LIP2018 & ELS-XVII international conferences, Texas A&M University, College Station, TX, USA from 4-9 March 2018
ON THE INFLUENCE OF DROPLET NON SPHERICITY ON THEIR FIRST RAINBOW PATTERN AND OUR CAPABILITY TO CORRECTLY ESTIMATE THEIR SIZE AND TEMPERATURE Fabrice R.A. ONOFRI1,*, Quentin GAUBERT 1, Séverine BARBOSA1 and Kuan Fang Ren2 1
Aix-Marseille Université, CNRS, IUSTI, UMR 7343, 13453, Marseille, France (*Corresponding author:
[email protected]) 2 Université de Rouen Normandie, INSA de ROUEN, CNRS, UMR 6614, 76801 Saint-Étienne-du-Rouvray, France
Grants ANR-13-BS09-0008-01, -02
Abstract The influence of droplet non-sphericity on their rainbow angle scattering patterns is investigated with the Vectorial Complex Ray Model (VCRM) and experiments carried under acoustic levitation. It is shown that quasi-imperceptible change in the morphology of droplets can significantly affect the resolution achievable on the determination of their size and temperature - unless proper particle shape and light scattering models are used.
VCRM: a Geometrical and Physical Optics Approximation (GOA-POA) Fig. 1 Sketch of VCRM wave fronts and particle surface curvature definitions [1]
Normalized intensity [-]
The core of VCRM is a GOA allowing to account, with a full 3D algebraic formalism, for change in the direction, amplitude, phase, polarization and the local wave front curvature (see Fig. 1) of complex rays interacting with large particles (e.g. x>>20-100) with a smooth surface [1]. Note that VCRM numerical implementation is actually limited to ellipsoids (semi-axis: a, b & c, refractive index m, tilt angle g) observed in one plane of symmetry.
Experimental setup and analysis:
Estim. diameter [µm]
Fig. 2 Setup: parts of the optics and fluid loop 800 600 400
Aspect ratio, x=b/a 0.90 1.01 0.95 1.02 0.98 1.05 0.99 1.10 1.00
Prolate
Oblate
y=x
0
200 400 600 Nominal diameter [µm]
30 Aspect ratio, x=b/a 20
40 20 0 -20
800
0.1 0.01
n=2, g;
ac, g
n=2, g
Exp. data VCRM
155
160
165
Scattering angle, [deg]
170
Ellip.
Sphere
Spheroids
0.001 0.000
-0.001 10 5 0 -5 -10
Invers. method global residual, [-]
Rainbow angle [deg]
n=2, g;
ac, g;
b/a=0.9608
40 20 0 -20
VCRM allows, in a few milliseconds, to predict accurately both the coarse and fine structures in the first rainbow angle region, except in 10 the extreme vicinity of the caustics) [2-5, 7]. For the latter region, the 0 0 100 200 300 400 500 coupling with POA(s) is required (e.g. [8,9]). For severely oblate or Semi-axis, b [µm] 160 prolate droplets, the quality of VCRM predictions, in term of droplet parameters retrievability, is far superior to any method based on the 150 g Moebius approximation or pure Geometrical Optics and, obviously, 140 electromagnetic approaches based on a spherical particle shape g model (i.e. Lorenz-Mie Theory). A numerical study reveals that the 130 g g b=137.47 effect of a tilt angle g (even smaller than a few degrees) is totally 0.90 0.95 1.00 1.05 1.10 Aspect ratio, x=b/a detrimental to any attempt to estimate, in a snapshot, the refractive Fig. 4 VCRM: effects of the aspect ratio x index (i.e. temperature) of a flowing droplet. and tilt angle g (T = 24 ° C; m = 1.3350). The analysis of experimental data with different particle shape models (see Tab. 1) shows that the oblate particle shape model is not always the one minimizing the standard deviation on the difference between the estimated and reference parameters (see Fig. 5 and Tab. 1). This jeopardises the common assumption made in the literature about the stability and symmetry that can be achieved, even with a carefully aligned trap, on the balance of the forces acting on the droplet (gravity, acoustic, drag, capillary, vibrations). Without surprise, it is the model with the higher degree of freedom (ellipsoid) which provides the best statistics at 1-s (i.e. -0.57±2.05°C and 0.30±4.59µm for, respectively, an absolute temperature of 29° and an equivalent spherical radius decreasing from 380 to 50µm in t=5’). It is like this particle shape model makes it possible to take better account for some asymmetry in the droplet shape (e.g. capillary waves, asymmetric resonant modes,…) and probably some residual tilt angle effects. ac, g;
Airy's fringes
ripple
40 20 0 -20
200 0
HUDC
Fig. 3 Recorded far-field pattern and comparison with VCRM predictions [5]
Difference on Difference on Difference on refractive index [-] Difference on Equiv. Difference on spher. radius [µm] Vert. radius [µm] Horiz. radius [µm] Temperature [°C]
Key results and conclusions:
1
1E-3 150
Ripple freq [deg-1]
The acoustic trap [2-6] is placed in a dedicated evaporation chamber allowing the precise control of the relative humidity (H) and temperature (T) of the atmosphere surrounding the droplet (see Fig. 2). The parameters of the droplets (a, b, c, refractive index m) under evaporation are retrieved by comparing directly, in the least square sense, the rainbow angle scattering patterns recorded with those simulated with VCRM (see Fig. 3) [5]. During the course of an experiment of duration t, the droplet size is also simultaneously monitored by a high resolution shadowgraph. Due to our operating conditions, the temperature of the droplet is expected to be quasistationary and quasi-identical to the temperature (controlled with thermocouples) of the gas phase.
Fold-caustic
10
Références [1] Ren KF, Onofri F, Rozé C, Girasole T, Opt Lett 36:370-372 (2011) [7] Nye JF , Nature 312 (5994), 531–532 (1984) [2] Marston P L , Trinh EH, Nature 312(5994), 529–531 (1984) [8] Onofri F, Radev St, Sentis M, Barbosa S, Opt Lett 37: 4780-4782 (2012) [3] Yu H, Xu F, Tropea C, Opt Express 21:25761-25771 (2013) [9] Sentis, MPL, Onofri FRA, Méès L, Radev St, JQSRT 170: 8-18 (2016) [4] Marston PL, JQSRT 162 :8-17 (2015) [5] Onofri FRA, Ren KF, Sentis M, Gaubert Q, Pelcé C, Opt Express 23:15768-15773 (2015) [6] Maconi G, Penttilä A , Kassamakov I, Gritsevich M, Helander P, Puranen T, Salmi A , Hæggström E, and Muinonen K, JQSRT 204, 159-164 (2018)
-5
3x10
-5
2x10
1
2
3
4
5
6
Particle shape model, n. Fig. 5 Fluctuation of experimental estimations depending on the particle shape model used for the inversion. T=29°C, H=60%, The droplet equiv. sph. radius decreases from 380 to 50µm in t≈5’. Particle Parameters : refractive index (m) shape plus: model, n. 1 a ≠b≠c: arbitrary ellipsoid 2 a =c≠b: spheroid with symmetry along gravity direction (i.e. classical assumption) 3 a =b≠c: spheroid with symmetry axis perpendicular to gravity direction and the optical axis 4 b =c≠a: spheroid with symmetry s along the optical axis 5 a =c≠b with b/a derived from shadowgraph data, spheroid with symmetry axis along the gravity direction 6 a =c=b : sphere
Tab. 1 Particle shape models and inputs to inverse experimental data
