Shadowgraphic imaging was employed to investigate the mid-IR laser induced heat transfer through a double layer thin film. The effect of thin metal coat on the polymer film enhanced the transfer of heat and shock waves due to rapid thermal expansion and the explosive evaporation of the thin fluid layer. Sixty two percent of deposited heat expended for water enthalpy and 38% for other factors. A power of 8.8 kW was launched at the surface of aluminium. The thermal coupling of 45% further reduced the input energy to the film and the non-adiabatic heat diffusion ( i.e., ) was transmitted instantaneously within the metal with very small loss. The temperature at the surface of the film was determined ≈301 K, well below the aluminium melting point. The Biot number showed that the metal as single layer and the whole film as double layer satisfies the thermally thin film ( i.e., ). Considering the Newtons’s law of cooling, the overall film heat transfer coefficient was found 3 k W·m -2·K -1 equivalent of 3.3 × 10 -3 W·m 2·K -1 thermal resistance. The analysis of images indicated a reducing percentage of heat transfer as a function of delay time based on the comparison of volume ratios. A calculated power of ≈3 kW was transmitted from the rear side of the film sufficient to thermalize the surrounding water layer and form vapor bubble.
Pulsed laser interaction with materials whether organic or inorganic and hence understanding the underlying mechanism in the process is important in various science and engineering applications such as laser material processing where welding, drilling, cutting and surface modifications or cleaning involves the removal material and for non-removal applications including medical diagnosis and industrial non-destructive testing, one requires process monitoring and on-line quality control [
In recent times a great interest has been shown in under water laser processing due to number of interesting features such as better process efficiency, quality and faster processing. For example, enhanced adhesion of metal films on polyethylene terephthalate (PET) using KrF excimer laser [
The experimental setup is shown in
The shadowgraphs observed for the fibre-film in contact mode under water are shown in
strong absorption of radiation by water which results in a hot, high-pressure vapour cavity. Evidently, the bubbles initially expand to form approximately a spherical cavity but is somewhat flattened at the fibre tip. A small hemispherical cavity has already developed around the fibre tip at 10 μs as a result of high pressure vapor cavity due to strong absorption of the beam, which indicates there exists a very thin layer of water between fibre tip and the metal film because of probably microscopic spatial variation. The hemispherical expansion continuous up to ~250 μs with a maximum diameter at 50 μs from there onwards it gradually decreases where it collapses and completely vanishes at ~300 μs. During the expansion and contraction phase, acoustic pressure waves are generated within the vapor which then propagate into the surrounding liquid through the interface between vapor and the liquid. Throughout the process the bubble on the rear side of the metal film demonstrated a corresponding behaviour. It was also noticed that at 15 and 50 μs where the amount of heat transferred is maximum, the film was slightly tilted and pushed away due to the radiation pressure and momentum transfer which then it returns to its original position afterwards.
To study the effect of heat transfer at a distance, the film was moved to about 1 mm away from the fibre tip,
law of thermodynamics for the given amount of heat δQ (J) provided by laser pulse, the internal energy δU is decreased by increasing the bubble volume δV at constant external pressure p.
The interaction of laser beam (Gaussian mode in our case) with liquid and hence its following consequences depends largely on the laser wavelength and type of liquid as they govern the degree of absorption of laser beam, which to first approximation is assumed to behave according to Beer’s-Lamberts law within the medium i.e., α ≫ β
I ( r , z ) = I 0 ( r , z ) ⋅ e − 2 r 2 / ω 2 e − α x (1)
where I(W・m−2) is the laser irradiance, r is the radial distance from the center of beam, ω(z) is the radius at which the field amplitudes fall to 1/e of their axial values, α(m−1) is the absorption coefficient and x(m) is the material thickness. At low fluences heating will result in thermoelastic stress and the rapid expanding water produces acoustic effects. At higher fluences boiling occurs i.e., T ≥ 373 K for P0 ≈ 105 Pa. Taking extinction coefficient of water, ke ≈ 0.059 at 2.75 μm [
τ r = δ 0 2 / 4 D t (2)
where δ0 ≈ α−1 ≈ 3.7 μm is the optical penetration depth in water and Dt ≈ 1.43 × 10−7 m2・s−1 is the water thermal diffusivity, so τr ≈ 28 μs, Also, the thermal diffusion depth is:
X T = 4 D t τ p (3)
Substituting the above values in Equation (3) yields XTW ≈ 0.45 μm, where the subscript TW stands for thin water. The simple calculation shows an adiabatic condition where heat is confined at the fibre tip i.e., τ p ≪ τ r and δ 0 ≫ X T W . Assuming a very thin layer of water xw with a thickness of about 1% of core diameter i.e., xw ≈ 5 μm between the fibre and metal film hence giving a thin disc type geometry, so the elemental volume is ≈ 9.8 × 10−4 mm−3. Thus, the output energy of fibre which was measured ≈10 mJ in air is now E = E 0 e − α w x w ≈ 2.6 mJ, corresponding to 3.3 × 1010 W・m−2. Thus, the amount of heat generated in the volume element of water due to power deposition is I0αw ≈ 9 × 1015 W・m−3 which corresponds to a power of P ≈ (I0αw)δV ≈ 8.8 kW.
Now, if a thin layer of liquid is evaporated in a short timescale by the absorption of laser energy, the increase in pressure on the surface will give rise to shock wave which then will propagate into the thin film. The formation of bubbles proceeds with a front velocity smaller than the shock wave velocity in the medium. Note that the input heating power is divided between number of factors involved in the interaction process mainly to bring the water temperature to boiling point, enthalpy of water (ΔH ≈ 2252 kJ/kg), superheating, heating the film surface part of which is transferred into the film and partly lost by Newton’s cooling law. In this case, ΔH is determined as (I0αwτp)/ρw ≈ 3600 kJ/kg where ρw = 1000 kg・m−3 is density of water. So that, ≈62% is expended for boiling and ΔH and the rest (≈38%) is utilized for other factors. Also, in our case where τp » the stress relaxation (αwca)−1 ≈ 2.5 ns where ca ≈ 1500 m・s−1 is acoustic velocity in water then the peak thermoelastic stress is [
σ T = f Γ I o / c a (4)
Substituting the above values and Γ ≈ 0.1 as the Gruneisen constant for water [
V ( t ) = V i t 3 (5)
where Vi is the initial vapor volume at the early stage of growth and t is time. The maximum velocity when Pi » Po where Pi and Po are the initial and atmospheric pressure respectively, is given by [
ρ R ˙ 2 ≈ 2 P i 3 ( 1 − γ ) [ ( R i R ) 3 γ − ( R i R ) 3 ] (6)
where γ = 4/3 and at d R ˙ / d R = 0 gives maximum when R ˙ / R ≈ γ 1 3 ( γ − 1 ) , then
ρ R ˙ 2 ≈ 2 P i 3 ( 1 − γ ) × 0.105 (7)
using ρ = 1000 kg/m−3, output fluence of 5.5 J・cm−2 and R ˙ ≈ 180 m ⋅ s − 1 , it gives P i ≈ 1.5 × 10 8 Pa .
Despite the initiation of bubble growth, the maximum rate at which energy can be transferred to the vapor is limited by the large difference in volume between the liquid and vapor below the critical point as well as the finite bubble growth velocity. However, if this falls below the rate at which the energy is input from the laser then the liquid temperature will continue to increase and superheating occurs. Therefore, the liquid is heated at approximately constant pressure (105 Pa) to the critical temperature (Tc = 647 K) at which the distinction between liquid and vapor is lost. The pressure then increases and growth of a vapor cavity can take place. The characteristic collapse time of the gas bubble is [
τ c = 0.91 R m ( ρ / p 0 ) 1 / 2 ( 1 + P b / P 0 ) (8)
where Rm ≈ 1.4 mm is the maximum bubble radius (at 50 μs), P0 is the water atmospheric pressure, Pb is the pressure in fully expanded bubble and taking Pb/P0 ≤ 2.7 × 10−2 it gives τc ≈ 100 μs. This is clearly, higher than the experimentally observed value i.e. 50 μs seen in
E o = 4 π R m 3 P 0 / 3 (9)
It yields a value of ≈ 1.1 mJ = 2.6 mJ of calculated value at the fibre tip. The difference can be explained by the difference in enthalpy of water in expanded vapor and some contribution due to heat conduction loss to the fibre tip and also some acoustic waves energy.
1) Thermal coupling:
Laser-metal surface interaction depends on the laser beam parameters; such as laser wavelength and pulse power density. In addition, the metal thermal and mechanical properties including microstructure, chemical composition, thermal conductivity and absorption are crucial factors. The interaction results are also affected by the surrounding medium. During the interaction process some energy is absorbed by resistive losses e.g. electron-phonon while the remainder is reflected. A longitudinal wave as an elastic wave with high irradiance can carry and redistribute radiation momentum through the film while it propagates. However, this to a larger extend depends on the dimensionless thermal coupling coefficient, ηt which in the case of IR radiation is relatively low,
η t = ρ c l A T / E (10)
where density ρ = 2700 kg/m−3, specific heat capacity c = 900 J・kg−1・c−1, irradiated area A = 2 × 10−7 m2, temperature at water boiling point T = 373 and the input laser energy E ≈ 2.6 mJ (after interaction with the water volume element described above). Using these values in Equation (10) gives ηt ≈ 4.4 × 10−3 (0.44% = 1) i.e., only 1.2 mJ equivalent to 1.5 × 1010 W・m−2 is now coupled to the surface of film. However, the intensity falls to e−1 (37%) of its original value at skin depth calculated by [
δ s = ( π σ μ r μ 0 υ ) − 1 / 2 = 8 nm (11)
where σ = 1.5 × 1010 (Ω・m)−1 is the electrical conductivity, μr, μ0 are the relative and vacuum permeability and υ is the light frequency. The relation (11) does not apply to higher frequencies in the visible or higher. Now taking αA ≈ 50 × 106 m−1 (reflection at 2.75 μm ≈ 90%), it gives δ0A ≈ 20 × 10−9 m and substituting it in relation (2), τr ≈ 250 ps and similarly from relation (3) we get XTA ≈ 800 nm = ϕf ≈ 500 μm (core diameter), where the subscript A stands for aluminium. Thus a 1-D model can be assumed and that one obtains a non-adiabatic where the generated heat is diffused within the metal film i.e., τp » τr and δ0A = XTA. The consequences of this situation are: a) since, δ0w ≈ 4 μm < xw ≈ 5 μm, so no photons are reached the metal surface and only the heat and shock wave are expected to traverse the film, b) XTA ≈ 800 nm » dA ≈ 80 nm (i.e. about 10%), hence it is highly expected to have a uniform heat transfer through the film with minimum temperature difference. It is shown that such shock waves can travel up to 1676 ms−1 using a Nd:glass laser and a thin plastic coated metallic film [
interface surface area. Thus, the useful W m = ∫ 0 t P v d V ( t ) d t d t of the explosive
vaporization is
W m = ∫ 0 t [ P v − P o − ξ ( 32 π 3 V ( t ) ) 1 / 3 ] d V ( t ) d t d t (12)
where x is water surface tension and by integrating the Equation (12) we obtain the corresponding power (W = J/s)
W m / d t = ∫ 0 t [ P v − P o − ξ ( 32 π 3 V ( t ) ) 1 / 3 ] d V ( t ) d t d (13)
2) Surface temperature:
The next step is to determine the temperature distribution which in turn produces stresses and strain elastic waves. Assuming that the incident power is sufficiently low such that it only raises the surface temperature without melting it and since in our case αAϕf » 1, therefore, the laser acts as a plane transient heat source. The absorbed energy in small element of area dA is
δ T ( x ) = 1 − R C ρ A δ s ∫ t I ( x , t ) d t (14)
where R and C are the aluminium specific heat capacity and radiation reflection from the surface. The temperature distribution across the surface is the same as the energy density distribution in the optical pulse. For 1-D treatment we have
∂ 2 T ( z , t ) ∂ z 2 − 1 D t ∂ T ( z , t ) ∂ t = − Q ( z , t ) K (15)
where Q is the heat produced per unit volume (W・m−3). From Carslaw and Jaeger, the solution of Equation (15) is
T ( z , t ) = 2 I 0 ( D t t ) 1 / 2 K i e r f c ( z 2 ( D t t ) 1 / 2 ) (16)
i e r f c ( ψ ) = 1 π e − ψ 2 − 2 ψ π ∫ ψ ∞ e − ψ 2 d ψ (17)
T ( 0 , t ) = 2 I 0 ( D t t ) 1 / 2 π K (18)
Substituting the values of aluminium, I0 =1.5 × 1010 W・m−2, Dt ≈ 4 × 10−7 m2・s−1・K ≈ 240 W・m−1・K−1 in Equation (18) gives a value of T ≈ 301 K (i.e., 80% of boiling temperature −373 K is transferred to the surface) = melting temperature Tm ≈ 933 K of aluminium.
3) Heat transfer:
Schematic representation of heat transfer through the thin film is shown in
The amount of heat produced at the surface (T1) is transferred to the back of aluminium film at (T2) by parabolic Fourier heat conduction where the heating occurs instantaneously is given by
Q A = K A x Δ T (19)
For QA ≈ 1.2 mJ, ΔT ≈ 2 × 10−6 ˚C. By definition this implies that T1 ≈ T2 due to high conductivity and being thermally thin film so that there is virtually no heat loss. This is justified by the fact that Biot number (i.e., the ratio of the
resistance at the surface to within the film) = hx/K = 0.1 where h (W・m2・K−1) is heat transfer coefficient for a single layer. The direct effect of thin metal coat on the polymer film is generation and faster transfer of heat and shock waves due to rapid thermal expansion and the explosive evaporation of the thin fluid layer and possibly the metallic layer. The amount of power transferred to back of polymer is approximately given by ≈ 8 . 8 kW ⋅ e − α p x p ≈ 3 kW where αp ≈ 2 × 104 m−1 is the absorption coefficient of PET at 2.75 μm and xp is the thickness.
However, for a multilayer film the overall heat transfer (u) is defined as
1 u = 1 h A + x A K A + x p K p + 1 h p (20)
where h A = K A / δ F and h p = K p / δ F and δF is the fluid thickness. Using the corresponding values one obtains athermal resistance per unit area of 1/u ≈ 3.3 × 10−3 m2・K・W−1. Thus u ≈ 3000 W・m−2・K−1. Substituting this for Biot No. ≈ u・∑x/K ≈ 6.3 × 10-3 = 0.1, therefore, the overall film is also considered thermally thin. Finally, it is suggested that the work can be extended to nano or microscale possibly in conjunction with embedded nanoparticles within thin films or in the form of coated films where the mechanism of heat transfer is expected to be different to a bulk film.
Mid-IR laser was used to study the heat transfer through metal-polymer film using shadowgraphy technique. The growth and collapse of cavitation bubble from fibre tip in contact with film demonstrated the heat transfer through the film with corresponding bubble volume. As distance increased to about 1 mm, no heat transfer was observed. In our case, the Biot number in both the single aluminium layer and metal-polymer double film was less than 0.1. Therefore, in both cases the overall film is considered as thermally thin. The thermal coupling of radiation was less than 1 and that temperature at the surface of metal was far below its melting temperature. The practical application of such situation plays a key role in number of scientific, engineering and biomedical applications.
Khosroshahi, M.E. (2018) Shadowgraphic Imaging of Fibre-Delivered Pulsed IR Laser-Induced Heat Transfer across Thin Aluminized Polymer Film. Optics and Photonics Journal, 8, 75-89. https://doi.org/10.4236/opj.2018.84008