Chapter 9
Proceedings of the 8th International Conference on Nanochannels, Microchannels, and Minichannels (ICNMM) August 1-5, 2010, Montreal, CANADA
FEDSM-ICNMM2010-31173
NUMERICAL STUDY OF SOLUTAL AND THERMAL INSTABILITIES IN
MINI-CHANNELS FOR MEMBRANE-LESS APPLICATIONS
C. S. Iorio
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
C. Perfetti
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
Q. Galand
Universite Libre de Bruxelles Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
S. Van Vaerenbergh
Universite Libre de Bruxelles Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
ABSTRACT
Many industrial processes make extensive use of membranes to separate fluxes while allowing some of the constituent species to diffuse into each other. In recent years, high production and maintenance costs induced by fouling, poisoning and clogging of the membrane pores due to impurities have create conditions to study alternative way of making liquid and/or gaseous streams interact and diffuse without the presence of a physical barrier.
One of the possibilities is offered by the essentially laminar character of the flow in microfluidic devices that allows two or more different fluid streams to merge without mixing in a large range of experimental and industrial conditions. In this work, we will study, numerically, the case of two streams of different composition merging in a micro-channel. The upper and lower sides of the micro-channel are heated differentially and the inlet velocity of the streams is set independently in the range 0-1m/s. Simulations are carried out in 2D and 3D while fluids are chosen by considering their industrial importance and application. The main results are that the stability of the streams is very sensitive to the inlet conditions and that it is possible to modulate the mixing layer thickness by acting on thermal gradients, geometrical constraints and slip flow conditions.
INTRODUCTION
The possibility of having laminar flow in devices of mini and micrometric size has been exploited since decades especially in the bio-physical domain where different degree of mixing and/or separation of reactive, samples and fluxes was required. In recent years, a novel intriguing way of exploiting the essentially diffusive-dominated regimes characteristic of laminar flows in mini/micro devices was introduced in the pioneering works of Choban et alii [4][8], Burke[5], Ghangrekar[5]. The main point of their works was that, in many applications, the presence of membranes as physical barriers to separate interacting fluid streams is the limiting factor from both the economical and technical point of view. The costs of membranes , though constantly decreasing over years due to technological advances remain still high and, even more critical, it stands the problem of fouling, poisoning and clogging. Such aspects influence strongly the lifetime duration and maintenance costs and represents a real bottleneck in the market diffusion of membrane-based devices.
By eliminating the physical barriers some problems are solved but many also arise due to the fact that differences in densities, the presence of temperature gradients in addition to concentration ones, influences of physical boundaries of the micro-devices make the flow sensitive to disturbances that break-down the laminar character of the flow and eventually creates unwanted mixing and separation loss.
This situation is particularly critical in applications like fuel cells, reverse electro-dialysis systems or bio-reactors where a stable and robust diffusion-driven flow is required. The analysis of the effects of thermal and solutal perturbations is then critical.
In this paper, we studied numerically the flow patterns and the mixing degree of two fluids streams flowing in co-current direction in a mini-channel. The two streams interact in presence of a thermal gradient that is imposed parallel to the gravity vector. The density gradient is also parallel to the direction of the gravity vector resulting in a spectrum of cases where thermal and concentration gradients reinforce or oppose each others – see Figure 1.
To get some valuable information concerning the potentially unstable cases, we studied 2D and 3D cases where the thermal gradient is potentially unstable, i.e. parallel and directed in the direction of the gravity vector, and the concentration gradient is both stabilizing or destabilizing, i.e. the heavier fluids is the lower or upper stream respectively.
Figura 1 The geometrical section of the 3D domain used in calculation. The observation sections are at 2mm, 50mm and 100mm from the point where the two streams merge.
For different combinations of the thermal and concentration gradients, the study focused on the effects of the stream velocity on the separation ratio and on the thermal and concentration patterns along the channel length. Because the final goal is to develop an experimental setup devoted to the study of membraneless applications for energy harvesting, this study should be considered as a non-exhaustive, on-going
contribution to the numerical modeling of this kind of applications.
NUMERICAL MODEL
To solve numerically the above-cited set of equations, the commercial software FluentTM has been used together with the mesh generator GambitTM to discretize the domain. Fluent belongs to the class of full Navier-Stokes equations solvers. It allows for dealing with very complex geometry as well as for adding custom made terms both in the set of boundary conditions and equations.
In our study, the evolution of a multi-component fluid flow in presence of temperature and concentration gradients parallel to the gravity vector has been studied for a 3D channel characterized by two 2,8mm long entries that are perpendicular to the channel axis. They join after a L-turn bend that is 20mm long. The outlets are symmetric to the inlets across the middle of the channel. The total length of the channel is 139,6mm while the distance where the liquids can interact is 100mm long. The width of the each inlet is 1 mm, so the width of the channel is 2mm. In the 3D model, the depth of the channel is also 2mm – see Figure 1.
For what concerns the velocity field, the two streams are injected with an even velocity varying in the 0-0.01 range. This assures that the flow itself is laminar in the channel and that instability patterns are exclusively due to the presence of thermal and concentration gradients and/or to the interaction of those gradients with the imposed flow.
From the usual definition of the Reynolds number
Re
v
D
H
where DH is the hydraulic diameter of the channel, it is possible
to infer that in the range of velocity studied the flow is everywhere laminar. As a matter of fact, the highest velocity tested is 0.01m/s to which corresponds a Re of about 30, far below the turbulent threshold.
The 3D model has been discretized with hexahedral volumes that assure for a better computational management of the concentration and thermal gradients. The total number of nodes composing the meshed geometry is 667,907 as shown in Figure 2.
All fluid properties are assumed to be independent from the temperature and concentration, except from the density which is computed as a linear function of both temperature and concentration - see table 1 in Annex.
The complete set of equations solved reads as follows: Continuity:
0
v
Momentum: INLET Fluid 1 INLET Fluid 2Wall where T is applied
dv
dt
v
p
gwj
Species without chemical reactions:
t
i
v
i
J
i Where:
i
i
Where the index i =1,2 identifies the two fluids, ρ is the density, μ is the dynamic viscosity, p the pressure.
Despite the relative importance that the thermal diffusion process can have in similar cases, the only mass diffusion contribution has been computed and the relative coefficient considered constant. The associated diffusive flux is evaluated as:
J
i
D
i,m
iHere, Di,m is the binary diffusion coefficient.
The general form of the energy conservation equation is expressed in a multi-component flow as:
t
E
v
E
p
.
T
h
iJ
i
v
i
S
h Where
S
h
0
since there is no chemical reaction,
h
iJ
ii
0
since the effect of enthalpy transport due to species diffusion is negligible,
v
0
since the viscous heating is negligible.In the case of incompressible flow of several species, the total energy
E
is defined as the following expression:
E
i i
c
p i T0 T
dT
v
22
Boundary conditions:At the inlets, velocity is imposed and pressure calculated from the Bernoulli condition. In the frame of the present calculations, the flow velocity ranges from 0 to 0.01m/s
Outflow boundary condition is applied at the outlet section of the channel. This condition consists in imposing that no diffusion flux exists in the direction normal to the outlet section. As a result, Fluent extrapolates the outflow conditions from within the domain.
At the wall the no-slip boundary conditions is applied as well as the condition of no-diffusion flux.
0
0
iY
v
The temperature of the lower wall and the upper wall are alternatively fixed to Tw = 275K and Tw = 325K.
y
0 and y
h
T
T
wallThe average temperature at the beginning of the calculations is set to
T
0= 300K.Figura 2 - The mesh for the 3D geometry studied.
RESULTS
The main parameter used to evaluate the degree of mixing of the two interacting streams is the standard deviation of the mass fraction Ni of one of the interacting species σc :
x
x
0
2 i1 n
n
Where
x
is the cell value of the selected variables at each facet,
x
0 is the mean of
x
x
0
x
i1 n
n
and
n
is the total number of facets.Given this definition, the case where the two streams occupy half of the channel height, correspond to a σc = 0.5. As long as
the streams mix, the variance is supposed to decrease because the number of facets where the mass fraction is different from the average mass fraction decreases.
In simulations where the thermal gradient is present, the thermal gradient has been set to 2.5K/mm. If we consider the Rayleigh number as a stability parameter respect to thermal perturbations:
Ra
g
c
p.
T
w
3
w
=2mm and of the order of 10-3,
Ra
5370 far above the theoretical threshold .The thermal gradient is supposed to generate convection patterns of the Bénard type in absence of stabilizing contributions.
Figure 3 reports the standard deviation of the mass fraction in the three observation sections (see Figure 1) for the case where both the thermal gradient and the concentration gradient are stabilizing and there is no velocity at the inlets. In that case, the diminution of the σc is due essentially to the diffusion at the
interface between the two fluids.
0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 70 80 90 100 Time (s) Stan da rd Devi a tio n Stable Begin Stable Middle Stable End
Figure 3 - The standard deviation in the case of a stabilizing temperature and concentration gradient
Figure 4, 5 and 6 show the temporal distribution of the standard deviation in the case where the both the thermal gradients and the concentration gradient are destabilizing or absent, for the three observation sections.
It is worthy to note that when no velocity at the inlet is present – lines red and green, the mixing of the two streams is always strong, by taking into account that the σc changes in less than 10
seconds from 0.5 to 0.1 and then continue to constantly decrease. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 70 80 90 100 Time (s) Stan da rd Devi a tio n DT50-V0,001 DT50-V0 DT50-V0,01 DT0-V0 DT0-V0,001 DT0-V0,01 inv-DT50-V0
Figure 4 The computed standard deviation for the section at the beginning of the channel
For velocities at the inlets of the order of 1mm/s – violet and blue lines, the mixing is less pronounced that in the previous
case, but the standard deviation seems to stabilize around a value of 0.2-0.3 with a pronounced degradation of the separation as long as the streams flow along the channel, as expected.
Brown and yellow lines refers to the case where the velocity at the inlet is of 0.01m/s. in that case it is possible to observe that the mixing is strongly reduced with a standard deviation of the order of 0.4 all along the channel length.
It is interesting to note that in the cases where the velocity is present, the standard deviation firstly decrease in time and then increases again. This is due to the fact that the curve concerns the cases where the concentration gradient is destabilizing.
0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 70 80 90 100 Time (s) Stan da rd Devi a tio n DT50-V0,001 DT50-V0 DT50-V0,01 DT0-V0 DT0-V0,001 DT0-V0,01
Figure 5 The computed standard deviation for the section at the middle of the channel
This means that at first the heavier fluid sink down and occupy the place of the lighter in the evolution of the system, i.e. there is an inversion of the density streams and then the velocity of the streams stabilizes the layer respect to the case of absence of flow. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 70 80 90 100 Time (s) Stan da rd Devi a tio n DT50-V0,001 DT50-V0 DT50-V0,01 DT0-V0 DT0-V0,001 DT0-V0,01 inv-DT50-V0
Figure 6 The computed standard deviation for the section at the outlet of the channel
Figure 8 that reports the temporal evolution of the mass fraction profile in the middle section of the channel for different velocities and in the case the denser fluid represents the upper current. It is possible to observe that when the velocity increases from ~1mm/sec to ~ 1cm/sec, the inversion of the density profile induced by the gravity is not only quicker but sharper. In this latter case, the final stage is a co-current flow of the two stream with no or negligible mixing.
CONCLUSIONS
Numerical simulations performed has shown that when in a channel two streams interact without the presence of a physical separation barrier like a membranes, the system become more sensitive to thermal and solutal perturbations. More specifically, when both temperature and concentration gradient are destabilizing respect to the gravitational equilibrium, the mixing of the concurrent streams is unavoidable. In those cases, the presence of a velocity field – or of a pressure gradient in the direction of the channel length – can be strongly beneficial.
This paper should be considered as a partial and non-exhaustive contribution to the study of membrane-less systems. A more complete analysis of the full spectra of stability issues is under investigations.
Figure 7 The mass fraction distribution in the middle section of the channel for V=0m/s, V=0.001m/s and V=0.01m/s when no temperature gradient is imposed
REFERENCES
[1] A. Nepomnyashchy, I. Simanovskii, J.C. Legros “Interfacial Convection in Multilayer Systems”, Springer Monographs in Mathematics, 2006, ISBN-10: 0-387-22194-8
[2] J. C. Legros, J. K. Platten ,“Two-Component Benard Problem with Poiseuille Flow”, J. Non-Equilib. Thermodyn. Vol. 2 (1977), pages 211-232
[3] M. M. Ghangrekar and V. B. Shinde, “Simultaneous sewage treatment and electricity generation in membrane-less microbial fuel cell”, Water Science & Technology—WST 58.1 2008
[4] Eric R. Choban, Larry J. Markoski, Andrzej Wieckowski, Paul J.A. Kenis, “Microfluidic fuel cell based on laminar flow” Journal of Power Sources 128 (2004) 54–60
[5] Jeffrey M. Burke, Colin D. Smith and Cornelius F. Ivory, “Development of a membrane-less dynamic field gradient focusing device for the separation of low-molecular-weight molecules”, Electrophoresis 2010, 902 31, 902–909
[6] Min-Hsing Changa, Falin Chen, Nai-Siang Fang, “Analysis of membraneless fuel cell using laminar flow in a Y-shaped Microchannel”, Journal of Power Sources 159 (2006) 810–816
[7] Natacha Callens, Mauricio Hoyos, Pascal Kurowski, and Carlo S. Iorio, “Particle Sorting In a Mini Step-Split-Flow Thin Channel: Influence of Hydrodynamic Shear on Transversal Migration”, Anal. Chem. 2008, 80, 4866–4875
[8] Eric R. Choban, Piotr Waszczuk, and Paul J. A. Kenisa, ”Characterization of Limiting Factors in Laminar Flow-Based Membraneless Microfuel Cells”, Electrochemical and Solid-State Letters, 8 (7) A348-A352 (2005)
ANNEX A
TABLE 1 – MODEL PARAMETER USED IN COMPUTATIONS
Symbol Unity Fluid 1 Fluid 2 Mixture
Density
kg.m-3 1060.188-0,2066274T 1110.829-0.28693T Volume weighted mixing law Specific heat
c
p J.kg-1.K-1 1482 3903 Mixing law Thermal conductivity
W.m-1.K-1 0.6 0.596 Mass weighted mixinglaw Viscosity
kg.m-1.s-1 0.001003 0.001008 Mass weighted mixing lawMass Diffusivity
Proceedings of the 9th International Conference on Nanochannels, Microchannels, and Minichannels (ICNMM) June 18th-22th, 2011, Edmonton, CANADA
ICNMM2011-58196
FAST MIXING IN MICROCHANNELS BY INPUT MODULATION: A NUMERICAL
AND EXPERIMENTAL STUDY
C. S. Iorio
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
C. Perfetti
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
F. Dubois
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
ABSTRACT
Efficient mixing in micro-channels is one of the most debated topics in the design of microfluidic devices for the outmost importance it has in many industrial processes. Different mixing mechanisms could be easily found in literature but a usual accepted classification divides the different devices in three major categories: diffusion, distribution-based and convective devices. For all of them, the goal is to break the intrinsic laminar character of very small Reynolds number flows typical of microfluidic to enhance the mixing of the different interacting streams.
In this study, we focused on the numerical modeling of the so-called injection mixer. In these devices, the mixing is driven by the dynamic of the injection streams. Attention is given to the inlet region where the different streams first mix together. Computations tackled with the case of a three inlet micro-channel – thickness: 400µm,
width: 3mm, length: 30mm – where the injection rates are modulated according to prescribed wave form and normalized to have a constant flow rate at the outlet. Linear waveforms have been tested. For each configuration, an assessment of the mixing efficiency based on standard deviation of the stream concentration is evaluated together with a typical mixing length and time.
Results are then compared with the case where the injection rate is constant. Preliminary results shows that injection mixer with modulated injections can achieve mixing efficiency that are at least comparable with the diffusion based systems. The waveform that is more suitable depends on the characteristic injection period and on the phase shift between different injections. Pulse waveform determines high efficiencies, but requires higher injection rates and creates pressure fluctuations that could be disturbing in applications.
provide some hint to reduce the mixing length by coupling a preliminary mixing due to modulation of the inlet streams with other mixing configurations.
INTRODUCTION
Many industrial processes require mixing steps in mini or micro-channels where several components are gathered to achieve a transformation such as a chemical reaction, a dilution, an emulsion. Because of the intrinsic laminar character of the interacting flow streams in micro-channels, mixing has always represented a difficult task to achieve [1].
Nevertheless, many alternatives have been proposed based on the three main mechanisms: diffusion, fluid distribution, forced convective non-stationary motions. Several studies [2][3] focused on micromixers based on convective and diffusive motions to achieve higher degree of mixing. For this class of mixers, the length of the channel where mixing is obtained could be a critical point, even though, generally, they assure a good mixing quality at the outlet.
In this paper, with the support of experimental evidences, a numerical study concerning the so-called injection mixers has been performed. We focused our attention on a standard channel with 3 inlets and 1 outlet. Each inlet is 1mm wide and 400µm deep. They join in a main channel - 3mm wide and 400microns deep and 23 mm long - where the mixing is studied (Figure 1).
Figure 1 - The micro-mixer configuration studied
The flow rate of each inlet is modulated independently. Two different fluids are injected, one of them through the central inlet, and the others through the lateral inlets.
NUMERICAL MODEL
For isothermal streams of different composition mixing in a channel, the set of equations to be solved read as follows:
Continuity:
v
0
t
Momentum:
v
v
v
p
g
v
jˆ
dt
v
d
Species without chemical reactions:
i
v
i
J
it
Where:
i
i
Where the index i =1,2 identifies the two fluids, ρ is the density, μ is the dynamic viscosity, p the pressure,
jˆ
the versor in the direction of the gravity . The mass diffusion contribution has been computed and the relative coefficient considered constant. The associated diffusive flux is evaluated as:i
i
D
J
Here, D is the binary diffusion coefficient.
To solve numerically the above-cited set of equations, the commercial software FluentTM has been used together with the mesh generator GambitTM to discretize the domain. Fluent belongs to the class of full Navier-Stokes equations solvers. It allows for dealing with very complex geometry as well as for adding custom made terms both in the set of boundary conditions and equations.
The 3D model has been discretized with hexahedral volumes that assure for a better computational management of the concentration gradients. The total number of nodes composing the meshed geometry is 469,395.
Figure 2 - The hexahedral grid
The properties of the fluid resulting from mixing are calculated as a volume weighted average to take into account for the relative abundance in the mixing channel.
Boundary conditions:
combinations of injection rates have been tested both numerically and experimentally.
At the outlet section of the channel, a constant, atmospheric pressure is applied. This condition is also consistent with the real experimental configurations tested.
At the wall the no-slip boundary conditions is applied as well as the condition of no-diffusion flux.
0
Y
0
v
i
The modulation of the injection is obtained by a dedicated subroutine (known in Fluent as a UDF or User Defined Function) that reads as follows for the case of sinusoidal mixing:
EXPERIMENTAL SETUP
The micro-channel used in experiments is an Ibidi µ-Slide III3in1. This channel presents 3 inlets that converge to a main channel connected to the outlet. Each inlet is 1mm wide and 400m high while the main channel is 3mm wide and 400m high. Since the sum of the inlet sections is equal to those of the main section, we do not expect hydrodynamic effect on the flow induced by the geometry. Three independent pumps are required for this experiment. We used programmable KD Scientific KDS250 P and KDS270 P pumps as well as a non-programmable KDS100 basic pump. Programmable pump are controlled by a LabVIEW™ interface. Water slightly colored with a blue dye is injected in the central inlet while clear, distilled and degassed water is injected in both side inlets. The three independent, programmable syringe pumps allow for dispensing and independent volume rate at each inlet.
The mixing degree is calculated through color analysis of the flow. Images of the flow are recorded through a CCD camera with a 60mm AF microNikkor objective. Before each run a reference image of the background is taken for tackling the non-homogeneous illumination effects.
Figure 3 shows the complete setup and a zoom of the Ibidi cell;
Figure 3 - Up, the experimental setup; down, a zoom of the Ibidi cell
RESULTS
The main parameter used to evaluate the degree of mixing is the mixing quality αv evaluated
by reference to the instantaneous velocities in different cross sections:
c
c
1
2 v 2 v V MAX
Where
V
the volume flow rate, c is is the concentration of the streams and σ is the standard deviation of concentration defined as follows:In the previous formulas, <> indicates the average value in a cross-section and AM is the area
of the cross section.
At first, experiments and simulations have been performed by considering the injection at the three inlets as constants in time, but with different ratios. In Fig. 4, two of such cases are depicted. The first row shows the case where the central injection is in a ratio 1:10 respect to the lateral ones. The volumetric flow rate is then 10ml/min at the lateral inlets and 1ml/min at the central one. It is possible to observe that the central stream is split in two main branches and that the flow, although symmetric become three-dimensional. This behavior is confirmed by numerical simulations. The mixing quality factor corresponding to this situation is equal to 0.6.
The bottom row in Fig.4 corresponds to an injection ratio 1:1 between the central and lateral inlets. The three streams remain practically un-mixed all along the channel and each of them occupies one third of the channel width. Because the three streams enter the channel with equal velocities and equal volumetric flow and the channel is rectilinear, it is possible to infer that in that case the mixing is assured mainly by diffusion.
Figure 4 Experimental (left) -numerical (right) concentration profiles for two different constant injection rates. Up, the case where the ratios of the central injection to the lateral ones is 1:10; down the ratio of the flows is 1:1
Figure 5 Evolution of the concentration profiles for the injection ratios 1:10. Left, Experimental profiles, Right numerical profiles. Each row correspond to a 0.5 seconds delay
When a linear modulation of the injection rates is applied, it is possible to observe, via colorimetric
analysis that the streams mix together in a more efficient way, even if because of the periodic character of injection modulation the mixing quality factor has a periodic oscillation too. Numerical simulations (Figure 5 right column) confirm, qualitatively, the experimental evidences.
In Figure 6 and Figure 7, the mixing factor as a function of the time is drawn for different cases. Figure 6 presents results from numerical modeling whereas Figure 7 presents the corresponding experimental results. A very good agreement of the mixing quality between experimental and numerical results is observed in the two cases of a constant flow injection (Const 1_1_1 and Const 10_1_10). When the diffusion is the main driver for the mixing (Const 1_1_1), as expected for a short channel, the mixing factor is the lowest possible, and equal to 0.08. The best mixing is achieved for situation where a three-dimensional flow field is generated in the channel (Const 10_1_10). A mixing factor is calculated equal to 0.6. This situation corresponds to a constant injection rate at the three inlets and a flow rate in the ratio 1:10 between the central and lateral inlet channels.
When linear modulation is applied (Lin 1_1_1 and Lin 10_1_10), mixing quality increases respect to the cases where a fully laminar two-dimensional flow. Experimental results are not so closed to numerical ones because data were extracted from a single experiment, and they are not average. But the general behavior of the experimental quality mixing is similar to the numerical one. The mixing quality fluctuates in a wide range during a single period, from 0.1 to 0.5, for instance in the numerical modeled case Lin 10_1_10. This behavior could be a problem for some mixing applications.
Figure 7 Mixing quality factor for several ratio of injection rates (experimental results)
A sinusoidal modulation with several signal frequencies was also investigated numerically. In the case where the ratio of the central injection to lateral is 1:10, the mixing quality increases deeply with a higher signal modulation frequency (Figure 8 and Figure 9).
Figure 9 Comparison of mixing quality in the case of injection 1:10 with lineal and sinusoidal modulation, and without modulation.
In this case, the fluctuations of the mixing quality are really small (Sin 10_1_10-5Hz).
The 3D patterns observed in the case of a constant flow injection 1:10 (Const 10_1_10) induced a convective mixing with a high quality mixing (0.6). In the case of a modulated injection with a high frequency signal, the mixing quality reached the even higher value of 0.77.
CONCLUSION
Mixing in micro-channels by modulating the injection rate of the interacting streams with a linear or sinusoidal waveform, can help to reduce greatly the mixing length and make more effective other
mixing techniques that often require longer and geometrically complicated channels. By modulating the injection volumetric flow rate from 0.5 to 5Hz frequency, while keeping the total flow constant, it is possible to induce a constant mixing of 80% quality in less than 30mm.
ACKNOWLEDGEMENT
We gratefully thank Patrick Queeckers for his technical support to design the software for pump programming and Christophe Minetti for his software for image processing.
REFERENCES
[1]N.Kockmann (2008) “Transport Phenomena in Micro Process Engineering”, Heat and Mass
Transfer, chap 5, pp 163-165
[2]T. R. Shih and C. K. Chung, ”A high-efficiency planar micromixer with convection and diffusion mixing over a wide Reynolds number range”, Microfluid Nanofluid 5,175–183 -2008
[3]John T.Adeosun and Adeniyi Lawal,” Numerical and experimental studies of mixing characteristics in a T-junction microchannel using residence-time distribution”, Chemical Engineering Science, 64 2422 – 2432 -2009
[4]Shaowei Li, Jianhong Xu,YujunWang and Guangsheng Luo,“Mesomixing scale controlling and its effect on micromixing performance”, Chemical Engineering Science 62 , 3620 – 3626
-2007
[5]Ian Glasgow, Samuel Lieber, and Nadine Aubry, “Parameters Influencing Pulsed Flow Mixing in Micro-channels”, Anal. Chem. 76 48254832
-2004
[6]Nam-Trung Nguyen and Xiaoyang Huang,” Mixing in microchannels based on hydrodynamic focusing and time-interleaved segmentation: modeling and experiment”, Lab Chip, 5, 1320– 1326 - 2005
[7]T. Fujiwara, H. Ohue and T. Urata (2010) “Demonstration of The Enhanced Mixing and Reaction Ability of an Alternate Pumping Microreactor with Visualization of the Mixing Field and the Reaction Field”. Proc. ASME 2010
FEDSM-ICNMM2010
[8]Mranal Jain and K. Nandakumar, ”Novel index for micromixing characterization and comparative analysis”, Biomicrofluidics 4, 031101 - 2010 Figure 8 Numerical concentration profile for a 5Hz
Proceedings of the 11th International Conference on Nanochannels, Microchannels, and Minichannels (ICNMM) June 16-19, 2013, Sapporo, JAPAN
ICNMM2013-73207
3D FOCUSING OF MICRO-PARTICLES BY SHEATH FLOW WARPING C. Perfetti
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
C. S. Iorio
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
ABSTRACT
Observation of biological samples is a common issue in many applications relative to marine environment and in the field of water treatments. In particular, the ability to detect the presence of bacteria such as Criptosporidium and Giardia Lamblia in freshwater contributes to prevent people from critical diseases even in developed countries. The main challenge in this field is to analyze a large enough volume of biological sample to make it representative of the selected environment, while characterizing the species of interest whose size is often many order of magnitude smaller.
In order to obtain detailed information of the observed species, the magnification of the visualization systems – often optical microscopes- should fit the size of the objects, involving a restrained field of view. As a result; the rate of analysis is lowered and the characterization of the samples time-consuming. To tackle this issue, an increase of the flow rate is possible by focusing of particles in the observation field of view. Such technique allows for increasing the overall flow rate, inversely related to the sampling time.
In this article a new 3D hydrofocusing device is presented. A square section glass capillary (400x400µm²) used as the nozzle is inserted into a square section glass channel (2x2mm²). The inlets are fixed on a custom device that enables the sheath flow to completely wrap the sample flow after the injection. The 3D position of the particles used as representative substitutes of the biological species has been measured thanks to digital holographic microscopy
and their distribution in cross-sections 2mm and 30mm downstream the injection nozzle compared to numerical simulations. A successful match of the location has been observed.
The carrier fluid used in the experiments was water seeded with 27-45µm diameter neutrally buoyant particles. Several flow rates have been tested for both samples and sheath flow to investigate the shape of the focused stream line and to validate the prototype design. A maximum constriction - ratio between the part of the cross-sections where particles are present with and without focusing sheath flow - of 47% has been observed confirming the potentiality of the technique.
INTRODUCTION
In the field of life sciences, the monitoring of the observation of biological samples has become a great concern to control the ecosystem evolution. Most of the time, the size of the organism of interest is several magnitude order smaller than the size of the sample in analysis and the characterization of the samples time-consuming. To tackle this issue, an increase of the flow rate is possible by focusing of particles in the observation field of view. Such technique allows for increasing the overall flow rate, inversely related to the sampling time
Hydrodynamic focusing is widely used for the manipulation of flow streams in the frame of microscopy observation [ 1]. However, in most of microfluidic devices
F. Dubois
Universite Libre de Bruxelles
only 2D focusing is achieved because 3D focusing requires a more complex geometry and advanced machining process [ 2] [ 3][ 4].
In this paper, experimental and numerical investigations on the shape of the sample flow in 3D focusing case have been performed. We pointed our attention on a standard glass channel with 2 inlets and 1 outlet. The diameter of the sheath flow inlet is 2mm while the sample inlet has a square cross-section of 0.16mm². They join in a main glass channel with a square section of 4 mm² and a total length of 50mm. The position of particles, added to the sample flow is investigated at cross-sections 2mm and 30mm apart from the injection nozzle (Figure 1).
Figure 1 - The 3Dfocusing configuration studied
The flow rate of each inlet is modulated independently thanks to two different pumping systems. At the sheath flow inlet, only water is injected while at the sample inlet a flux of water seeded with 27-45µm neutrally buoyant synthetic particles mimicking biological objects is imposed.
Digital Holographic Microscopy presents a lot of advantages compared to usual optical microscopy for non-invasive visualization in biological and environmental applications. At present, it is successfully used for characterizing cell cultures by cell counting and cell viability analysis. Most of living cells are transparent or semi-transparent objects and, as a result, they are difficult to observe with traditional microscopy. But since the refractive index of their constituents is different from the one of the medium, they are suitable for visualization by Digital Holographic Microscopy (DHM).
The second major advantage of DHM over traditional microscopy is its capability to increase the depth of investigation. In traditional microscopy, particles that are going out of the focal plane of the microscope during the record are rapidly blurred and cannot be studied. On the contrary, a hologram contains the global information of the investigated volume; as a result, a focused image of the object can be calculated anywhere from a vertical range depending of the magnitude of the objective. This feature is important for studying 3D structures of microorganisms, and also for dynamic investigation of particles in flows.
NUMERICAL MODEL
The two streams are modeled as two different species with same physical properties to enable the visualization of the interface. For incompressible and isothermal streams mixing in a channel, the set of equations to be solved read as follows: Continuity:
0
u
Momentum:
u
u
u
p
dt
u
d
1
Species without chemical reactions:
i i iJ
u
t
Where:
i
i
Where the index i =1,2 identifies the two fluids, ρ is the density, ν is the kinematic viscosity, p the pressure. The mass diffusion contribution has been computed and the relative coefficient considered constant. The associated diffusive flux is evaluated as:
i
i
D
J
Here, D is the binary diffusion coefficient estimated at 10-9m2/s.
To solve numerically the above-cited set of equations, the commercial software FluentTM has been used together with the mesh generator GambitTM to discretize the domain. Fluent belongs to the class of full Navier-Stokes equations solvers. It allows for dealing with very complex geometry as well as for adding custom made terms both in the set of boundary conditions and equations.
The 3D model has been discretized with hexahedral volumes that assure for a better computational management of the concentration gradients. The total number of nodes composing the meshed geometry is about 320,000.
Spherical particles have been numerically modeled as a discrete phase of a low volume fraction (< 10%) with a diameter normal distribution centered around 30µm and their trajectories have been individually calculated at specified time during the fluid phase computation. The force balance on each particle is:
( )
( )
Where u is the fluid phase velocity, is the particle velocity, ( ) the drag force.
Boundary conditions:
At the inlets, a volumetric flow rate of the streams is assigned in the range 10 to 500 µl/min. Different combinations of injection rates have been tested both numerically and experimentally.
At the outlet section of the channel, a constant, atmospheric pressure is applied. This condition is also consistent with the real experimental configurations tested.
At the wall the no-slip boundary conditions is applied as well as the condition of no-diffusion flux.
EXPERIMENTAL SETUP
The experimental setup consists in a fluidic circuit and a holographic microscope (Figure 2).
The channel and the nozzle used for these experiments are glass tubes with square section from Vitrocom© company. The nozzle is inserted into the channel (Figure 3) thanks to a custom developed device where inlets are orthogonally drilled. To enable a tight position of the nozzle inside the channel at the inlet, it is the external face of the nozzle that is glued in the device whereas the inner faces of the channel are glued on the other side. Commercially available Luer Ibidiconnectors complete the fluidic circuit by linking the experimental cell to two independent pumping systems - KD Scientific KDS250 P and KDS270 P.
Opaque blue polyethylene microspheres from Cospheric© that are neutrally buoyant (1g/cm³) added to distilled water and a surfactant is used as the sample visualization target. Distilled and degassed water is injected in the sheath flow inlet as the wrapping flow.
Figure 3 - Flow cell with the nozzle
Optical system
The 3D position of particles in the flow is calculated through numerical reconstruction of holograms recorded from a digital holographic microscope, from an inner development).
DHM working principle (see Figure 4) consists in splitting (BS2) the light from laser into an object beam and a reference beam. The object illuminated (MC) by the beam gives the object wavefront that is collected by the objective. Then the two beams are combined (BS1) to interfere and create the hologram on a camera sensor (CCD).
Figure 4 - Optical Setup of the Digital Holographic Microscope
The recorded focus plane for the experiments is set manually to the middle of the channel depth, at the nozzle injection so that the major particles would be optically focused in this area. The magnification used during these experiments is x10, which lead to a field of view of 720µm and a capability to calculate with a 10µm accuracy, the Z-location of particle in a range of -400µm to +400µm from the recorded plane.
Figure 5 - A: Hologram of the nozzle injection, B: Intensity Image, C: Phase Image.
S PS Channel BS2 BS1 L2 L1 L3 L5 L4 RGG M2 M3 M1 CCD Laser Nozzle A B C 720µm x y
RESULTS
The 3D coordinates of each particle recorded on holograms are calculated thanks to a software developed by the optical visualization team of our laboratory [ 5]. On each hologram, the phase and intensity images are extracted with the Fourier method. Since the particles used in this experiment are opaque, they appear as black holes on the intensity image. For any location on the field of view (x,y), an associated focus plane can be calculated. As a result, when the center of the particle is highlighted in the field of view, the focus plane of the particle is calculated, giving the vertical position (z) of the particle in the channel.
Several flow rates have been investigated experimentally. Figure 6 presents the experimental values for the sheath and sample flow rate.
Exp Sheath Flow rate (mm³/s) Sample Flow rate (mm³/s) Sheath velocity (mm/s) Sample velocity (mm/s) 1 5.55 0.17 1.65 1.04 2 1.39 0.17 0.41 1.04
Figure 6 - Flow rate values
The 3D focusing capability of the device has been evaluated thanks to the comparison between the particle lateral and vertical position – plane yz - in two different cross-sections of the channel positioned (see Figure 1) at x=2mm – section A and x=30mm – Section B - downstream from the injection nozzle.
The measurement of particle location at the section A has allowed for taking into account the dynamic of the interaction between the two concurrent flows close to the sample injection. This interaction is extremely important for the focalization efficiency of the device, especially when the sheath flow and sample flow are of comparable rate, as in the case of Exp2. In Figure 7, the position of a number of particles as outcome of the numerical simulations and experiments is plotted against time. Numerical trajectories are indicated as Xi (i=1 to 4) , while Pi (i=1 to 5) represents the particles paths extracted from measurements.
In the latter, the period between two recorded location corresponds to a frame rate of 24Hz.
Figure 7 - Exp 2, Comparison between measured and simulated particles trajectories from the nozzle injection
Experimental and numerical data show a very good balance as it is summarized by Figure 8 to Figure 11. On this figures, the vertical position of each particle is plotted against its lateral position in the channel cross sections at 2mm downstream the nozzle injection, and at the end of the channel (30mm).
Figure 8 - Exp1; Position of particles in the cross section A.
Figure 10 - Exp 2; Position of particles in the cross section A
Figure 11 - Exp2; Position of particles in the cross section B.
By taking the ratio between the part of the cross section at the inlet (section A) and at the outlet (section B) effectively occupied by the particles, it is possible to estimate the focusing efficiency for the two experiments. Evidences show that in Exp 1, it is possible to achieve a focusing efficiency of 47% with a relative low flow velocity ratio of 1.59 (Figure12). Exp Vsheath/ Vsample Focusing (%) Section B/ Section A 1 1.59 47.3% 2 0.40 138%
Figure 12 - Focusing results based on velocity ratio between the 2 flows
CONCLUSION
Focusing in 3 dimensions shows a major interest for proper observation of particles from biological and environmental samples as it can prevent from clogging and sedimentation in the flow cell. It is also widely used for an efficient mixing [ 6 ].
However, achieving a real sheath flow warping remains a technical issue for building robust fluidic flow through devices. The device presented in this paper showed an ability to contract the sample stream section to 47% as well as to expand it to 137% using hydrodynamic focusing.
ACKNOWLEDGEMENT
We gratefully thank Ahmed El Mallahi and Christophe Minetti for their kind contribution in image processing and software implementation.
REFERENCES
[ 1 ] X. Xuan • J. Zhu • C. Church. “Particle focusing in microfluidic devices” Microfluid Nanofluid 9, pp 1-16, 2010 [ 2 ] N. Sundararajan, M. Pio, L. Lee, and A. Berlin “Three-Dimensional Hydrodynamic Focusing in Polydimethylsiloxane (PDMS) Microchannels” Journal of Microelectromechanical Systems, Vol. 13, no. 4, 2004
[ 3] D. Kim *, D. (Danny) Kim, K. Han, W.Yang “An efficient 3-dimensional hydrodynamic focusing microfluidic device by means of locally increased aspect ratio”, Microelectronic Engineering 86, pp 1343-1346, 2009
[ 4] T. A. Lin, A. E. Hosoi, D.J. Ehrlich “Vertical hydrodynamic focusing in glass microchannels” Biomicrofluidics 3, 014101-1, 2009
[ 5 ] A. El Mallahi, C. Minetti, F. Dubois “Automated three-dimensional detection and classification of living organisms unsing digital holographic microscopy with partial spatial coherent source: application to the monitoring of drinking water resources “Applied Optics, Vol 52, N°1,
2013
[ 6 ] C. Iorio, C. Perfetti, F. Dubois. “Fast Mixing in Microchannels by Input Modulation: A Numerical and Experimental Study” ICNMM2011-58196 pp. 165-169,
3D Focusing Of Microparticles By Acoustic Standing Waves In A Flow
Through Channel
C. S. Iorio
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
C. Perfetti
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
V. Vancauwenberghe
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
F. Dubois
Universite Libre de Bruxelles
Service de Chimie-Physique E.P., Av. Roosevelt 50, B-1050 Brussels, Belgium
ABSTRACT
Analysis of environmental changes has become a great issue nowadays with the increase of pollution and global warming. Surveys about growing populations of species and apparition of new parasites are more and more relevant to preserve our environment and populations needs. The ability to observe for instance the presence of bacteria such as Criptosporidium and Giardia Lamblia in freshwater contributes to prevent people from diseases even in developed countries. The main issue in the observation of such species is that the size of the biological sample should be large enough to be representative of its surrounding environment, meaning that the amount of the scanned sample is several orders superior to the size of the micro species of interest.
A major limitation for optical instruments in performing this kind of analysis is that the magnification required should fit the size of the particles, severely constraining the field of view. As a result, the rate of analysis is often so slow to be compatible with the large samples to analyze. One way to increase the rate of analysis is to manipulate particles in order to focus them in the field of view of the visualization system.
In this article we use acoustic standing waves to achieve this goal by directing particles in the observation region.
A 1mm x 1mm square section glass channel, excited by a piezo transducer is used. The carrier fluid is water while several types of particles, both synthetic and biological are tested. The dynamic behaviour of particles under the acoustic field has been investigated and the 3D position of each particle is reported.
In order to increase the depth of investigation, we used a Digital Holographic Microscope. This technology permit to scan a larger volume of fluid and also to calculate the 3D position of each detected particle flowing in the channel.
A focusing streamline of as thin as 1/20 of the channel cross section has been successfully achieved.
INTRODUCTION
Different phenomena could be associated with ultrasonic radiation, depending on the specific acoustic energy at stake. High-intensity/low-frequency ultrasounds (above 10W/cm² and under 1MHz) are often used for inducing cavitation and/or cell lysis while low-intensity/high-
1 Copyright © 2013 by ASME
Proceedings of the ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels ICNMM2013 June 16-19, 2013, Sapporo, Japan
frequency ultrasounds (tipically around 1 W/cm² and above 1MHz) are often applied in particle manipulation[1]. In this latter domain, an acoustic standing wave is created in a suitable channel where the sample flow is injected. The pressure field associated with the standing wave is then responsible for the focalization effects on the sample dispersed phase. Particle manipulation finds its main usefulness in flow cytometry [2]. This technique of particles and cells counting consists in the observation of the light reflection of a particle flow induced by a laser beam.
In order to be correctly analyzed, the particles must be focalized in the observation region. Usually, the particle focalization is obtained by hydrodynamic forces. Basically the particle confinement takes advantage of the shear flows induced on the sample by large volumes of lateral sheath flows.
By this way, the particles are confined in the analysis area where the laser beam performs the optical measurements.
The important difference to notice between hydrodynamic and acoustic focalization resides in the confinement action that impacts the global flow in the former, and each single particle in the latter. Thus, the acoustic focalization can replace this traditional focusing with the advantage to be sheath-less and to allow for a better flexibility of the flow rate (slowing down, inversion…) without loss of the focalization efficiency. Moreover, the acoustic forces applied on the focused particles seem to have no effect on the cell viability contrarily to the important shear stresses induced by hydrodynamic forces.
Particles in acoustic field
When a particle is placed in an acoustic field, it is subject to a static force due to pressure variations induced by the wave. This force is associated to the gradient of a scalar potential U:
U
F
PrF=
−∇
(1) Particles are directed and stabilized at equilibrium positions corresponding to potential minima [3][4]. Yosiaka and Kawasima (1955) proposed an explicit formulation for this force in the case of a spherical compressible particle, given by:
)
x
4
sin(
)
,
(
2
V
P
F
0 2 0 F Prλ
π
ρ
β
φ
λ
β
π
−
=
(2)Where corresponds to the so-called acoustic contrast factor:
)
,
(
β
ρ
φ
0 p 0 p 0 p2
2
5
)
,
(
β
β
−
ρ
+
ρ
ρ
−
ρ
=
ρ
β
φ
(3)The parameters intervening in these equations are: •
P
0 , the pressure amplitude of the standing wave •V
, the volume of the particle•
ρ
p,ρ
0 , the volume mass of the fluid and the particle, respectively•
β
p,β
0, the isothermal compressibility of the fluid and the particle, respectivelyThis force is responsible for the particle translation towards the nodes or the antinodes of the acoustic wave.
The expression of the acoustic force shows that its intensity depends on parameters such as the pressure amplitude, the wavelength and the particle volume. Thus, in the case of a spherical particle, the volume is directly proportional to the cubic root of the particle radius implying that the intensity of the acoustic force is strongly impacted by the size of the particle. Decreasing the particle size can change dramatically the acting force. Because of this strong size dependence, the fractioning of particles that have dissimilar size is also possible within this technique. The bigger particles move to the equilibrium positions faster than the smaller ones and they can be separated easily from the mixture [5][6].
If a piezoelectric transducer [7] is used to generate the standing acoustic wave, the pressure fluctuations raise with the increasing of the piezoelectric voltage. Moreover, equation shows that the force intensity varies with the squared pressure amplitude. So, the increase of the piezoelectric voltage can enhance the intensity of the acoustic force and improve the focusing efficiency.
The primary acoustic force is also inversely proportional to the wavelength of the acoustic wave meaning that it is directly proportional to the frequency.
Impact of the contrast factor
The contrast factor
φ
(
β
,
ρ
)
can be positive or negative depending on the properties of the fluid and of the sample dispersed phase. Thus, the sign of this factor determines the direction of the acoustic force and, as a consequence, if a particle moves towards the node (positive sign) or the antinode (negative sign) of the acoustic wave. Generally, solid particles have a positive contrast factor contrarily to gas bubbles, lipids and mineral oils that have a negative factor [8].If particles have a positive contrast factor, their migration to the equilibrium positions, which corresponds to the pressure nodes, is illustrated by Figure 1 in the case of the first and second harmonic mode. On the same figure, the intensity of the acoustic force acting on particles and varying
with the position in the channel width is represented.
Figure 1 on left side: representation of the acoustic force and the pressure field for the first (n = 1) and second (n = 2) harmonic mode. On the right side: representation of the acoustic potential for the same harmonic mode. The potential minima constitute the pressure mode; the stable equilibrium positions [10].
Secondary acoustic force
While multiple particles are simultaneously subjected to an acoustic field, each one experiences additional forces caused by the acoustic radiation force of the surrounding particles. These inter-particle forces are called secondary acoustic forces. The magnitude of this force depends strongly on the inter-particle distance and is responsible of the aggregate formation at the focalization plans when the concentration of particle or cell is high. The secondary force can be neglected for dilute solution.
EXPERIMENTAL SETUP
The acoustic cell used in our experiments can be split into two sub-systems. The first one is composed of the devices needed for the generation of the acoustic wave: the piezoelectric transducer and the required electrical connections for its functioning. The second consists mainly of the hydraulic circuit: the tubing, the syringes and the syringe pump apparatus ( see Figure 2 for details).
Figure 2 the experimental setup in detailed views
As target particles, polyethylene microspheres Cospheric™ having a diameter varying from 27 µm to 45 µm have been chosen. These opaque blue particles have a density of 0.99-1.01 g/cm³ and are suitable for flow visualization experiments and testing of fluid flow devices. These kinds of microspheres are made in hydrophobic polyethylene and they should be wet with a surfactant prior to use.
Digital Holography Microscopy (DHM)
Compared to the usual optical microscopy that only gives the intensity image of the observed object, Digital Holography Microscopy (DHM) enables the information record by holograms that also include the optical phase information as well as the intensity image. Then the object image is built by numerical reconstruction algorithm. The phase information allows the achievement of a great number of object features as the depth, the constituent materials or the internal organs of the organism. An entire object characterization and tomographic images can be obtained by the reconstruction algorithm.
The working principle of such microscopy is based on the splitting of a laser light into an object and a reference beams. This first goes through the sample involving a phase gap in comparison to the reference beam path. Then, the combination of two beams creates interference patterns that are caught on a camera sensor.
Figure 3 working scheme of the DHM
The DHM proposes a lot of advantages compared to the traditional optical microscopy in biological and environmental applications. Indeed, it is most suitable for the cell culture analysis due to their transparent or semi-transparent features, which that are difficult to visualize on classical microscope. With DHM, they are easy to observe due to the difference between the refractive index of their constituents and the medium.
Moreover, DHM has the capability to increase the depth of examination thanks to the hologram that contains the global information of the visualized volume. Thus a focused image can be reconstructed anywhere from a vertical range depending on the objective magnitude. This important property permits the study of 3D structures of microorganisms or dynamic repartition of particles in flows [9].
In this work, objects are analyzed with an x10 magnification that corresponds to an observation window having 720 x 720 µm dimension. By this mean, the whole width of the channel can almost be observed without loss of information.
RESULTS
Experiments are performed at frequencies corresponding to the 1st, 2nd and 3rd resonance mode of the channel (fn n = 1,2,3). To achieve those
modes, two piezoelectric transducers (Pz 400 KHz and Pz 1,3MHz) are used and the flow rate Q and the voltage V between the electrodes of the piezoelectric transducer tuned in order to increase the focusing accuracy. Using DHM, the particle distributions is then determined and analysis made by dividing the channel section in 8 sub-section (strip –like) for rapid counting.
Without acoustic field, the particles are distributed randomly through the width of the channel, Figure 4. The distribution curve, Figure 5, confirms the optical tendency. For each distribution analysis given in %, the total number Nt of particles is
analyzed.
Table 1 shows the operating conditions in which experiments were performed.
Figure 4 Particles of 27-45 µm visualized by the bright field microscope. No acoustic field, the flow rate Q = 3 ml/h
Figure 5 Distribution of particles of 27-45 µm without acoustic field using the bright field microscope. Q = 3 ml/h
Table 1. Operating Conditions
Operating conditions Pz 400 KHz Pz 1.3 MHz f1 742 KHz 813 KHz f2 1842 KHz 1841 KHz f3 2800 KHz 2442 KHz Q 3 ml/h 3 ml/h
First mode
Figure 6-7 show the intensity image and the corresponding distribution curve for the first harmonic mode using the Pz 400 KHz while Figure
Error! Reference source not found.8-9 refer to
the Pz 1.3 MHz. Although the particles are relatively small in size, so less influenced by the acoustic field, the focusing tendency is clearly detectable.
1 mm Flow
Figure 6 Particles of 27-45 µm visualized by the bright field microscope. Acoustic field activated, the flow rate Q = 3 ml/h
Figure 7 distribution of particles of 27-45 using DHM. Pz 400 KHz, f1 = 742 KHz, Q = 3 ml/h
Figure 8 Intensity image of particles of 27-45 using DHM. Pz 1.3 MHz, f1 = 813 KHz, Q = 3 ml/h
Figure 9 distribution of particles of 27-45 using DHM. Pz 1.3 MHz, f1 = 813 KHz, Q = 3 ml/h
Second mode
The analysis of the second mode, given by Figure 10-13, confirms a substantial focusing effect for both piezo systems tested. It is also interesting to remark that the trace of the particles is sometimes out-of-focus. This could be interpreted as a dispersion of the particles in the width of the channel (plane orthogonal to the field of view).
Figure 10 Intensity image of particles of 27-45 using DHM. Pz 400 KHz, f2 = 1842 KHz, Q = 3 ml/h and Vg=77V
Figure 11 distribution of particles of 27-45 using DHM. Pz 400 KHz, f2 = 1842 KHz, Q = 3 ml/h
Figure 12 Intensity image of particles of 27-45 using DHM. Pz 1.3 MHz, f2 = 1841 KHz, Q = 3 ml/h
Figure 13 distribution of particles of 27-45 using DHM. Pz 1.3 MHz, f2 = 1841 KHz, Q = 3 ml/h
Third mode
The third focalization mode is shown in figures 14-17 for the piezo resonating at 400 KHz and 1.3 MHz respectively. The overall tendency is clear and the three band separation is confirmed by the automatic recognition distribution in the channel field-of-view plane.
Figure 14 Intensity image of particles of 27-45 using DHM. Pz 400 KHz, f3 = 2800 KHz, Q = 3 ml/h
Figure 15 distribution of particles of 27-45 using DHM. Pz 400 KHz, f3 = 2800 KHz, Q = 3 ml/h
Figure 16 Intensity image of particles of 27-45 using DHM. Pz 1.3 MHz, f3 = 2441 KHz, Q = 3 ml/h
Figure 17 distribution of particles of 27-45 using DHM. Pz 1.3 MHz, f3 = 2441 KHz, Q = 3 ml/h and V=33V
CONCLUSION
Acoustic focalization proves to be an interesting technique for the manipulation of particle in mini-micro-channels. In this paper, a channel of 1mm2 section has been successfully tested for focusing 27-45µm particles in different resonating modes. The DHM technique for counting and determining the spatial distribution of particles has also been applied. The results indicate that the 3D-focusing effects could be achieved by fine tuning the acoustic frequency.
ACKNOWLEDGEMENT
We gratefully thank Patrick Queeckers for the technical support in programming the software for pump control and Dr. Christophe Minetti for the image processing software.
REFERENCES
1. Bruneau, Michel. Fundamentals of Acoustics. London : ISTE Ltd, 2006.
