In this paper, an additive manufacturing process has been used to deposit nanoparticles on a substrate. In this innovative technique called the nano-electrospray laser deposition process, droplets of various nanosuspensions are dispensed onto a silicon substrate where subwavelength structures and bouncing droplets have been observed. An analytical model is presented for determining the temperature distribution in the substrate by considering the microdroplet as a ball lens. This lens continuously changes the focus of the laser beam as the droplet travels toward the substrate. The laser is either defocused or focused on the substrate forming locally decreased or enhanced heating near the center of the laser beam depending on the distance of the droplet from the substrate. It is found that the enhancement in heating differs for the nanosuspensions since their optical properties are different. The subwavelength structures determined from the post-pulse temperature qualitatively match with the experimental results. The steady end-period temperature is also compared with the experimentally observed temperature for bouncing droplets and the temperatures are in good agreement.

1.
E.
Castillo-Orozco
,
R.
Kumar
, and
A.
Kar
, “
Laser electrospray printing of nanoparticles on flexible and rigid substrates
,”
J. Laser Appl.
31
,
022015
(
2019
).
2.
P.
Buffat
and
J.
Borel
, “
Size effect on the melting temperature of gold particles
,”
Phys. Rev. A
13
,
2287
2298
(
1976
).
3.
E.
Castillo-Orozco
,
A.
Kar
, and
R.
Kumar
, “
Electrospray mode transition of microdroplets with semiconductor nanoparticle suspension
,”
Sci. Rep.
7
,
1
10
(
2017
).
4.
E.
Castillo-Orozco
,
A.
Kar
, and
R.
Kumar
, “
Non-dimensional groups for electrospray modes of highly conductive and viscous nanoparticle suspensions
,”
Sci. Rep.
10
,
1
10
(
2020
).
5.
E.
Castillo-Orozco
,
R.
Kumar
, and
A.
Kar
,
Proc. SPIE
10667
,
106670M.
6.
E.
Castillo-Orozco
,
R.
Kumar
, and
A.
Kar
, “
Laser-induced subwavelength structures by microdroplet superlens
,”
Opt. Express
27
,
8130
8142
(
2019
).
7.
P.
Eshuis
,
K.
van der Weele
,
D.
van der Meer
, and
D.
Lohse
, “
Granular leidenfrost effect: Experiment and theory of floating particle clusters
,”
Phys. Rev. Lett.
95
(
25
),
258001
(
2005
).
8.
I. V.
Roisman
,
J.
Breitenbach
, and
C.
Tropea
, “
Thermal atomisation of a liquid drop after impact onto a hot substrate
,”
J. Fluid Mech.
842
,
87
101
(
2018
).
9.
J.
Breitenbach
,
I.
Roisman
, and
C.
Tropea
, “
Drop collision with a hot, dry solid substrate: Heat transfer during nucleate boiling
,”
Phys. Rev. Fluids
2
,
074301
(
2017
).
10.
G.
Liang
,
X.
Mu
,
Y.
Guo
,
S.
Shen
,
S.
Quan
, and
J.
Zhang
, “
Contact vaporization of an impacting drop on heated surfaces
,”
Exp. Therm. Fluid Sci.
74
,
73
80
(
2016
).
11.
J.
Breitenbach
,
I.
Roisman
, and
C.
Tropea
, “
Heat transfer in the film boiling regime: Single drop impact and spray cooling
,”
Int. J. Heat Mass Transfer
110
,
34
42
(
2017
).
12.
B. S.
Gottfried
,
C. J.
Lee
, and
K. J.
Bell
, “
The Leidenfrost phenomenon: Film boiling of liquid droplets on a flat plate
,”
Int. J. Heat Mass Transfer
9
,
1167
1188
(
1966
).
13.
G.
Castanet
,
T.
Liénart
, and
F.
Lemoine
, “
Dynamics and temperature of droplets impacting onto a heated wall
,”
Int. J. Heat Mass Transfer
52
,
670
679
(
2009
).
14.
M.
Shirota
,
M.
Limbeek
,
C.
Sun
,
A.
Prosperetti
, and
D.
Lohse
, “
Dynamic Leidenfrost effect: Relevant time and length scales
,”
Phys. Rev. Lett.
116
,
064501
(
2016
).
15.
L.
Villegas
,
S.
Tanguy
,
G.
Castanet
,
O.
Caballina
, and
F.
Lemoine
, “
Direct numerical simulation of the impact of a droplet onto a hot surface above the Leidenfrost temperature
,”
Int. J. Heat Mass Transfer
104
,
1090
1109
(
2017
).
16.
T.
Mao
,
D.
Kuhn
, and
H.
Tran
, “
Spread and rebound of liquid droplets upon impact on flat surfaces
,”
AIChE J.
43
,
2169
2179
(
1997
).
17.
A.
Karl
and
A.
Frohn
, “
Experimental investigation of interaction processes between droplets and hot walls
,”
Phys. Fluids
12
,
785
796
(
2000
).
18.
H.
Fujimoto
,
O.
Yosuke
,
O.
Tomohiro
, and
T.
Hirohiko
, “
Hydrodynamics and boiling phenomena of water droplets impinging on hot solid
,”
Int. J. Multiph. Flow
36
,
620
642
(
2010
).
19.
T.
Tran
,
H.
Staat
,
A.
Prosperetti
,
C.
Sun
, and
D.
Lohse
, “
Drop impact on superheated surfaces
,”
Phys. Rev. Lett.
108
,
036101
(
2012
).
20.
B. S.
Yilbas
and
S. Z.
Shuja
, “
Laser short-pulse heating of surfaces
,”
J. Phys. D Appl. Phys.
32
,
1947
1954
(
1999
).
21.
B. S.
Yilbas
and
M.
Pakdemirli
, “
Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film
,”
Physica B
382
,
213
219
(
2006
).
22.
B. S.
Yilbas
,
A. Y.
Al-Dweik
, and
S.
Bin Mansour
, “
Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating
,”
Physica B
406
,
1550
1555
(
2011
).
23.
A. K.
Nath
,
A.
Gupta
, and
F.
Benny
, “
Theoretical and experimental study on laser surface hardening by repetitive laser pulses
,”
Surf. Coat. Technol.
206
,
2602
2615
(
2012
).
24.
G.
Chen
,
Y.
Wang
,
J.
Zhang
, and
J.
Bi
, “
An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material
,”
Int. J. Heat Mass Transfer
104
,
503
509
(
2017
).
25.
L. L.
Taylor
,
R. E.
Scott
, and
J.
Qiao
, “
Integrating two-temperature and classical heat accumulation models to predict femtosecond laser processing of silicon
,”
Opt. Mater. Express
8
,
648
658
(
2018
).
26.
T. T.
Lam
, “
A generalized heat conduction solution for ultrafast laser heating in metallic films
,”
Int. J. Heat Mass Transfer
73
,
330
339
(
2014
).
27.
A.
Rahaman
,
A.
Kar
, and
X.
Yu
, “
Thermal effects of ultrafast laser interaction with polypropylene
,”
Opt. Express
27
,
5764
5783
(
2019
).
28.
J.
Durnin
, “
Exact solutions for nondiffracting beams. I. The scalar theory
,”
J. Opt. Soc. Am. A
4
,
651
654
(
1987
).
29.
G.
Indebetouw
, “
Nondiffracting optical fields: Some remarks on their analysis and synthesis
,”
J. Opt. Soc. Am. A
6
,
150
152
(
1989
).
30.
D.
MCgloin
and
K.
Dholakia
, “
Bessel beams: Diffraction in a new light
,”
Contemp. Phys.
46
,
15
28
(
2005
).
31.
G.
Gbur
and
E.
Wolf
, “
The Rayleigh range of Gaussian Schell-model beams
,”
J. Mod. Opt.
48
,
1735
1741
(
2001
).
32.
J. A. A.
Engelbrecht
, “
Modelling the reflectance of silicon
,”
Infrared Phys. Technol.
35
,
701
708
(
1994
).
33.
D. W.
Hahn
and
M. N.
Özisik
,
Heat Conduction
(
John Wiley & Sons
,
New York
,
2012
).
34.
E.
Castillo-Orozco
,
A.
Kar
, and
R.
Kumar
, “
Thermal response of Bessel beam-heated microdroplets carrying nanoparticles for deposition
,” in
ICALEO 2020 Conference Proceedings
, Orlando, FL, 19 October 2020 (LIA, Orlando, 2020).
You do not currently have access to this content.