COHESIVE PROPERTIES OF MOLTEN PARTICLE
DEPOSITED ONTO SUBSTRATE BY A FREE FALL
M. Arai*1, H. Toyama*2 and Y. Ochi*2
*1 Materials Science Research Lab.
Central Research Institute of Electric Power Industry
Tokyo, JAPAN 201-8511
*2 Dept. of Mechanical Engineering and Intelligent Systems
University of Electro-communication
Tokyo, JAPAN 182-8585
ABSTRACT
In a thermal spraying process, a lot of molten powders are impinged continuously onto a substrate due to a high-temperature
gas flow, and coating layer is deposited consequentially. Thus, powder size, powder material, powder velocity, the temperature
and substrate temperature as the process parameter affect mechanical properties of the coating deposited on the substrate.
An understanding of the fundamental physical principles for spread and solidification of powder when impacting on the
substrate is essential to determine the relation between the coating properties and the process parameter. Relatively few
experimental studies have been done to examine molten metal droplet impact. The simple model was also developed to
estimate quantitatively a flattening of the splat. However, there are no papers for the splat-substrate cohesion, in spite of an
essential property as characterizing the coating structure. In this study, splat-substrate cohesion properties for molten metallic
particle (Sn60%-Pb40%) dropped onto substrate (Type 304 stainless steel) were examined based on a free fall experimental
procedure, which could simply simulate a powder deposition process. Especially, influence of kinetic energy of the impact
droplet on the flattening of the splat, which is solid spread and solidified on the substrate, and the cohesion was shown here.
The cohesion mechanism was discussed with a detailed observation of the splat morphology by a scanning electron
microscope (SEM).
Introduction
The impact of a liquid droplet onto a solid or liquid surface is an interesting phenomenon. A lot of researchers have continued
to observe such complex shapes when a droplet spreading and splashing on the target. Engineering applications were also
born from the interest observation for an impact of a liquid droplet-solid surface. The applications includes spray cooling of hot
surface, ink jet printing, spray painting, thermal spray coating and so on. Our research into the impact of the droplet on a solid
surface is addressed on thermal spray coating technology. This technology is an industrial process in which metal or ceramic
powders are injected into a high temperature gas flow, the partially molten powders are accelerated towards the substrate to
be coated. Molten powders are rapidly solidified when they impact on the substrate. Thermal spray coatings are widely used to
protect components exposed to corrosion, wear and high-temperature environments. The mechanical properties of coatings
are known to depend strongly on splat shape formed by spread and solidification of a droplet impacted on the substrate. An
understanding of the fundamental physical principles is important to determine the relation between the coating properties and
the process parameter (such as substrate temperature, particle velocity, the temperature, powder size and powder material).
Madejski [1], who is pioneer in this area, has modeled deposition process that droplet spreads on the substrate, and showed
the simplified formula for the flattening ratio, which is given by:
D
(1)
ξ = = f (Re)
d
where D is diameter of maximum spread and d is diameter of droplet, respectively. He has proposed that the flattening ratio
varies simply as function of Reynolds number Re as characterizing a particle flying motion. Clyne [2] has analyzed numerically
about a rapid solidification process for droplet spreading on the substrate in consideration with a heat exchange at the contact
boundary between the splat and the substrate. Zhang [3] has modeled spread and solidification process of the splat, which
accounts for simultaneous effect of surface tension, solidification of metal and thermal contact resistance at the contact
boundary. He has obtained an analytic solution for the flattening ratio as function of Reynolds, Weber, Prandtl and Jakob
numbers. As having an attention for mechanical property of the droplet, Matejicek et al. [4] have measured residual stress in
the surface of the single flattening splat by using X-ray diffraction method, and indicated that the residual stress reduces with
elevating substrate temperature. However, there are no papers for the splat-substrate cohesion, in spite of an essential
property as characterizing the coating structure.
In this study, splat-substrate cohesion properties for molten metallic particle (Sn60%Pb40%) dropped onto the substrate (Type
304 stainless steel) are examined based on a free fall experimental procedure, which could simply simulate a particle
deposition process. A wire-type Sn60%Pb40% is chosen as the material used for dropping onto the substrate and Type 304
stainless steel as the substrate, which is a polished plate shape. All tests are performed under a free fall-type deposition
device. After dropping tests, flattening shape of solidified particle (it is called as "splat" in this study) on the substrate is
examined quantitatively and also the peeling tests for the splat are done by a tensile test. It is examined that influence of
kinetic energy Kd of the droplet before impacting onto the substrate on the flattening of the splat and the splat cohesion is
examined. The cohesion mechanism will be discussed with a detailed observation of the splat morphology by a scanning
electron microscope (SEM).
Experimental Procedure
A wire-type Sn60%-Pb40% (Senjyu kinzoku kogyo, Inc.) was employed as a dropped material, and Type 304stainless steel
was chosen as substrate in this study. A surface of the substrate was polished (Ra=0.1µm). A free fall drop test device used in
this study is shown in Figure 1a, and schematic illustration of the testing device is also shown in Figure 1b. The main
components were the droplet generator, a test substrate on which the droplet landed and temperature measurement
instrument. The droplet generator consists of an infrared gold image furnace (Sinku-riko, Inc., P610) and the nozzle that has a
cavity 3.0mm in diameter and 5.0mm deep. The nozzle was heated by the image furnace, and the dropped material was
melted inside the cavity of the nozzle. The space above the molten material was filled with nitrogen gas, and the droplet was
formed by increasing a gas-pressure. The substrate was also heated with an electro-heater. The dropping distance between
the nozzle and the substrate was set as 500 to 1500mm in this study. The substrate temperature was also set as 293 to 413K.
In order to measure the splat cohesion, the splat was peeled from the substrate by a tensile test after finishing free fall tests.
Critical load Pc, when the splat is peeled from the substrate, was monitored by a load cell (Tokyo Sokki Kenjyujyo Co., Ltd,
load capacity 100N).
Figure 1a. Free fall dropping testing device.
Figure 1b. Schematic illustration of the testing device.
Flattening ratio, which is defined as following form, was measured in order to characterize maximum spread of the splat
deposited on the substrate.
ξ=
D
d
(2)
where D is a diameter of the splat and d is a diameter of the droplet during the free fall. Herein, the diameter of droplet was
obtained from following equation by measuring mass m of the splat peeled from the substrate.
1
⎛ 6m ⎞ 3
d =⎜ ⎟
⎝ πρ ⎠
where ρ is a density of the droplet.
(3)
The cohesion σc of the splat was obtained by:
σc =
4 Pc
(4)
πD 2
Results and Discussion
Reynolds number Re has been used to characterize a motion of the droplet during a free fall, and the relation between
flattening ratio and Re has been examined experimentally. In order to check validity for our experimental results obtained in
the free fall dropping test, the same relation is examined here. Figure 2 indicates the flattening ratio as function of Re. Figure
includes cases for four kinds of substrate temperature 293K, 323K, 373K and 413K, and also solid line estimated by following
[5]:
ξ = 7.18 × 10 −3 Re 0.6
(5)
where V involved into Re number is a droplet velocity before impacting onto the substrate, which can be given by V = 2 gH as
known well in a free fall expression. This result shows that our experiment results are almost coincident with the solid line
obtained by Eq. (5). However Eq. (5) does not include influence of the substrate temperature, our experimental result indicates
that the flattening ratio somewhat increases with the substrate temperature.
Figure 3. Variation of flattening ratio with Kd .
Figure 2. Variation of flattening ratio with Re.
Here, we have some attentions for a physical meaning of Reynolds number Re. The number is defined as value of a ratio of
inertia of fluid to the viscosity, and means to express a difficulty for fluid motion. However, the Re number used in previous
researches has been interpreted as difficulty for droplet motion. This interpretation is quite different to a true physical meaning
for Re number. If we enforce to apply this number into our droplet problem, Re number for an ambient air surrounding a
droplet should be used but it is nonsense. In this study, we take kinetic energy Kd before the droplet impacting onto the
substrate, instead of Re number. The kinetic energy is given:
Kd =
1
mV 2
2
(6)
The flattening ratio of splat as a function of kinetic energy is shown in Figure 3. Figure indicates that the flattening ratio
increases with kinetic energy in lower kinetic energy level, but approaches to constant value. On the other hand, the flattening
ratio increases with the substrate temperature. This result shows that the substrate temperature strongly affects the spread
size of droplet on the substrate.
The splat cohesion as a function of kinetic energy is shown in Figure 4. It is found that the splat cohesion increases with the
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kinetic energy until reaching to 50X10 J, and then decreases with the kinetic energy. This result recommends that higher
kinetic energy does not necessarily lead to stronger cohesion at the splat-substrate boundary. Relationship between maximum
cohesion of the splat in the same substrate temperature condition and the substrate temperature is shown in Figure 5. It is
found that the splat-substrate cohesion increases with elevating substrate temperature. The splat-splat cohesion in the
sprayed coating would become strong with an elevated substrate temperature, but not with higher impact kinetic energy onto
the substrate.
Figure 4. Variation of splat cohesion with Kd .
Figure 5. Variation of maximum splat cohesion and
substrate temperature.
A surface of the splat observed by an optical microscope (OM) is shown in Figure 6. The drop condition was substrate
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temperature 363K and kinetic energy 51.467X10 J. It is found that the splat is formed as a disk shape, and the splat surface
has small cell structure. The size of this cell structure became smaller with lower substrate temperature. Here, it was
considered from those experimental evidences that this cell structure was generated based on Benard convection [6]. As
known well, Benerd cell, that is illustrated in Figure 7, is caused by a fluid motion in splat with a thin hexagon structure
between cool and hot boundaries. This Benard cell formation indicates that the splat had huge difference of temperature
during spread of the hot droplet and was quickly cooled down with keeping the cell. A typical cross section of the splat
observed by OM is shown in Figure 8. It is found that the disk-shape splat has thinner thickness region at the center of it, and a
contact angle at tip of the splat is sharp less than 90deg. This picture also reveals that spherical-shape molten droplet spreads
onto the substrate with keeping a balance of surface tension and spreading kinetic energy until the solidification of the splat.
Figure 6. Surface observation of deposited splat.
Figure 7. Schematic illustration of Benard convection [6].
Splat Shape Characterization
Here, we try to characterize the splat shape by using following parameters as defined:
(1) Splat thickness ratio (tc/ts), which is expressed by a ratio of thickness at center of the splat to the edge thickness,
(2) Contact angle (θ) at the tip of the splat, and
(3) Flattening ratio (ξ).
Relationship between the splat thickness ratio and the kinetic energy is shown in Figure 9. The splat thickness is smaller than
1.0, and the thickness at center of the splat is thinner than the edge thickness of the splat for various kinetic energies. It was
indicated from this result to be no relation between kinetic energy of the droplet and the splat thickness.
Figure 8. Cross section of single splat.
Relationship between the contact angle and the kinetic energy is shown in Figure 10. The contact angle decreases with kinetic
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energy up to reaching to about 50X10 J, and then increases with kinetic energy again. The substrate temperature leads to
decrease of the contact angle because of being better wetting condition between the splat and the substrate. Here, it should
be noticed that this tread for the contact angle against the kinetic energy is quite similar to the trend for the splat cohesion as
shown in Figure 4. The result rearranged as relationship between the splat cohesion and the contact angle is shown in Figure
11. It is found from this relation that the splat cohesion decreases with the contact angle for various substrate temperature
conditions. That is, the splat cohesin has sensitivity for the contact angle at the tip of the splat-to-substrate, and becomes
stronger with smaller contact angle.
Figure 9. Variation of splat thickness ratio with Kd.
Figure 10. Variation of contact angle with Kd.
Finally, variation of the splat cohesion with the flattening ratio is shown in Figure 12. The splat cohesion also increases with the
flattening ratio for various substrate temperature conditions. It was found that the splat cohesion becomes stronger with larger
area of the contact between the splat and the substrate.
Figure 11. Variation of splat cohesion with contact angle.
Figure 12. Relationship between splat cohesion and
flattening ratio
Quantitative Estimation for Flattening Ratio and The Splat Cohesion
Flattening Ratio: In this study, the flattening ratio is tried to estimate quantitatively based on Pasandideh-Fard model [7-8], in
which the expression for a flattening ratio with variables as Weber, Reynolds, Stefan and Peclet numbers was obtained, and is
also compared with our experimental data.
The initial kinetic energy (Kd) and surface energy (Sd) of a liquid droplet before impact are:
⎞π
⎛1
K d = ⎜ ρV 2 ⎟ d 3
⎠ 6
⎝2
(7)
Sd = πd 2γ d
(8)
where γd is surface tension of the droplet. When the droplet spreads to maximum diameter (D) on the substrate after impact,
the associated kinetic energy becomes zero and the surface energy (SD) is:
SD =
π
4
D 2γ d (1 − cosθ )
(9)
where θ is the contact angle. The work done in deforming the droplet against viscosity (W) is:
π
W=
3
1
ρV 2 dD 2
Re
(10)
The effect of solidification in restricting droplet spread is modeled by assuming that all kinetic energy stored in the solidified
layer is lost. If the solid layer has average thickness s and diameter ds when the splat is at its maximum extension, then the
loss of kinetic energy (∆KE) is approximated by:
⎞
⎞⎛ 1
⎛π
∆KE = ⎜ d s2 s⎟ ⎜ ρV 2 ⎟
⎠
⎠⎝ 2
⎝4
(11)
ds varies from 0 to D during droplet spread: a reasonable estimate [9] of its mean value is that ds takes D/2. The solidification
thickness s could be expressed [7]:
s=
2d
π
Ste
t *γ w
Peγ d
(12)
where Ste = C ∆T , ∆T = Td − Ts , t * = Vt , Pe = Vd , C: specific heat, Hf: latent heat, Td: temperature of the droplet, Ts:
Hf
d
α
substrate temperature, and α: thermal diffusivity. In this study, t* takes 8 obtained with continuous observation of the droplet
3
by Pasandideh-Fard et al. [7]. Thus, Eq. (12) can be reduced:
s=
2d
π
Ste
8γ w
3 Peγ d
(13)
where γ is kρc, k: thermal conductivity, subscript w indicates the substrate and d indicates the droplet. Substituting Eqs. (7) (13) into the energy balance Kd + S d = S D + W + ∆KE yields an expression for the flattening ratio against kinetic energy Kd:
⎛ D⎞
⎟=
⎝d⎠
ξ=⎜
⎛K ⎞
1+ ⎜ d ⎟
⎝ Sd ⎠
(14)
16 ⎛ Kd ⎞
3 1 ⎛ γ w ⎞ ⎛ Kd ⎞
⎛ 1 − cosθ ⎞
⎜
⎟+
⎜ ⎟ Ste⎜
⎟
⎟+
⎜
⎝
4 ⎠
Re ⎝ Sd ⎠
2π Pe ⎝ γ d ⎠ ⎝ Sd ⎠
This expression includes all factors for droplet spread: surface energy, dissipation energy due to viscosity, and contact
resistance between the splat and the substrate. Figure 13 shows comparison between our experimental results and Eq. (14)
for flattening ratio against kinetic energy of the droplet. The graph involves three kinds of substrate temperature condition.
However the previous model based on ξ expression as function of Re number only could not express about the substrate
temperature effects, it is found that the model can estimate our experimental data with a good accuracy.
Figure 13. Comparison of experimental data and the estimation.
Splat Cohesion: Next, we try to estimate the splat cohesion based on our experimental results. In this study, consider the
disk-shape splat deposited on the substrate for modeling simply. The splat cohesion energy Wad can be expressed:
Wad = Aγ (1 + cosθ )
(15)
where A is cohesion area, γ is splat surface tension and θ is contact angle at tip of the splat. On the other hand, the splat
cohesion obtained by a tensile test can be obtained through following strain energy stored in the splat:
U=
1 σ c2
( Ah)
2 E
(16)
where h is average of the disk-shape splat and E is elastic modulus of the splat. From Eqs. (15) and (16), the associated splat
cohesion becomes:
σc =
2γE
(1 + cos θ )
h
(17)
Thus, this cohesion expression can be deformed with h = 2 d :
2
3ξ
σc = ξ
3γE
(1 + cos θ )
d
(18)
Here, it should be noticed that splat surface tension is a value for the solidification state, however it is difficult to measure
actually such surface tension. In this study, we rewrite the cohesion expression Eq. (18) to following form:
K≡
σc
ξ
d ≈ 1 + cos θ
(19)
Dimension of K is similar to one of stress intensity factor appeared in fracture mechanics. Relationship between K and the
contact angle θ is shown in Figure 14. Circle symbol indicates the experimental results, and solid line indicates the results
evaluated by Eq. (19). It is found that K expression can universally express the splat cohesion with including all factors such as
an influence of flattening ratio, diameter of the droplet and the substrate temperature.
Figure 14. K expression of splat cohesion
Conclusions
In this study, cohesion property between substrate and splat that was formed by droplet impact onto smooth substrate was
examined based on a free fall technique. Flattening ratio that was defined as a ratio of maximum spread to diameter of the
droplet, and the cohesion were evaluated. As obtained results from the experiment, the flattening ratio of the droplet took a
constant value for increasing kinetic energy, however the ratio increased with elevating substrate temperature because of
being better wetting contact condition. The splat cohesion had an interesting behavior that the cohesion increased with the
kinetic energy until reaching to a critical value, and decreased over its critical value. The splat cohesion became stronger with
elevating substrate temperature as well as the trend as seen in the flattening ratio. Detailed observation of the splat revealed
that small contact angle and large contact area led to strong cohesion of the splat. In order to estimate quantitatively the
spread of the droplet, Pasandideh-Fard model was applied to our experiments, and was compared with the flattening ratio.
The model involves all factors such as surface energy, dissipation energy due to viscosity, and contact resistance between the
splat and the substrate, and then showed a good agreement for our experimental data. Finally, K expression as new physical
parameter was proposed to evaluate the splat cohesion.
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