Cavitation
Cavitation in fluid mechanics and engineering normally refers to the phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, called "bubbles" or "voids", collapse and can generate shock waves that may damage machinery. These shock waves are strong when they are very close to the imploded bubble, but rapidly weaken as they propagate away from the implosion. Cavitation is a significant cause of wear in some engineering contexts. Collapsing voids that implode near to a metal surface cause cyclic stress through repeated implosion. This results in surface fatigue of the metal, causing a type of wear also called "cavitation". The most common examples of this kind of wear are to pump impellers, and bends where a sudden change in the direction of liquid occurs. Cavitation is usually divided into two classes of behavior: inertial (or transient) cavitation and non-inertial cavitation.
For other uses, see Cavitation (disambiguation).
The process in which a void or bubble in a liquid rapidly collapses, producing a shock wave, is called inertial cavitation. Inertial cavitation occurs in nature in the strikes of mantis shrimp and pistol shrimp, as well as in the vascular tissues of plants. In manufactured objects, it can occur in control valves, pumps, propellers and impellers.
Non-inertial cavitation is the process in which a bubble in a fluid is forced to oscillate in size or shape due to some form of energy input, such as an acoustic field. The gas in the bubble may contain a portion of a different gas than the vapor phase of the liquid. Such cavitation is often employed in ultrasonic cleaning baths and can also be observed in pumps, propellers, etc.
Since the shock waves formed by collapse of the voids are strong enough to cause significant damage to parts, cavitation is typically an undesirable phenomenon in machinery (although desirable if intentionally used, for example, to sterilize contaminated surgical instruments, break down pollutants in water purification systems, emulsify tissue for cataract surgery or kidney stone lithotripsy, or homogenize fluids). It is very often specifically prevented in the design of machines such as turbines or propellers, and eliminating cavitation is a major field in the study of fluid dynamics. However, it is sometimes useful and does not cause damage when the bubbles collapse away from machinery, such as in supercavitation.
Physics[edit]
Inertial cavitation[edit]
Inertial cavitation was first observed in the late 19th century, considering the collapse of a spherical void within a liquid. When a volume of liquid is subjected to a sufficiently low pressure, it may rupture and form a cavity. This phenomenon is coined cavitation inception and may occur behind the blade of a rapidly rotating propeller or on any surface vibrating in the liquid with sufficient amplitude and acceleration. A fast-flowing river can cause cavitation on rock surfaces, particularly when there is a drop-off, such as on a waterfall.
Vapor gases evaporate into the cavity from the surrounding medium; thus, the cavity is not a vacuum at all, but rather a low-pressure vapor (gas) bubble. Once the conditions which caused the bubble to form are no longer present, such as when the bubble moves downstream, the surrounding liquid begins to implode due its higher pressure, building up momentum as it moves inward. As the bubble finally collapses, the inward momentum of the surrounding liquid causes a sharp increase of pressure and temperature of the vapor within. The bubble eventually collapses to a minute fraction of its original size, at which point the gas within dissipates into the surrounding liquid via a rather violent mechanism which releases a significant amount of energy in the form of an acoustic shock wave and as visible light. At the point of total collapse, the temperature of the vapor within the bubble may be several thousand Kelvin, and the pressure several hundred atmospheres.[1]
The physical process of cavitation inception is similar to boiling. The major difference between the two is the thermodynamic paths that precede the formation of the vapor. Boiling occurs when the local temperature of the liquid reaches the saturation temperature, and further heat is supplied to allow the liquid to sufficiently phase change into a gas. Cavitation inception occurs when the local pressure falls sufficiently far below the saturated vapor pressure, a value given by the tensile strength of the liquid at a certain temperature.[2]
In order for cavitation inception to occur, the cavitation "bubbles" generally need a surface on which they can nucleate. This surface can be provided by the sides of a container, by impurities in the liquid, or by small undissolved microbubbles within the liquid. It is generally accepted that hydrophobic surfaces stabilize small bubbles. These pre-existing bubbles start to grow unbounded when they are exposed to a pressure below the threshold pressure, termed Blake's threshold.[3] The presence of an incompressible core inside a cavitation nucleus substantially lowers the cavitation threshold below the Blake threshold.[4]
The vapor pressure here differs from the meteorological definition of vapor pressure, which describes the partial pressure of water in the atmosphere at some value less than 100% saturation. Vapor pressure as relating to cavitation refers to the vapor pressure in equilibrium conditions and can therefore be more accurately defined as the equilibrium (or saturated) vapor pressure.
Non-inertial cavitation is the process in which small bubbles in a liquid are forced to oscillate in the presence of an acoustic field, when the intensity of the acoustic field is insufficient to cause total bubble collapse. This form of cavitation causes significantly less erosion than inertial cavitation, and is often used for the cleaning of delicate materials, such as silicon wafers.
Other ways of generating cavitation voids involve the local deposition of energy, such as an intense focused laser pulse (optic cavitation) or with an electrical discharge through a spark. These techniques have been used to study the evolution of the bubble that is actually created by locally boiling the liquid with a local increment of temperature.
Hydrodynamic cavitation[edit]
Hydrodynamic cavitation is the process of vaporisation, bubble generation and bubble implosion which occurs in a flowing liquid as a result of a decrease and subsequent increase in local pressure. Cavitation will only occur if the local pressure declines to some point below the saturated vapor pressure of the liquid and subsequent recovery above the vapor pressure. If the recovery pressure is not above the vapor pressure then flashing is said to have occurred. In pipe systems, cavitation typically occurs either as the result of an increase in the kinetic energy (through an area constriction) or an increase in the pipe elevation.
Hydrodynamic cavitation can be produced by passing a liquid through a constricted channel at a specific flow velocity or by mechanical rotation of an object through a liquid. In the case of the constricted channel and based on the specific (or unique) geometry of the system, the combination of pressure and kinetic energy can create the hydrodynamic cavitation cavern downstream of the local constriction generating high energy cavitation bubbles.
Based on the thermodynamic phase change diagram, an increase in temperature could initiate a known phase change mechanism known as boiling. However, a decrease in static pressure could also help one pass the multi-phase diagram and initiate another phase change mechanism known as cavitation. On the other hand, a local increase in flow velocity could lead to a static pressure drop to the critical point at which cavitation could be initiated (based on Bernoulli's principle). The critical pressure point is vapor saturated pressure. In a closed fluidic system where no flow leakage is detected, a decrease in cross-sectional area would lead to velocity increment and hence static pressure drop. This is the working principle of many hydrodynamic cavitation based reactors for different applications such as water treatment, energy harvesting, heat transfer enhancement, food processing, etc.[5]
There are different flow patterns detected as a cavitation flow progresses: inception, developed flow, supercavitation, and choked flow. Inception is the first moment that the second phase (gas phase) appears in the system. This is the weakest cavitating flow captured in a system corresponding to the highest cavitation number. When the cavities grow and becomes larger in size in the orifice or venturi structures, developed flow is recorded. The most intense cavitating flow is known as supercavitation where theoretically all the nozzle area of an orifice is filled with gas bubbles. This flow regime corresponds to the lowest cavitation number in a system. After supercavitation, the system is not capable of passing more flow. Hence, velocity does not change while the upstream pressure increase. This would lead to an increase in cavitation number which shows that choked flow occurred.[6]
The process of bubble generation, and the subsequent growth and collapse of the cavitation bubbles, results in very high energy densities and in very high local temperatures and local pressures at the surface of the bubbles for a very short time. The overall liquid medium environment, therefore, remains at ambient conditions. When uncontrolled, cavitation is damaging; by controlling the flow of the cavitation, however, the power can be harnessed and non-destructive. Controlled cavitation can be used to enhance chemical reactions or propagate certain unexpected reactions because free radicals are generated in the process due to disassociation of vapors trapped in the cavitating bubbles.[7]
Orifices and venturi are reported to be widely used for generating cavitation. A venturi has an inherent advantage over an orifice because of its smooth converging and diverging sections, such that it can generate a higher flow velocity at the throat for a given pressure drop across it. On the other hand, an orifice has an advantage that it can accommodate a greater number of holes (larger perimeter of holes) in a given cross sectional area of the pipe.[8]
The cavitation phenomenon can be controlled to enhance the performance of high-speed marine vessels and projectiles, as well as in material processing technologies, in medicine, etc. Controlling the cavitating flows in liquids can be achieved only by advancing the mathematical foundation of the cavitation processes. These processes are manifested in different ways, the most common ones and promising for control being bubble cavitation and supercavitation. The first exact classical solution should perhaps be credited to the well-known solution by Hermann von Helmholtz in 1868.[9] The earliest distinguished studies of academic type on the theory of a cavitating flow with free boundaries and supercavitation were published in the book Jets, wakes and cavities[10] followed by Theory of jets of ideal fluid.[11] Widely used in these books was the well-developed theory of conformal mappings of functions of a complex variable, allowing one to derive a large number of exact solutions of plane problems. Another venue combining the existing exact solutions with approximated and heuristic models was explored in the work Hydrodynamics of Flows with Free Boundaries[12] that refined the applied calculation techniques based on the principle of cavity expansion independence, theory of pulsations and stability of elongated axisymmetric cavities, etc.[13] and in Dimensionality and similarity methods in the problems of the hydromechanics of vessels.[14]
A natural continuation of these studies was recently presented in The Hydrodynamics of Cavitating Flows[15] – an encyclopedic work encompassing all the best advances in this domain for the last three decades, and blending the classical methods of mathematical research with the modern capabilities of computer technologies. These include elaboration of nonlinear numerical methods of solving 3D cavitation problems, refinement of the known plane linear theories, development of asymptotic theories of axisymmetric and nearly axisymmetric flows, etc. As compared to the classical approaches, the new trend is characterized by expansion of the theory into the 3D flows. It also reflects a certain correlation with current works of an applied character on the hydrodynamics of supercavitating bodies.
Hydrodynamic cavitation can also improve some industrial processes. For instance, cavitated corn slurry shows higher yields in ethanol production compared to uncavitated corn slurry in dry milling facilities.[16]
This is also used in the mineralization of bio-refractory compounds which otherwise would need extremely high temperature and pressure conditions since free radicals are generated in the process due to the dissociation of vapors trapped in the cavitating bubbles, which results in either the intensification of the chemical reaction or may even result in the propagation of certain reactions not possible under otherwise ambient conditions.[17]
Acoustic cavitation and ultrasonic cavitation[edit]
Inertial cavitation can also occur in the presence of an acoustic field. Microscopic gas bubbles that are generally present in a liquid will be forced to oscillate due to an applied acoustic field. If the acoustic intensity is sufficiently high, the bubbles will first grow in size and then rapidly collapse. Hence, inertial cavitation can occur even if the rarefaction in the liquid is insufficient for a Rayleigh-like void to occur.
Ultrasonic cavitation inception will occur when the acceleration of the ultrasound source is enough to produce the needed pressure drop. This pressure drop depends on the value of the acceleration and the size of the affected volume by the pressure wave. The dimensionless number that predicts ultrasonic cavitation is the Garcia-Atance number. High power ultrasonic horns produce accelerations high enough to create a cavitating region that can be used for homogenization, dispersion, deagglomeration, erosion, cleaning, milling, emulsification, extraction, disintegration, and sonochemistry.
Applications[edit]
Chemical engineering[edit]
In industry, cavitation is often used to homogenize, or mix and break down, suspended particles in a colloidal liquid compound such as paint mixtures or milk. Many industrial mixing machines are based upon this design principle. It is usually achieved through impeller design or by forcing the mixture through an annular opening that has a narrow entrance orifice with a much larger exit orifice. In the latter case, the drastic decrease in pressure as the liquid accelerates into a larger volume induces cavitation. This method can be controlled with hydraulic devices that control inlet orifice size, allowing for dynamic adjustment during the process, or modification for different substances. The surface of this type of mixing valve, against which surface the cavitation bubbles are driven causing their implosion, undergoes tremendous mechanical and thermal localized stress; they are therefore often constructed of extremely strong and hard materials such as stainless steel, Stellite, or even polycrystalline diamond (PCD).
Cavitating water purification devices have also been designed, in which the extreme conditions of cavitation can break down pollutants and organic molecules. Spectral analysis of light emitted in sonochemical reactions reveal chemical and plasma-based mechanisms of energy transfer. The light emitted from cavitation bubbles is termed sonoluminescence.
Use of this technology has been tried successfully in alkali refining of vegetable oils.[18]
Hydrophobic chemicals are attracted underwater by cavitation as the pressure difference between the bubbles and the liquid water forces them to join. This effect may assist in protein folding.[19]
Biomedical[edit]
Cavitation plays an important role for the destruction of kidney stones in shock wave lithotripsy.[20] Currently, tests are being conducted as to whether cavitation can be used to transfer large molecules into biological cells (sonoporation). Nitrogen cavitation is a method used in research to lyse cell membranes while leaving organelles intact.
Cavitation plays a key role in non-thermal, non-invasive fractionation of tissue for treatment of a variety of diseases[21] and can be used to open the blood-brain barrier to increase uptake of neurological drugs in the brain.[22]
Cavitation also plays a role in HIFU, a thermal non-invasive treatment methodology for cancer.[23]
In wounds caused by high velocity impacts (like for example bullet wounds) there are also effects due to cavitation. The exact wounding mechanisms are not completely understood yet as there is temporary cavitation, and permanent cavitation together with crushing, tearing and stretching. Also the high variance in density within the body makes it hard to determine its effects.[24]
Ultrasound sometimes is used to increase bone formation, for instance in post-surgical applications.[25]
It has been suggested that the sound of "cracking" knuckles derives from the collapse of cavitation in the synovial fluid within the joint.[26]
Cavitation can also form Ozone micro-nanobubbles which shows promise in dental applications.[27]
Cleaning[edit]
In industrial cleaning applications, cavitation has sufficient power to overcome the particle-to-substrate adhesion forces, loosening contaminants. The threshold pressure required to initiate cavitation is a strong function of the pulse width and the power input. This method works by generating acoustic cavitation in the cleaning fluid, picking up and carrying contaminant particles away in the hope that they do not reattach to the material being cleaned (which is a possibility when the object is immersed, for example in an ultrasonic cleaning bath). The same physical forces that remove contaminants also have the potential to damage the target being cleaned.
In nature[edit]
Geology[edit]
Some hypotheses relating to diamond formation posit a possible role for cavitation—namely cavitation in the kimberlite pipes providing the extreme pressure needed to change pure carbon into the rare allotrope that is diamond. The loudest three sounds ever recorded, during the 1883 eruption of Krakatoa, are now understood as the bursts of three huge cavitation bubbles, each larger than the last, formed in the volcano's throat. Rising magma, filled with dissolved gasses and under immense pressure, encountered a different magma that compressed easily, allowing bubbles to grow and combine.[50][51]
Vascular plants[edit]
Cavitation can occur in the xylem of vascular plants.[52][53] The sap vaporizes locally so that either the vessel elements or tracheids are filled with water vapor. Plants are able to repair cavitated xylem in a number of ways. For plants less than 50 cm tall, root pressure can be sufficient to redissolve the vapor. Larger plants direct solutes into the xylem via ray cells, or in tracheids, via osmosis through bordered pits. Solutes attract water, the pressure rises and vapor can redissolve. In some trees, the sound of the cavitation is audible, particularly in summer, when the rate of evapotranspiration is highest. Some deciduous trees have to shed leaves in the autumn partly because cavitation increases as temperatures decrease.[53]
Spore dispersal in plants[edit]
Cavitation plays a role in the spore dispersal mechanisms of certain plants. In ferns, for example, the fern sporangium acts as a catapult that launches spores into the air. The charging phase of the catapult is driven by water evaporation from the annulus cells, which triggers a pressure decrease. When the compressive pressure reaches approximately 9 MPa, cavitation occurs. This rapid event triggers spore dispersal due to the elastic energy released by the annulus structure. The initial spore acceleration is extremely large – up to 105 times the gravitational acceleration.[54]
Marine life[edit]
Just as cavitation bubbles form on a fast-spinning boat propeller, they may also form on the tails and fins of aquatic animals. This primarily occurs near the surface of the ocean, where the ambient water pressure is low.
Cavitation may limit the maximum swimming speed of powerful swimming animals like dolphins and tuna.[55] Dolphins may have to restrict their speed because collapsing cavitation bubbles on their tail are painful. Tuna have bony fins without nerve endings and do not feel pain from cavitation. They are slowed down when cavitation bubbles create a vapor film around their fins. Lesions have been found on tuna that are consistent with cavitation damage.[56]
Some sea animals have found ways to use cavitation to their advantage when hunting prey. The pistol shrimp snaps a specialized claw to create cavitation, which can kill small fish. The mantis shrimp (of the smasher variety) uses cavitation as well in order to stun, smash open, or kill the shellfish that it feasts upon.[57]
Thresher sharks use 'tail slaps' to debilitate their small fish prey and cavitation bubbles have been seen rising from the apex of the tail arc.[58][59]
Coastal erosion[edit]
In the last half-decade, coastal erosion in the form of inertial cavitation has been generally accepted.[60] Bubbles in an incoming wave are forced into cracks in the cliff being eroded. Varying pressure decompresses some vapor pockets which subsequently implode. The resulting pressure peaks can blast apart fractions of the rock.