|Introduction to Sonochemistry|
The chemical effects of acoustic cavitation were first noticed in the 1930's but the process was essentially untouched until the mid 1980's. At this time inexpensive ultrasound equipment became commonplace and the process was rediscovered with various applications explored (Suslick et al. 2000). With the discovery of single bubble sonoluminescence (SBSL) in 1990 (Gaitan et al. 1990) many researchers rushed to explain this fascinating phenomenon of turning sound into light through a single micron sized bubble. SBSL provided a technique for isolating a single, stable acoustically forced cavitation bubble that was undergoing many of the same processes as the bubbles in sonochemistry. This growth in SBSL research activity led to theoretical investigations of the behavior of the gas in the interior of strongly forced bubbles (Brenner et al. 2001). While theory and experiments have converged on a consistent understanding of single bubble behavior, little is understood about the true multi-bubble SC process and there are at best only vague connections between theory and experimental reality (Mason 1999).
Applications of sonochemistry (SC)
Typically the bubbles in SC are driven below their natural frequency at high pressure amplitudes; the bubbles undergo slow expansions and rapid, catastrophic collapses. The bubble compression is so violent that the gas in the bubble has been estimated (through computations and experiments) to reach ~5,000-8,000 Kelvin and >10,000 atmospheres on a nanosecond time scale. This intense local heating can drive significant gas phase chemical reactions which are important in a variety of applications.
One interesting application is the manufacture of protein micro-spheres. Proteins are dissolved in a liquid which is then irradiated with intense ultrasound to induce acoustic cavitation. When the bubbles are heated during the rapid collapse, water vapor in the bubble is dissociated into OH radicals. These radicals cause the protein molecules to cross link and a solid, spherical, protein shell is formed where the bubble once existed. The shells can be manufactured filled with liquid or gas; liquid filled spheres can be used for targeted or time released drug delivery and air-filled spheres are used as echo contrast agents in medical ultrasound (Suslick et al. 1999).
Due to the rapid heating and cooling rates inside the bubble, SC is also useful for making amorphous nano-phase particles. These nano-particles can be useful as catalysts and have other unusual magnetic and electric properties (Suslick et al. 1999). Other applications of SC involve the overall degradation of organic species in contaminated water (Mason 1999). The remediation concept has been successfully tested using jet cavitation (Kalumuck 2001).
There are potential bio-medical applications of SC; sonodynamic therapy is a medical procedure that destroys tumor cells with ultrasound. Cavitation in the tissue promotes chemical reactions which activate certain drugs (sonosensitizers) that locally destroy tumor cells through focused ultrasound (Umemura et al. 1996). In shockwave lithotripsy (the destruction of kidney stones with focused shocks), bubbles grow to very large sizes due to a long negative pressure tail which follows an initial shockwave. The bubbles subsequently undergo a free collapse, producing chemical reactions where the effect of the reactions on healthy tissue is unknown (Matula et al. 2001).
Current physical understanding
To orient the reader, typical radial dynamics for a gas bubble responding to a periodic sinusoidal forcing are shown in Figure 1: the non-linear growth and collapse is quite clear.
Most of the chemical action occurs in the first dramatic collapse when there is significant compression heating of the gas. The general dynamics of the bubble are a result of conservation of liquid momentum and can be captured with the well know Rayleigh-Plesset equation. The Rayleigh-Plesset equation is simply a reduction of the Navier-Stokes equations for an incompressible liquid surrounding a spherical bubble to a single ordinary differential equation (Prosperetti et al. 1988).
As the bubble volume oscillates with this periodic cycle, vapor evaporates and condenses in order to maintain a constant vapor pressure. The fraction of vapor in the bubble is high when the bubble is expanded (and the gas pressure is much lower than the vapor pressure) and much lower when the gas pressure is high at collapse. The amount of vapor during an acoustic cycle is shown in Figure 2; corresponding to the same parameters as Figure 1 (Storey & Szeri 2000).
The vapor is close to phase equilibrium (constant vapor pressure) during much of the cycle, though significant departure is found at the main collapse. Typically, the collapse becomes so rapid compared to the time it takes water to diffuse through the bubble interior that excess vapor becomes trapped inside. If the finite rate of inter-species gas diffusion in the interior were not taken into account the number of water molecules at the time of collapse would be reduced by several orders of magnitude, while the overall oscillations of Figure 2 would remain unchanged (Storey & Szeri 2000, Toegel et al. 2001, Colussi & Hoffman 1999). As the excess vapor is compressed by the collapse, the contents reach several thousand Kelvin and the trapped vapor is largely dissociated. In the case with water, it is the creation of hydroxyl radicals (OH) from the hot vapor that is often of interest in applications (Mark et al. 1998, Gong & Hart 1998, Storey & Szeri 2001). This trapped vapor significantly quenches the predicted temperature of collapse: >50,000 K when vapor is neglected to ~7,000 K when vapor and chemistry are taken into account (Storey & Szeri 2000).
Heat transfer plays an important role during the bubble collapse as well. When the bubble collapses rapidly with respect to the time that it takes heat to diffuse out of the bubble interior, the gas in the bubble is heated via adiabatic compression. As the bubble accelerates through the collapse, very little heat is lost through the bubble interface in the final collapse stage. Though little heat is lost with respect to the amount stored (a nearly adiabatic process), there is vigorous heat flux for a brief instant and a thin thermal boundary layer forms near the bubble interface. This thermal boundary layer isolates the chemistry to the hot bubble interior, away from the bubble wall (Prosperetti et al. 1988).
This insulating chemical boundary layer is shown as a snapshot in Figure 3; the distribution of OH in the bubble interior at the time the bubble reaches minimum radius. A thin boundary layer is maintained through the collapse and rebound when the OH production at the center reaches a maximum. This boundary layer is important in modeling the flux of chemical species from the bubble to the liquid. In the spherical case the liquid cannot "feel" the OH created at the bubble center through this thin boundary layer (Storey & Szeri 2000).
As the bubble expands on the afterbounce, the OH primarily recombines into stable species. Recombination reactions, however, typically proceed relatively slow resulting in a super-equilibrium (or frozen equilibrium) of OH through the remainder of the cycle. This extra OH will then diffuse to the liquid interface, undergo further reactions at the interface and in the liquid, and be carried away from the bubble. As long as the oscillations are stable, the bubble will create bursts of OH at each collapse which are diffused away across the bubble interface throughout the cycle. The reactions in the liquid are the cause of the useful chemistry in applications and their understanding a major focus of this proposal (Storey & Szeri 2000).
Currently, there are 2 models which are effective for studying the gas dynamics in the interior of collapsing bubbles. One model is direct numerical simulation (DNS), where the complete Navier-Stokes equations for the reactive, diffusive gas mixture are solved computationally (Storey & Szeri 2000). These DNS are too intensive for parameter studies of sonochemistry trends, complex chemical systems, or very strongly forced collapses. The second model is a zero dimensional time dependent "average" model (Storey & Szeri 2001, Toegel et al. 2001, Yasui 1996). While average models are efficient for predicting quantities such as the total production of OH, the interior spatial gradients are completely neglected. These gradients greatly influence the chemical production at the bubble interface and therefore these gradient effects cannot be neglected when studying the problem of reactions at the liquid boundary and interface.
The problem of the pressure distribution in the bubble interior can be more easily understood by the analytical approach outlined by Lin et al. (2001). This approach uses an analytical approximation for the pressure field (simply a version of the unsteady Bernoulli equation) that was found to be very accurate when compared to complete DNS. Figure 4 shows the comparison of the pressure difference in the bubble interior using the analytical expression and the DNS; the agreement is almost perfect. Also, note that there is significant pressure non-uniformity which will have a major impact on the thermal and chemical behavior of the bubble. Using the pressure approximation provides an effective solution of the gas momentum equation.
Direction of future understanding
At the heart of quantitative prediction of sonochemistry is the question, how do the reactive species produced in the gas actually disperse into the liquid? It is the fate of the reactive species (OH in the case described above) in the liquid which is of interest in this proposal since the liquid reactions (not the gas) are the useful reactions for applications. There are two simplified views of chemical dispersal. The first is that the bubble is not spherically symmetric and that the OH created on collapse is fully dispersed into the liquid when the bubble fragments (Colussi & Hoffman 1998, Storey & Szeri 2001). Collapsing bubbles are known to be Rayleigh-Taylor unstable and therefore the assumption is that bubble will shatter and disperse its chemical contents into the liquid. A model based on these ideas has been used by Brennen et al. (2001) in cavitating flows. The second dispersal mechanism is due to continuous deposition from spherically symmetric bubbles. In the symmetric case, OH is created by the collapse then transported across the bubble interface throughout the cycle (Storey & Szeri 2000).
It is these chemical dispersal mechanisms that this proposal will investigate through complete models of radical species production in the gas phase, the transport across the interface into the liquid, subsequent liquid chemical reactions, and potential non-spherical collapses. The research will work towards making the (currently unknown) connection between chemistry in the gas and chemistry in the liquid during SC processing.
The modeling of SC phenomenon described thus far occurs at a single bubble level, however applications involve bubble clouds. Multi-Bubble Sonochemistry (MBSC) is an extremely complex problem where single bubbles in a cloud are behaving (maybe) as described above, but the bubbles are also translating, growing, and interacting with each other. While we are currently unable to fully model MBSC, much can be done to improve the current state of our knowledge. Most of the problems in MBSC modeling revolve around understanding and characterizing multi-bubble fields: little is known about even deceptively simple parameters such as the bubble size distributions. The models created in this proposal will move towards complete, consistent models for cavitation dynamics in Multi-Bubble applications (Parlitz et al. 1999).
Despite the extraordinary problems involved in modeling multi-bubble systems, current state-of-the-art single bubble models do not even have all the relevant physics and chemistry built into them for SC applications. If one is not able to predict chemical output on the single bubble basis, then understanding at the multi-bubble level is surely impossible. The aim of this work is to create accurate single bubble models that can serve as the basis for quantitative MBSC studies. One can think of the single bubble model that is used in a MBSC study to be analogous to a sub-grid scale model used for turbulence modeling.
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