An official website of the United States government
Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. The traditional variable time-step scheme for the full form RP equation is difficult to be integrated with the CFD program since it requires a tiny time step at the singularity point for convergence and this step size may be incompatible with time marching of conservation equations. This paper presents two stable and efficient numerical solution schemes based on the finite difference method and Euler method so that the full-form RP equation can be better accepted by the CFD program. By employing a truncation bubble radius to approximate the minimum bubble size in the collapse stage, the proposed schemes solve for the bubble radius and wall velocity in an explicit way. The proposed solution schemes are more robust for a wide range of ambient pressure profiles than the traditional schemes and avoid excessive refinement on the time step at the singularity point. Since the proposed solution scheme can calculate the effects of the second-order term, liquid viscosity, and surface tension on the bubble evolution, it provides a more accurate estimation of the wall velocity for the vaporization or condensation rate, which is widely used in the cavitation model in the CFD simulation. The legitimacy of the solution schemes is manifested by the agreement between the results from these schemes and established ones from the literature. The proposed solution schemes are more robust in face of a wide range of ambient pressure profiles.
more »
« less
Cavitation in a soft porous material
Abstract We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh–Plesset equation to bubbles in soft porous media. The extended Rayleigh–Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.
more »
« less
- Award ID(s):
- 1805817
- PAR ID:
- 10370802
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- PNAS Nexus
- Volume:
- 1
- Issue:
- 4
- ISSN:
- 2752-6542
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)The fluid dynamics of a bubble collapsing near an elastic or viscoelastic material is coupled with the mechanical response of the material. We apply a multiphase fluid–solid coupled computational model to simulate the collapse of an air bubble in water induced by an ultrasound shock wave, near different types of materials including metals (e.g. aluminium), polymers (e.g. polyurea), minerals (e.g. gypsum), glass and foams. We characterize the two-way fluid–material interaction by examining the fluid pressure and velocity fields, the time history of bubble shape and volume and the maximum tensile and shear stresses produced in the material. We show that the ratio of the longitudinal acoustic impedance of the material compared to that of the ambient fluid, $$Z/Z_0$$ , plays a significant role. When $$Z/Z_0<1$$ , the material reflects the compressive front of the incident shock into a tensile wave. The reflected tensile wave impinges on the bubble and decelerates its collapse. As a result, the collapse produces a liquid jet, but not necessarily a shock wave. When $$Z/Z_0>1$$ , the reflected wave is compressive and accelerates the bubble's collapse, leading to the emission of a shock wave whose amplitude increases linearly with $$\log (Z/Z_0)$$ , and can be much higher than the amplitude of the incident shock. The reflection of this emitted shock wave impinges on the bubble during its rebound. It reduces the speed of the bubble's rebound and the velocity of the liquid jet. Furthermore, we show that, for a set of materials with $$Z/Z_0\in [0.04, 10.8]$$ , the effect of acoustic impedance on the bubble's collapse time and minimum volume can be captured using phenomenological models constructed based on the solution of Rayleigh–Plesset equation.more » « less
-
Natural convection in porous media is a fundamental process for the long-term storage of CO 2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number ( $Ra$ ) for high values of $Ra$ ( $$Ra\gg 1300$$ ). Here, we perform direct numerical simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto-plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.more » « less
-
Abstract Laser-Induced Forward Transfer (LIFT) printing is a highresolution, non-contact, laser-based direct-writing technology suitable for various materials. The LIFT process is limited by its one-to-one correspondence between laser pulses and jet formation, which restricts the printing throughput and complicates scaling for high-speed operations. To address this challenge, we propose a novel strategy to integrate a porous structure below the donor slide in the LIFT system. The porous structure is expected to facilitate the formation of multiple jets from a single laser pulse, thereby overcoming traditional throughput limitations. In this study, we developed a computational fluid dynamics (CFD) model to verify the proposed idea. The findings confirmed that the formation of multiple jets induced by a single laser pulse can be achieved by manipulating the dynamics of bubble expansion within the porous structures. The simulations also demonstrated that variations in the size, spacing, and positioning of the porous structures, along with the initial bubble pressure, can significantly influence jet characteristics. This enables precise control over jet width and length, suggesting a viable approach to achieving high-throughput, high-efficiency LIFT printing through the deployment of porous structures.more » « less
-
Accurate determination of high strain rate (>103 1/s) constitutive properties of soft materials remains a formidable challenge. Albeit recent advancements among experimental techniques, in particular inertial microcavitation rheometry (IMR), the intrinsic requirement to visualize the bubble cavitation dynamics has limited its application to nominally transparent materials. Here, in an effort to address this challenge and to expand the experimental capability of IMR to optically opaque materials, we investigated whether one could use the acoustic signature of the time interval between the bubble's maximum radius and first collapse time point, characterized as the bubble collapse time, to infer the viscoelastic material properties without being able to image the bubble directly in the tissue. By introducing a modified Rayleigh collapse time for soft materials, which is strongly dependent on the stiffness of the material at hand, we show that, in principle, one can obtain an order of magnitude or better estimate of the viscoelastic material properties of the soft material under investigation. Using a newly developed energy-based theoretical framework, we show that for materials stiffer than 10 kPa the bubble collapse time during a single bubble cavitation event can provide quantitative and meaningful information about the constitutive properties of the material at hand. For very soft materials (i.e., shear modulus less than 10 kPa), our theory shows that unless the collapse time measurement has very high precision and low uncertainties, the material property estimates based on the bubble collapse time only will not be accurate and require visual resolution of the full cavitation kinematics.more » « less
