**3.1 Laser-induced generation of micro-bubbles in a free water**

Formation of micro-bubbles in a free water was studied with the aid of the optical methods using a water filled plastic cell (the horizontal dimensions are 150 × 100 mm and the height is 15 mm) and glass capillaries with an inner diameter of 1 mm. In the most of experiments, the working fiber tip is preliminary blackened by a short (~1 s) contact of the fiber tip with a wooden plate at a laser power of about 3 W. The fiber tip surface thus covers by a thin carbon layer owing to the wood burning. Such a procedure is well reproduced, so that from 10 to 20% of the laser power is absorbed in the thin carbon layer. Computer controlled fiber lasers (LS-0.97 and LS-1.55 of IRE–Polus, Russia) with the wavelengths of 0.97 μm and 1.55 μm, 1–10 W in power were interfaced with a 400 μm core diameter silica fiber. Low intensity (up to 1 mW) green pilot beam from the built in diode laser was used to highlight the laser irradiated zone in the cell. The fiber is horizontally fixed in the cell, which is placed on the worktable of a MICROS MC300 microscope equipped with a Vision digital color camera interfaced with PC. The water cell was also placed on the table with illumination, and the processes in the vicinity of the heated fiber tip were visualized using a Photron Fastcam SA-3 camera at rates of 2000 or 10000 frames per second. To control the laser induced spectrum, an Ocean Optics USB4000 fiber spectrum analyzer was used, which is interfaced with PC and has an optical resolution of about 1.5 nm and 200–1100 nm wavelength range. For better visualization of hydrodynamic flows the collargol (albumin coated Ag nanoparticles) have been added to water in the cell (Yusupov et al., 2011b).

Hydrodynamic flows taking place nearby the fiber tip when laser power is on, can be clearly seen in a scattering mode using illumination with green light of pilot laser beam through the same transport fiber (Fig. 4). Such flows result in intrusion of collargol from neighboring area into the area in front of the fiber tip. One can also see here the initial process of new intrusion formation (outlined with a dashed line). The rate of rise-up front of a given intrusion (which is about 150 μm in average thickness) is found to be described by exponential low (Yusupov et al., 2011b)

$$V = 0.6 \cdot \exp(-1.5 \cdot r) \,, \tag{1}$$

where *r* is the distance from fiber tip: at 1 mm from fiber tip *V* = 150 μm/s, while at 2 mm from fiber tip *V* falls down to 30 μm/s.

The bubbles don't occur up to laser power of 10 W with non-blackened fiber tip and for 0.97 μm laser radiation, while for 1.56 µm laser radiation (which is much stronger absorbed by water) the bubbles are generated at about 1 W of laser power. Blackening of fiber tip results in generation of bubbles for both 0.97 µm and 1.56 µm laser wavelengths.

We believe that *effective hydrodynamic processes* play dominant role for the effect of a medium power laser-induced regeneration and healing of connective tissues diseases (intervertebral hernia, osteomyelitis and some other diseases) using laser puncture procedures (Chudnovskii & Yusupov, 2008; Chudnovskii et al., 2010a, 2010b). Main features of these

The key process for the mechanism of medium power laser-induced regeneration and healing of musculoskeletal system diseases is the generation of micro-bubbles in inter-tissue

Formation of micro-bubbles in a free water was studied with the aid of the optical methods using a water filled plastic cell (the horizontal dimensions are 150 × 100 mm and the height is 15 mm) and glass capillaries with an inner diameter of 1 mm. In the most of experiments, the working fiber tip is preliminary blackened by a short (~1 s) contact of the fiber tip with a wooden plate at a laser power of about 3 W. The fiber tip surface thus covers by a thin carbon layer owing to the wood burning. Such a procedure is well reproduced, so that from 10 to 20% of the laser power is absorbed in the thin carbon layer. Computer controlled fiber lasers (LS-0.97 and LS-1.55 of IRE–Polus, Russia) with the wavelengths of 0.97 μm and 1.55 μm, 1–10 W in power were interfaced with a 400 μm core diameter silica fiber. Low intensity (up to 1 mW) green pilot beam from the built in diode laser was used to highlight the laser irradiated zone in the cell. The fiber is horizontally fixed in the cell, which is placed on the worktable of a MICROS MC300 microscope equipped with a Vision digital color camera interfaced with PC. The water cell was also placed on the table with illumination, and the processes in the vicinity of the heated fiber tip were visualized using a Photron Fastcam SA-3 camera at rates of 2000 or 10000 frames per second. To control the laser induced spectrum, an Ocean Optics USB4000 fiber spectrum analyzer was used, which is interfaced with PC and has an optical resolution of about 1.5 nm and 200–1100 nm wavelength range. For better visualization of hydrodynamic flows the collargol (albumin coated Ag nanoparticles) have

Hydrodynamic flows taking place nearby the fiber tip when laser power is on, can be clearly seen in a scattering mode using illumination with green light of pilot laser beam through the same transport fiber (Fig. 4). Such flows result in intrusion of collargol from neighboring area into the area in front of the fiber tip. One can also see here the initial process of new intrusion formation (outlined with a dashed line). The rate of rise-up front of a given intrusion (which is about 150 μm in average thickness) is found to be described by

where *r* is the distance from fiber tip: at 1 mm from fiber tip *V* = 150 μm/s, while at 2 mm

The bubbles don't occur up to laser power of 10 W with non-blackened fiber tip and for 0.97 μm laser radiation, while for 1.56 µm laser radiation (which is much stronger absorbed by water) the bubbles are generated at about 1 W of laser power. Blackening of fiber tip results

in generation of bubbles for both 0.97 µm and 1.56 µm laser wavelengths.

*V r* 0.6 exp( 1.5 ) , (1)

processes will be considered below.

water (Yusupov et al., 2010).

**3. Laser-induced generation of micro-bubbles in water** 

**3.1 Laser-induced generation of micro-bubbles in a free water** 

been added to water in the cell (Yusupov et al., 2011b).

exponential low (Yusupov et al., 2011b)

from fiber tip *V* falls down to 30 μm/s.

Fig. 4. Microscope pictures (in scattering mode) of intrusions of Ag nanoparticles in water (outlined with dashed line) stimulated by laser induced hydrodynamics nearby optical fiber tip at 1.0 W of 0.97 µm laser power in 6 s (a), 12 s (b), and 18 s (c) of laser irradiation. Fiber tip is shown by dashed line (Yusupov et al., 2011b).

Energy of incident laser light is partly (10–20%) absorbed by the carbon layer on the blackened fiber, so that the fiber is heated. When laser radiation with a power of greater than 3 W is transmitted by the fiber tip in air, the spectrum of the optical radiation from the fiber tip contains the fundamental line (0.97 µm or 1.56 µm) and the broadband visible and near-IR radiation caused by the heating of the tip surface to relatively high temperatures. When a blackened tip is placed into water, the tip surface is effectively cooled and the absence of the broadband radiation means the substantially lower temperatures of the tip surface. However, a medium power laser radiation (1–5 W) is sufficient for surface heating and generation of vapor-gas bubbles. When water is heated, the dissolved gases are liberated in the vicinity of the tip surface and gas bubbles emerge. Water is evaporated inside the bubbles, so that the bubbles are filled with vapor and, consequently, increase in size. At the lower boundary of the above power interval, the bubbles increase in size residing on the tip surface (Fig. 5a). When a critical size is reached, the bubbles are detached and move to the surface.

Water molecules which approach the heated tip surface acquire additional kinetic energy and momentum. The component of the total momentum of vapor molecules that is directed perpendicularly to the tip surface of the fiber towards water appears insufficient for the detachment of the bubble. Figure 5a shows that the bubbles sizes can be close to the diameter of the silica fiber core (400 µm). In the experiments, the bubbles normally emerge at same spots on a tip surface, which correspond to a high temperature areas. Evidently, the presence of such spots is related to the nonuniformity of the carbon layer: the absorbed energy (and, hence, the temperature) is greater for thicker regions. The stabilization (i.e., the

Laser-Induced Hydrodynamics in Water and Biotissues Nearby Optical Fiber Tip 101

fiber to water (Fig. 5b) and, then, the velocity decreases due to viscosity. At a finite exposure time the tracks of bubbles moving in water was observed. Notice that the track length corresponds to the mean velocity of the bubble over the exposure time. Bright spots in the vicinity of the tip surface (Fig. 5) are related to stray light: the Vision video camera is

The side measurements (Fig. 6a) show that the bubbles come to the surface at a certain distance from the fiber. Knowing the vertical velocity of the bubbles (about 5 mm/s in accordance with visual observations) and the trajectories, we can estimate the horizontal velocity (Fig. 6b). The analysis of the trajectories yields an exponential decrease in the horizontal velocity with increasing distance from the fiber: for the slowest and fastest

respectively, where *V* is the horizontal velocity in mm/s and *r* is the distance from the fiber tip surface in millimeters. The relationships show that the velocity of bubbles at the moment

Fig. 6. a - Side view of the tracks of microbubbles in the vicinity of the blackened optical fiber tip surface in water; b - Plots of the horizontal velocity vs. distance from the end surface for slowest (1) and fastest (2) bubbles at a laser wavelength of 0.97 µm and a power

We have directly observed motion of bubbles even in the immediate vicinity of the surface tip (at the maximum velocities) in the experiments on the generation of microbubbles performed with the aid of the Photron Fastcam SA3. Fig. 7 shows the bubbles as dark circles with different sizes. Previous (at time step *Δt*) positions and sizes are shown as open circles, and the trajectories are shown as rectilinear segments. Table 1 presents the calculated sizes and velocities of the bubbles shown in Fig. 7. It is seen that the bubble with a diameter of 47 μm (bubble 7 in Fig. 7a and Table 1), which is initially located at a distance of about 100 μm from the fiber tip, moves at a mean velocity of 97 mm/s over the

of the detachment from the fiber tip (*r* = 0) ranges from 67 to 101 mm/s.

*V r* 67 exp( 0,82 ) (4)

*V r* 101 exp( 0,74 ) , (5)

sensitive to the near-IR laser radiation.

of 5 W (Yusupov et al., 2010).

observation interval (4.4 ms).

and

bubbles, we obtain the dependences(Yusupov et al, 2010)

Fig. 5. Laser-induced generation of microbubbles in the vicinity of the blackened end surface of the optical fiber in water for the laser radiation with a wavelength of 0.97 µm and a power of (a) 1 and (b) 5 W. The photograph is taken from above at an exposure time of 250 ms.

attachment of the vapor-gas bubbles to the high temperature spots) can be caused by two reasons. First, the temperature at the hot spot additionally increases owing to the formation of the bubble and the consequent decrease in the local heat sink to water. The second reason is related to the Marangoni effect (Berry et al., 2000): the temperature gradient gives rise to the gradient of surface tension, so that convective flows emerge on the surface of the bubble and cause the force that presses the bubble to the hot spot. The experiments on the growth of the bubbles in the vicinity of the tip surface show that the rate of growth gradually decreases and, finally, the growth is terminated. At a laser power of 1 W, the duration of a relatively fast growth is about 200 ms. Bubble size increases at this stage from zero to 25% of the maximum size. Then, over a few seconds, the growth is well described with the formula (Yusupov et al, 2010):

$$D \propto t^{4/5}\,,$$

where *D* is the diameter of bubble and *t* is time. When laser light is terminated (Fig. 5a), the size of bubble gradually decreases (the bubble remains attached to the tip surface of the fiber) and, finally, the bubble vanishes. Note that a decrease in the size is also nonmonotonic. At the first stage with a duration of less than 1 s, the diameter decreases by 8– 10%. Then, the slowing takes place. Such a non-monotonic behavior must be related to the fact that the size of bubble decreases at the first stage predominantly, due to a decrease in the temperature of the vapor-gas mixture inside the bubble to the temperature of water in the cell, whereas the second stage is isothermal. The lifetime of such bubbles ranges from 3 to 8 h, and the rate of a decrease in the diameter with time always monotonically increases. At the second stage, the dependence of the diameter on time is well approximated with the formula(Yusupov et al., 2010):

$$D = D\_0 \cdot (1 - t \;/\; \tau\_0)^{\alpha} \; , \tag{3}$$

where *D0* is the initial diameter, τ0 is the lifetime, and *α* = 0.1–0.5 is the empirical parameter. Note a similar decrease in the diameter with time at *α* = 0.5 in (Taylor & Hnatovsky, 2004). A qualitatively different scenario corresponds to higher laser powers. The explosive boiling of water is observed in the vicinity of the hot end: the vapor-gas bubbles are ejected from the fiber to water (Fig. 5b) and, then, the velocity decreases due to viscosity. At a finite exposure time the tracks of bubbles moving in water was observed. Notice that the track length corresponds to the mean velocity of the bubble over the exposure time. Bright spots in the vicinity of the tip surface (Fig. 5) are related to stray light: the Vision video camera is sensitive to the near-IR laser radiation.

The side measurements (Fig. 6a) show that the bubbles come to the surface at a certain distance from the fiber. Knowing the vertical velocity of the bubbles (about 5 mm/s in accordance with visual observations) and the trajectories, we can estimate the horizontal velocity (Fig. 6b). The analysis of the trajectories yields an exponential decrease in the horizontal velocity with increasing distance from the fiber: for the slowest and fastest bubbles, we obtain the dependences(Yusupov et al, 2010)

$$V = 67 \cdot \exp(-0.82 \cdot r) \tag{4}$$

and

100 Hydrodynamics – Advanced Topics

Fig. 5. Laser-induced generation of microbubbles in the vicinity of the blackened end surface of the optical fiber in water for the laser radiation with a wavelength of 0.97 µm and a power of (a) 1 and (b) 5 W. The photograph is taken from above at an exposure time of 250 ms.

attachment of the vapor-gas bubbles to the high temperature spots) can be caused by two reasons. First, the temperature at the hot spot additionally increases owing to the formation of the bubble and the consequent decrease in the local heat sink to water. The second reason is related to the Marangoni effect (Berry et al., 2000): the temperature gradient gives rise to the gradient of surface tension, so that convective flows emerge on the surface of the bubble and cause the force that presses the bubble to the hot spot. The experiments on the growth of the bubbles in the vicinity of the tip surface show that the rate of growth gradually decreases and, finally, the growth is terminated. At a laser power of 1 W, the duration of a relatively fast growth is about 200 ms. Bubble size increases at this stage from zero to 25% of the maximum size. Then, over a few seconds, the growth is well described with the formula

where *D* is the diameter of bubble and *t* is time. When laser light is terminated (Fig. 5a), the size of bubble gradually decreases (the bubble remains attached to the tip surface of the fiber) and, finally, the bubble vanishes. Note that a decrease in the size is also nonmonotonic. At the first stage with a duration of less than 1 s, the diameter decreases by 8– 10%. Then, the slowing takes place. Such a non-monotonic behavior must be related to the fact that the size of bubble decreases at the first stage predominantly, due to a decrease in the temperature of the vapor-gas mixture inside the bubble to the temperature of water in the cell, whereas the second stage is isothermal. The lifetime of such bubbles ranges from 3 to 8 h, and the rate of a decrease in the diameter with time always monotonically increases. At the second stage, the dependence of the diameter on time is well approximated with the

0 0 (1 / )

where *D0* is the initial diameter, τ0 is the lifetime, and *α* = 0.1–0.5 is the empirical parameter. Note a similar decrease in the diameter with time at *α* = 0.5 in (Taylor & Hnatovsky, 2004). A qualitatively different scenario corresponds to higher laser powers. The explosive boiling of water is observed in the vicinity of the hot end: the vapor-gas bubbles are ejected from the

*DD t*

4/5 *D t* , (2)

, (3)

(Yusupov et al, 2010):

formula(Yusupov et al., 2010):

$$V = 101 \cdot \exp(-0.74 \cdot r) \,, \tag{5}$$

respectively, where *V* is the horizontal velocity in mm/s and *r* is the distance from the fiber tip surface in millimeters. The relationships show that the velocity of bubbles at the moment of the detachment from the fiber tip (*r* = 0) ranges from 67 to 101 mm/s.

Fig. 6. a - Side view of the tracks of microbubbles in the vicinity of the blackened optical fiber tip surface in water; b - Plots of the horizontal velocity vs. distance from the end surface for slowest (1) and fastest (2) bubbles at a laser wavelength of 0.97 µm and a power of 5 W (Yusupov et al., 2010).

We have directly observed motion of bubbles even in the immediate vicinity of the surface tip (at the maximum velocities) in the experiments on the generation of microbubbles performed with the aid of the Photron Fastcam SA3. Fig. 7 shows the bubbles as dark circles with different sizes. Previous (at time step *Δt*) positions and sizes are shown as open circles, and the trajectories are shown as rectilinear segments. Table 1 presents the calculated sizes and velocities of the bubbles shown in Fig. 7. It is seen that the bubble with a diameter of 47 μm (bubble 7 in Fig. 7a and Table 1), which is initially located at a distance of about 100 μm from the fiber tip, moves at a mean velocity of 97 mm/s over the observation interval (4.4 ms).

Laser-Induced Hydrodynamics in Water and Biotissues Nearby Optical Fiber Tip 103

Figure 7b and Table 1 show that a short laser pulse with power of 6 W causes generation of many bubbles, whose diameters range from 10 to 41 μm. The velocities of bubbles are 60 and 20 mm/s in the vicinity of the fiber and at a distance of 300 and 800 µm, respectively. In spite of a twofold increase in the laser power, the maximum velocities of the bubbles in the vicinity of the fiber under the pulsed irradiation are significantly less than the velocities corresponding to the continuous wave irradiation. At a relatively large distance from the fiber end, the velocities corresponding to the pulsed irradiation are also less than the velocities corresponding to the continuous wave irradiation: the velocity of bubble 4 in Fig. 7a is almost equal to the velocity of bubble 5 in Fig. 7b, whose distance from the fiber tip is almost two times shorter. Such result indicates to the presence of water flows in the case of the continuous wave laser irradiation and shows that the flow velocity is comparable with

 Such liquid flows are more clearly observed in the microscopic measurements of the laserinduced hydrodynamic effects in the vicinity of the fiber tip surface of the fiber that is

Liquid flows are more clearly observed in the microscopic measurements of the laserinduced hydrodynamic effects in the vicinity of the fiber tip surface of the laser fiber that is

As it follows from Fig. 8, the attached vapor-gas bubbles at a laser power of 1–2 W emerge at the tip surface and the convective motion is observed in the liquid. A qualitatively different scenario corresponds to a power of 3 W: the microscopic bubbles ejected from the fiber tip move along arc shaped trajectories and entrain liquid flows (Fig. 8a). The intensity of the resulting vortices rapidly increases with increasing radiation power (Fig. 8b). In accordance with the estimations based on the frame-to-frame analysis of the video records, the period of the typical circulating liquid flows at laser powers of 3– 5 W ranges from 0.2 to 1 s. Note that the above effects can be observed in the experiments with the blackened fiber tip at both laser wavelengths (0.97 µm and 1.55 μm). In the absence of the preliminary blackening, the effects are observed only for a radiation wavelength of 1.55 μm. Such a difference is caused by the fact that the radiation with a wavelength of 1.55 μm (unlike the short wavelength

Fig. 8. Water flows that actively circulate inside the glass capillary (with a diameter of 1 mm) in the vicinity of the blackened tip surface I heated by the laser radiation with a wavelength

**3.2 Laser-induced generation of micro-bubbles in a glass capillary** 

placed in the glass capillary filled with water (model of the laser channel).

the mean velocity of bubbles.

placed in a glass capillary filled with water.

of 0.97 µm and a power of 3 W (a) and 5 W (b)

Closed circles 1–7 show positions of bubbles, open circles show previous positions, and rectilinear segments show bubbles trajectories.

The images are taken from above at rates of (a) 10000 and (b) 2000 frames per second.

Laser powers of (a) 3 and (b) 6 W, time intervals *Δt* = (a) 4.4 and (b) 2.0 ms, and a laser wavelength of 0.97 µm.

The pulse duration is 50 ms and the interval between pulses is 500 ms.

Fig. 7. Displacements of microbubbles (that are generated in the vicinity of the schematically shown blackened tip surface of quartz fiber **I**) over short time intervals *Δt* in the presence of laser radiation (Yusupov et al., 2010). **a** - CW laser radiation. **b** - Pulsed laser radiation.

Such result is in good agreement with the above estimations of the initial velocities in the vicinity of the fiber tip. The velocities of the bubbles rises rapidly with increasing distance from the fiber: the velocities are not higher than 50 and 20 mm/s at distances of 0.5 mm and 2 mm, respectively (Table 1). When bubbles are generated in a viscous liquid over a relatively long time interval the steady-state flow results in increase of the bubbles velocities. To determine the relative contribution of such a flow, we have measured the motion of microbubbles under the pulsed laser irradiation (Fig. 7b). It is seen that the bubbles predominantly move at relatively large angles relative to the fiber axis. That is caused by the features of the tip surface and hydrodynamic effects. Note that the asymmetry also corresponds to the motion of microbubbles under the continuous wave laser irradiation.


Table 1. Parameters of the bubbles shown at Fig. 7

Closed circles 1–7 show positions of bubbles, open circles show previous positions, and rectilinear

Laser powers of (a) 3 and (b) 6 W, time intervals *Δt* = (a) 4.4 and (b) 2.0 ms, and a laser wavelength of

Fig. 7. Displacements of microbubbles (that are generated in the vicinity of the schematically shown blackened tip surface of quartz fiber **I**) over short time intervals *Δt* in the presence of laser radiation (Yusupov et al., 2010). **a** - CW laser radiation. **b** - Pulsed laser radiation.

Such result is in good agreement with the above estimations of the initial velocities in the vicinity of the fiber tip. The velocities of the bubbles rises rapidly with increasing distance from the fiber: the velocities are not higher than 50 and 20 mm/s at distances of 0.5 mm and 2 mm, respectively (Table 1). When bubbles are generated in a viscous liquid over a relatively long time interval the steady-state flow results in increase of the bubbles velocities. To determine the relative contribution of such a flow, we have measured the motion of microbubbles under the pulsed laser irradiation (Fig. 7b). It is seen that the bubbles predominantly move at relatively large angles relative to the fiber axis. That is caused by the features of the tip surface and hydrodynamic effects. Note that the asymmetry also corresponds to the motion of microbubbles under the continuous wave laser irradiation.

Velocity,

1 26 9 17 38 2 26 9 10 37 3 200 3 10 5 4 58 16 41 60 5 42 12 21 20 6 63 48 21 52 7 47 97 27 32

Parameters of radiation

mm/s Diameter, μ<sup>m</sup>

pulsed radiation, 6W (Fig. 7b)

> Velocity, mm/s

The images are taken from above at rates of (a) 10000 and (b) 2000 frames per second.

CW radiation, 3 W (Fig. 7a)

Diameter, μm

Table 1. Parameters of the bubbles shown at Fig. 7

The pulse duration is 50 ms and the interval between pulses is 500 ms.

segments show bubbles trajectories.

0.97 µm.

Number of the bubble (Fig. 7)

Figure 7b and Table 1 show that a short laser pulse with power of 6 W causes generation of many bubbles, whose diameters range from 10 to 41 μm. The velocities of bubbles are 60 and 20 mm/s in the vicinity of the fiber and at a distance of 300 and 800 µm, respectively. In spite of a twofold increase in the laser power, the maximum velocities of the bubbles in the vicinity of the fiber under the pulsed irradiation are significantly less than the velocities corresponding to the continuous wave irradiation. At a relatively large distance from the fiber end, the velocities corresponding to the pulsed irradiation are also less than the velocities corresponding to the continuous wave irradiation: the velocity of bubble 4 in Fig. 7a is almost equal to the velocity of bubble 5 in Fig. 7b, whose distance from the fiber tip is almost two times shorter. Such result indicates to the presence of water flows in the case of the continuous wave laser irradiation and shows that the flow velocity is comparable with the mean velocity of bubbles.

 Such liquid flows are more clearly observed in the microscopic measurements of the laserinduced hydrodynamic effects in the vicinity of the fiber tip surface of the fiber that is placed in a glass capillary filled with water.
