics in benchmarked viscoelastic liquids and solids.

Universal non-monotonic drainage in large bare viscous bubbles.

Bubbles will rest at the surface of a liquid bath until their spherical cap drains sufficiently to spontaneously rupture. For large film caps, the memory of initial conditions is believed to be erased due to a visco-gravitational flow, whose velocity increases from the top of the bubble to its base. Consequently, the film thickness has been calculated to be relatively uniform as it thins, regardless of whether the drainage is regulated by shear or elongation. Here, we demonstrate that for large bare bubbles, the film thickness is highly nonuniform throughout drainage, spanning orders of magnitude from top to base. We link the film thickness profile to a universal non-monotonic drainage flow that depends on the bubble thinning rate. These results highlight an unexpected coupling between drainage velocity and bubble thickness profiles and provide critical insight needed to understand the retraction and breakup dynamics of these bubbles upon rupture.

A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down.

Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role: The same collapse and wrinkling arise independently of the bubble's orientation. We found that surface tension drives the collapse and initiates a dynamic buckling instability. Because the film weight is irrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible for aerosol production from exhalation events.

Shooting Rubber Bands: Two Self-Similar Retractions for a Stretched Elastic Wedge.

Stretching and shooting rubber bands is a familiar experience for both children and adults, yet the initial dynamics are so quick that they are generally missed. When a cut elastic strip is stretched from its end and suddenly released, the dynamics depend on a balance of stretching and inertia. However, when a rubber band is stretched, a region of high curvature is created and it is unclear how this curvature affects the dynamics. Here, we demonstrate that during the retraction of a circular rubber band, a wavelength develops at the rear which increases in size as time progresses. Through a combination of experiments and modeling, we investigate the speed at which the back of the elastic retracts and observe a self-similar shape that depends on stretching, inertia, and bending. These retraction dynamics illuminate how a rubber band can pass by a thumb when discharged without hitting it.

A simple fluid dynamic model of renal pelvis pressures during ureteroscopic kidney stone treatment.

Ureteroscopy is an endoscopic kidney stone removal procedure which increases the internal pressure in the renal pelvis, the kidney's urinary collecting system. Elevated renal pelvic pressure may result in systemic absorption of irrigation fluid and urine, which can increase the risk of postoperative fever and sepsis. Urologists have investigated the effects of various surgical parameters on the renal pelvic pressure. However, it still remains unknown which surgical parameter has the most dominant effect on the renal pelvic pressure over time. Here we develop a physical model that computes the renal pelvic pressure as a function of time based on parameters that can be varied during ureteroscopy. The model is developed by applying pipe network analysis to the regions of the urinary tract that are involved in a representative ureteroscopic procedure. Our model unifies the findings of the previously published studies on this topic; an ex-vivo porcine study and an in-vivo human study. Furthermore it allows simulation of surgical procedures based on various techniques. Our simulation demonstrates that the two strong regulators of renal pelvis pressure during ureteroscopy are the size of the gap between ureteroscope and ureteral access sheath and the frequency and duration of ureteroscope withdrawal.

Capillary induced twisting of Janus cylinders.

At the appropriate length scales, capillary forces exerted by a liquid in contact with a compliant solid can cause the solid's deformation. Capillary forces are also able to align particles with discrete wettabilities - or Janus particles - at liquid interfaces. Their amphiphilic properties enable Janus particles to orient themselves at liquid interfaces such that both of their surfaces are facing their preferred fluid. However, it is unclear how to spontaneously obtain varying degrees of rotational alignment. Here we extend ideas of elasto-capillarity to modulate rotational alignment by connecting amphiphilic Janus cylinders in an antisymmetric configuration. As the Janus cylinders rotate they cause a twisting deformation of rod. We develop both a mathematical model and a physical macroscale setup to relate the angle of twist to the elastic and interfacial properties, which can be used to tune the extent of alignment of Janus particles at air-water interfaces. We additionally extend our analysis to calculate the twist profile on a compliant element with a distributed capillary torque.