Lattice Boltzmann simulation of droplets manipulation generated in lab-on-chip (LOC) microfluidic T-junction

Journal Pre-proof Lattice Boltzmann simulation of droplets manipulation generated in lab-on-chip (LOC) microfluidic T-junction Batool Hoseinpour, Ali Sarreshtehdari PII:

S0167-7322(19)32592-9

DOI:

https://doi.org/10.1016/j.molliq.2019.111736

Reference:

MOLLIQ 111736

To appear in:

Journal of Molecular Liquids

Received Date: 8 May 2019 Revised Date:

7 September 2019

Accepted Date: 10 September 2019

Please cite this article as: B. Hoseinpour, A. Sarreshtehdari, Lattice Boltzmann simulation of droplets manipulation generated in lab-on-chip (LOC) microfluidic T-junction, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.111736. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Lattice Boltzmann simulation of droplets manipulation generated in lab-on-chip (LOC) microfluidic T- junction

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Batool Hoseinpour PhD student, Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Semnan, I. R. of Iran Email: [email protected]

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Ali Sarreshtehdari1 Assistant prof, Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Semnan, I. R. of Iran Email: [email protected]

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Abstract There are various researches about microfluidic systems to appraise influential parameters such as viscosity ratio, volumetric flow rate and Capillary number (Ca). But microfluidic processes are involved in other issues such as valving or making delay in dispersed phase releasing and attaining smooth mixture for chemical reactions. The aim of this paper is investigation of the influential parameters such as Ca number and particularly geometric parameters on droplet releasing, amplifying droplet generation rate in Lab-On-Chip (Laboratory-On-Chip or LOC) microfluidic T-junction using Lattice Boltzmann Method (LBM), applicable in encapsulation, drug delivery, diagnosis of the cancer cells, blood tests and Nucleic Acid (NA) assays. To fulfill this purpose, an asymmetry has been imposed on height of the junction. The results indicated that at a specific difference in height of the junction, the dispersed phase delayed to inter the main duct performing like an active valve instead of utilizing wax to postpone dispersed fluid entrance in the main channel resulting in fluids contamination. Combination of different Ca and asymmetry of the junction amplified droplet generation, desirable in Nucleic Acid assays. Various widths of lateral channel ratio, imposed on the junction illustrated its influence on size and number of droplets. Different entrance velocity ratios were set on the unequal height T-junction indicated its impact on droplet size without any change in

Postal code: 3619995161 P.O. Box: 316, Shahrood, Iran

Postal code: 3619995161 P.O. Box: 316, Shahrood, Iran

1

Corresponding author: Ali Sarreshtehdari, Assistant Professor, Mechanical Engineering Department. Shahrood University of Technology, Shahrood, Semnan, I. R. of Iran, P.O. Box 316. Iran, Semnan province, Shahrood, Daneshgah Blv, Postal Code: 3619995161. E-mail : [email protected]

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other parameters such as volumetric rate of fluids (Q). Change of junction angle caused forming of the slug-like thread providing a slow movement, enhancing contact surface of two phases and consequently smooth mixing of fluids for reaction without any vibration or shaking which is impossible in microfluidic systems. .

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Introduction Simulations of two immiscible fluids or gas-liquid systems in the micro channel are of the interesting and growing topics of many industrial and experimental studies which their applications spread out in different fields such as gas and oil industry, biomedical, bioengineering, medicine, pharmacology and chemical processes [1,2]. Koppula et al. [3] introduced a new microfluidic system with additional orifice to separate suspended water drops in oil in order to produce purer oil. The performance of the orifice is that the most of suspended drops passed through the orifice and the main fluid (oil) exited from other outputs embedded in the system. They claimed that this method led to an effective separation of water droplets in the oil industry. A performed research in a Y-junction system by Xue et al. [4] revealed that the difference between the flow rates of two branches helped to better separation of suspended droplets. Drops can join together and create different regimes. Feng et al. [5] investigated joining droplets mechanism in the microfluidic system theoretically using additional ingredients in the surface and change in the geometry of the micro channel. They concluded that any change in T-junction geometry is more influential factor than the other ones in collision of the droplets. Experimental observations of Zhang et al. [6], in T-junction, showed that the parameters such as size of generated droplets depends on the volumetric flow rate ratios of the two immiscible fluids and the capillary number. In addition, they resulted that geometrical parameter was the most effective factor in frequency of the drops generation. Pani’c et al. [7] studied five different micromixers to understand the quality of their performance on final mixture. They found that the higher pressure drop in mixer resulted in the better quality of the mixture. Therefore, according to their findings, multi-lamination micro mixer performed better mixing remarkably. Gorkin et al. [8] studied on the microfluidics in biomedical assays and they concluded that change in the geometry such as expansion and contraction, surface tension and viscosity of the fluids were prominent parameters in these assays. Due to the significance of multi-phase and droplet-based issues, lots of attentions have been drawn to this subject and along with empirical researches, numerical methods entered to these fields to decrease costs of the time and expenses [9-14]. Recently, Lattice Boltzmann Method (LBM) has been implemented, as one of the efficient and robust methods, for wide range of phenomena such as reaction flows [15], porous media [16], heat transfer [17-19], turbulent flows [20], Nano fluids [2124], Non-Newtonian fluids [25-26], invers analysis [27], and multi-phase flows [28-29], entropy generation and natural convection [30-35], thermal flows [36-38] and fluid in MHD (magnetohydrodynamic) field [39-44]. In majority of two phase flows studies, different geometries such as T-junction, Y-junction and flow-focusing devices have been investigated. Li et al [45]

Keywords: LOC, microfluidics, Droplet manipulation, Lattice Boltzmann Method (LBM), two-phase flow

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considered three mentioned geometries, as a droplet-based microfluidic devices, to investigate the droplet motion governed by thermo-capillary force using Lattice Boltzmann Method. They revealed that different microfluidic functions such as sorting and splitting can be performed using several micro channel geometries. Liu et al [46] utilized an additional equation in their LBM model and simulated the temperature field to study the droplet motion under thermo-capillary forces in the micro channel. Relatedly, Liu et al [47] promoted their previous thermo-capillary flows [46] using potential form of interfacial forces in LBM in order to control the droplet behavior. They demonstrated that potential form of interfacial tension can simulate interaction of the two fluids better with more stability. At Gupta et al. [48] research in the flow-focusing micro channel, it was found that geometry parameters such as length and width of the orifice were influential on the size and in the formation process of the droplet. Shi et al. [49] investigated the difference in the shape of the generated droplets between T-junction and flow-focusing devices and the related geometrical parameters. They resulted that T-junction generated spherical drops due to the wall restriction but flow-focusing generated the elliptical ones. Rriaud et al. [50] combined two methods of LBM, Latva-koko and Shan-Chen, to step up this method in simulation of two-phase flow in the T-junction micro channel. They showed that proposed method can successfully decrease spurious current around the interfacial of two fluids. Lee and Amaya-Bower [51] studied formation of the bubble in the microfluidic T-junction under influence of capillary number, viscosity and volumetric flow rate ratio. They focused on the shape of the bubble due to changes on the regime transfer under different capillary numbers. This research has been conducted to assess the effects of the influential parameters such as geometrical ones and capillary number on the flow, shape, size and number of the droplets, which are of the significant issues in Lab-On-Chip (Laboratory-On-Chip or LOC) microfluidic T-junction employing Lattice Boltzmann Method (LBM). At first a brief explanation of microfluidic systems and its application and LBM method proposed by Lee have been introduced. After the validation of the model with experimental results, current achievements and its related discussion have been presented ultimately.

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Nomenclature

h( x + eα δt , t + δt )

Distribution function for order parameter calculation

g ( x + eα δt , t + δt ) Distribution function for velocity and pressure calculation τ Relaxation time x Position t Time ρ Density µ Chemical potential σ Surface tension C Composition P Pressure Q Volumetric flow rate u Velocity v Kinematic viscosity

cs Speed of sound wα Weighting factors in LBM

ρ l Density of heavy phase ρ v Density of light phase

vl

Kinematic viscosity of heavy phase

vg Kinematic viscosity of light phase ∇ χ First order derivative ∇χ Ca φ t* W

2

Second order derivative Capillary number contact angle Dimensionless time Width of channel

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2. Microfluidic Systems Constrains and demands of samples in some assays in various fields of study such as biomedicine ones encouraged researchers to take some initiatives to mitigate these problems and these attempts resulted in newfound devices known as microfluidic ones. Microfluidics is contributing to the science and study of the systems in which the scale of involving fluids varies from a few microns up to millimeters [52]. Recently, microfluidic devices have been employed for fluid transport in many 4

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applications particularly in biomedical assays, biomedicine investigation and pharmacological industry. The usage of microfluidic systems has been broadened to other areas comprising chemical analysis and environmental assays. Furthermore, some process including mixing, separation, encapsulation, particle manipulation and flow control are performed through these devices passively or actively [53]. The capability of microfluidic systems known as lab-on-a-chip or lab-on-a-disk is that they can integrate and parallelize various processes through engraved micro channels in different desirable patterns on a chip or disk rapidly and simultaneously with noticeably small amount of essential samples [54-57]. All these characteristics accentuate their status in the researches. Among diverse microfluidic systems, droplet-based ones have enticed attentions because they enable the miniaturization and compartmentalization of involved fluids into microliter-volume droplets through possibility of the reaction of fluids in separately designed sections on a chip without any crosscontamination with other sections. This means that droplet-based microfluidic systems represent high throughput platforms in different fields of science. Various streams of immiscible fluids, with different certain rates, flow through a propellant caused by micro pumps in LOC, which is the focus of the current research, into micro channels and the interaction between fluids, due to shear forces causes breaking up of the another fluid into small droplets [58]. This process is performed through various regimes of the flow, consist of squeezing regime and dripping one. For instance, in squeezing regime, dispersed phase enters to the main channel and blocks the whole path of continuous phase. Because of accumulation of main phase behind the injected dispersed phase, a pressure is imposed on it and breaking up happen in the junction. Meanwhile, the immiscibility of the fluids ensures the isolation of the generated droplets. Droplet generation in this dimension can be employed for drug delivery to the cells or even gene manipulation in NA (Nucleic acid Assays) assays. In this regard, typically, junction geometries, including co-flowing, T-junction and flow focusing, are considered as the desired ones to produce droplets [59]. Due to considerably small size of these equipment, very small amount of both fluids are required. This means that not only possibility of precise investigation but also incredibly decline in economic expenses of utilized fluids can be achieved. Fig.1 indicates some schemes of these platforms.

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3. Numerical model: Lattice Boltzmann Equations Since its inception more than twenty years ago, LBM has proved to be a versatile computational fluid dynamic method in various subjects. Multiphase flows were one of the interesting points of view for researchers because of its helpful capability in different applications. The first improved LBM procedure for multiphase systems was introduced by Gustensen and Rothman [60] which known as Color-Method in literatures. The path of progress continued through proposed methods by Shan and Chen [61] as pseudo-potential method. Swift et al. [62] enhanced interaction forces by free energy potential approach in their method. In 2005, Lee [63] improved LBM introducing new approach in multiphase flow with two separate distribution functions gα and hα to evaluate momentum and

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density respectively in high viscosity and density ratio and spurious currents diminished remarkably 5

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by entering chemical potential as the most appropriate form to track interfacial surface in functions. The numerical implementation used is that of Lee and Liu [64] in which the Cahn-Hilliard model [65] has been employed for binary and immiscible fluids to evaluate the composition of fluids, C, devoting volume fraction of 1 and 0 to phases and representing mixture density as ρ = C ρ1 + (1 − C ) ρ 2 which

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is linear function of the composition. In which the ρ1 and ρ 2 represent density of heavy and light

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fluids respectively. Ultimately, the Cahn-Hilliard convective equation recovering continuity one is given by ∂C (1) + ∇.(uC ) = −∇. j ∂t Here u and j are the local velocity and volume diffusive flow rate of the phase. Relatedly, the

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proposed equations in [63] were verified to more complete and stable form through revision in forcing term (F) used to recover influence of surface tension through replacing term C ∇ µ at the

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initial equations by µ∇ C which indicated more stability in higher surface tension values [66] as follows F = ∇ρcs2 − (∇p + µ∇C ) (2)

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and placed in the equations of discrete Boltzmann equations (DBE) for mass and momentum ones in a new definition of distribution function gα = fα cs2 + ( p − ρ cs2 )Γ (0) . In this method, an additional

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distribution function, hα = (C ) f α was introduced to track the order parameter. Here fα , ρ , p , µ

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and cs are the traditional distribution function, density, hydrodynamic pressure, chemical potential

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and speed of sound respectively and Γα = fαeq / ρ . Therefore, the DBEs for distribution functions

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became

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ρ

eq ∂g 1 + eα .∇gα = − ( gα − gα ) + (eα − u ).[∇ρcs2 (Γα − Γα (0)) + µ∇CΓα ] ∂t τ

(3)

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eq ∂h 1 C + eα .∇hα = − (hα − hα ) + M∇ 2 µΓα + (eα − u ).[∇C − 2 (∇p − µ∇C )]Γα ∂t τ ρcs

(4)

In these equations τ is relaxation time, microscopic particle velocity is eα and M defines as mobility in Lattice Boltzmann Method. The macroscopic equations can be achieved by the Chapman-Enskog expansion of equations (3) and (4) which detailed information can be found in [49]. By imposing trapezoid rule along characteristics over time step, modified LBE’s equations became g α ( x + eα δt , t + δt ) − g α ( x, t )

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=−

cq 1 ( g α − g α )( x, t ) + δt (eα − u ).[∇ MD ρcs2 (Γα − Γα (0)) + µ∇ MD CΓα ]( x ,t ) . τ + 0.5

6

(5)

h a ( x + eα δt , t + δt ) − hα ( x, t ) 192

=−

eq 1 C (hα − hα )( x, t ) + δt (eα − u ).[∇ MDC − 2 (∇ MD pt − µ∇ MDC )]Γα τ + 0.5 ρcs

+ δt∇. ( M∇µ )Γα

( x,t )

( x,t )

(6)

.

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Here ρ l and ρ g are density of liquid and gas respectively, and µ is chemical potential which can be

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achieved from the bulk energy E0 (C ) of mix energy Emix (C , ∇C ) = E0 (C ) +

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K 2 ∇C , that follows 2 2 2 E 0 (C ) ≈ β C (C − 1) with β constant and this equation can be related to chemical potential at

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equilibrium by µ = µ 0 − K∇ 2 C = const where µ 0 = ∂ c E0 . The plane interfacial profile at

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equilibrium becomes C ( z ) =

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1 1 R−z − tanh ( ) where z is the coordinate normal to the interface and 2 2 D D is the interfacial thickness. Given β and D , gradient parameter K and fluid-fluid interfacial

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tension σ can be calculated as

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βD 2

2 Kβ 8 6 To ensure no mass flux due to chemical potential gradient n.∇µ

K=

σ=

(7) s

= 0 is required in which the mirror

scheme of the solid domain into the fluid one can guarantee it and can be stated as

φ ( xs + eα δt ) = φ ( xs − eα δt ) φ ( xs + 2eα δt ) = φ ( xs − 2eα δt ) (8)

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Where φ is a variable in the solid boundaries. And another boundary condition established by minimizing free energy is stated

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n.∇C s =

φc

(

)

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C s − C s2 . The equilibrium contact angel is given by Young’s equation k cos θ eq = (σ sg − σ sl ) / σ = −φc , where σ sg and σ sl are the interfacial tension between the solid-gas and

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the solid-liquid respectively. Macroscopic variables such as dynamic pressure p , velocity u and

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density ρ are calculated from relevant distribution functions

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p = ∑ gα + α

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ρu =

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(10)

δt 2

u.∇ρ CD cs2

(9)

δt 1 e g + µ∇CDC 2 ∑ α α cs α 2

7

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C = ∑ hα

(11)

α

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The relaxation time τ is presented as τ (C ) = Cτ 1 + (1 − C )τ 2 in which τ 1 and τ 2 are dimensionless relaxation time of the heavier and lighter fluids respectively, contributing to the kinematic viscosity by ν = τcs2δt . And required derivations can be achieved as the first derivation by ∂ϕ ∂x ∂ϕ ∂x

[

] [

]

[

]

(12)

[

] [

]

[

]

(13)

(i , j )

= ϕ(i+1. j ) −ϕ(i−1. j ) / 3 + ϕ(i+1. j+1) −ϕ(i−1. j−1) /12 + ϕ(i+1. j−1) −ϕ(i−1. j+1) /12

(i , j )

= ϕ(i. j +1) −ϕ(i. j −1) / 3 + ϕ(i+1. j+1) −ϕ(i−1. j−1) /12 + ϕ(i−1. j+1) −ϕ(i+1. j−1) /12

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And the second one is as follow

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 ∂ 2ϕ ∂ 2ϕ  (∇CD ) 2 ϕ =  2 + 2  ( i , j ) = (ϕ (i +1. j +1) + ϕ( i −1. j +1) + ϕ( i +1. j −1) − ϕ( i −1. j −1) )/ 6 ∂y   ∂x + (2ϕ( i +1. j ) + 2ϕ( i −1. j ) + 2ϕ( i. j +1) + 2ϕ( i . j −1) − 10ϕ (i . j ) ) / 3

(14)

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where ϕ is a parameter which its derivation should be calculated. The boundary condition for ∇ 2ϕ

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and ∇ 2 C must be imposed precisely. The boundary condition for ∇ 2 µ can be treated as other physical

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quantities through mirror scheme, but ∇ 2 C should be imposed carefully to recover wall wettability. In this regard, nodes located in solid wall should be replaced by following statement in boundaries particularly for boundaries recovering wettability [64]. φ (15) C ( xs + eα ∂t ) = C ( xs − eα ∂t ) − 2 c (C ( xs ) − C ( xs ) 2 ) k In fact, Laplacian form of C ( ∇ 2 C ) can be stated in the following form for nodes located inside the solid walls

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(∂teα .∇ CD ) 2 C ( xs ) = 2[C ( xs − eα ∂t ) − C ( xs ) −

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φc k

(C ( xs ) − C 2 ( xs ))]

(16)

φc (17) (C ( xs ) − C ( xs ) 2 ) k Where xs and φc indicate boundary nodes at solid surfaces and parameter of wettability which can be C ( xs + eα ∂t ) = C ( xs − eα ∂t ) − 2

achieved from Young's equation [66]. In addition, mixed derivation is used to noticeably minimize spurious currents in interfacial surface of two phase which can be defined as 1 ∇ MDϕ x = [∇ BDϕ + ∇ CDϕ ] 2 (15) ϕ indicates every variable which should be calculated and Biased derivation ( BD ) is expressed as

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∇BDϕ =

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(16)

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1 tα eα (∂teα .∇ BDϕ x ) ∑ c ∂t α ≠ 0 2 s

1 ∂teα .∇ BDϕ x − eα ∂t = [ −ϕ ( x + eα ∂t ) + 4ϕ ( x ) − 3ϕ ( x − eα ∂t )] 2 (17) In which superscript labels MD and CD denote mixed difference and central difference gradients respectively.

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4. Validation of the simulation 4.1. Contact angle validation First step of investigation in two-phase flows, in which the fluids contact the solid walls, is wettability because it plays very significant role in droplet generation process. As the solid wall becomes more wetting, gas or lighter phase is repelled from the wall resulting in enhancement of the pinch-off process. Generally, wetting, partially wetting and non-wetting walls are simulated with different static contact angles of the droplet on the surface such as 30, 60 and 150 respectively. In fact, the angle is defined according to the concept of hydrophobic or hydrophilic property of the surface. In this regard, a circular droplet, with radius 25 is deposited on the solid bottom wall and half-way bounce back scheme is applied on four boundary conditions. Lee [67] employed following equations to evaluate contact angle of the droplet in density ratio 0.2 and surface thickness D=4 in which θ eq represents desired contact angle on the wall. In these equations, C s1 and Cs 2 are the

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parameters related to the solid wall. To validate the contact angle, the results of present research have been compared with the results of Lee et al. [67] in different angles of 30, 60 and 150 in fig.2 indicating a droplet on the wall at equilibrium state. Good agreement between two achievements has been depicted.

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C s1 =

1+ 1+ Ω 2

C s2 =

1− 1− Ω 2

Ω = − cos θ eq

(18)

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4.2. Method validation According to the previous studies [51,68], there are three different regimes based on capillary number: squeezing, dripping and jetting ones. The squeezing regime corresponds to Ca<0.01 and Ca=0.1 is the transient number from dripping regime to jetting one. This category was considered as a criterion to evaluate droplet or bubble generation in various density ratios.

Van Steijn et al. [69] experimentally investigated bubble formation with ethanol and air, as working fluids , in a T- junction microfluidic system with 800 µ m as height (H) of the channel and the length 9

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L=200H with fully wetting surfaces in the squeezing regime experimentally. First stages of the droplet generation process in this regime correspond to the penetration of the bubble in the main channel and filling it gradually. Consequently, the bubble blocks the whole main duct, hindering the flow of the continuous phase, the pinch-off is driven due to the pressure of upstream and a plug-like droplet is formed. To approve, the results of present study have been compared with the experimental results of Van Steijn et al. [69] and the numerical simulation of Lee [51]. As fig.3 (A) demonstrates good agreement between the results can be observed.

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To confirm the present achievements at density ratio of the unity, a comparison has been conducted with the results of Menech et al. [70] in squeezing regime at density ratio 1 and viscosity ratio 1/4. They verified their experimental achievements numerically to assess breakup dynamics of the droplet generation and its influential parameters in details. Fig.4 represents a match well between the both results.

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Garsteki et al. [49] pointed out that in squeezing regime, Ca<0.01, effect of shear stress can be ignored because in this regime breaking up of the emerging droplet has been happened due to the increasing pressure behind of the droplet which has blocked approximately entire of the main duct. Furthermore, they acclaimed that this pressure and length of the generated droplet is proportional to the rate of continuous phase over dispersed one respectively. This statement can be formulated as

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L = α 1 + α 2Q W

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(19)

Where L represents length of the generated droplets, W is height of the main duct related to Q continuous phase and Q = d . α 1 and α 2 are the constant of the order of unity depending on the Qc

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geometry of the channel which here are 1 and 2 respectively [49,63] and subscriptions d and c refer to dispersed phase and continuous one. As fig.5 indicates, length of the droplet is increased with the increasing flow rate ratio and a good agreement can be observed in the present results with the results of Shi [49] and equation 19.

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5. Results and discussions 5.1. Effect of geometry on dispersed phase releasing Numerical simulation benefits greatly from the features that can provide more assessments of impactful paremetrs in different processes in details with acceptable accuracy. In different simulations on the microfluidic systems, numerical evaluation of physical parameters has been performed on the size and the shape of the droplets mostly. But fig.6 reperesnts different heights at

10

H t in which tn = where νg tn

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the left side of the cross section in a non-dimensinal time defined as T =

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H is the height of the channel and ν g the gas velocity [66], with other specified parameters according

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to Menech [70] with density ratio 1, viscosity ratio1/4 while working fluids are oil and water. A discrepancy has been imposed between two sides of the junction to investigate its influence on droplet generation. Fig.6(a) indicates the state in which both heights are equal at certain Ca number. Afterward, in fig.6(b) H L was increased to 1.5 H R . where H L and H R are height of left and right of the junction, respectively. As can be observed, this increment in height declined size of the droplts and increased their numbers. But in fig.6(c) and fig.6(d), with escalation of H L to 2 H R and 2.5 H R respectively, a considerable reprieve was apperceived so that in comparison with fig.6(a), only one droplet but with elongated length was generated. This growth of the droplet length is due to the height discrepancy of the both sides compeling dispersed phase to fill the gap with moving in the opposite direction of the main channel flow. This movement can be resulted in the delay on entering of disperesed phase into the main duct. But because of the accumolation of the dispersed phase in the junction, length of the generated droplet would be elongated. One of the significant issues in drug delivery, encapsulation and droplet generation is concentrated on valving. The concept of valving is making delay in releasing of the dispersed phase from latral channel in microfluidic systems. There are two general working valves: passive valves and active ones [71]. Most of applied strategies to make delay have their constrains or sometimes they have been resulted in fluid contamination because of melting special wax through laser radiation in lateral channel which is used to harness relaese of dispersed phase. So it can be concluded that particular discrepancy between both sides of the junction can have the same performance as a valve.

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5.2. Effects of Capillary and geometry on number of droplets Apparently, as reported in previous researches [43,45], capillary number was influential on the regime of the flow and increased rate of droplet formation. In other words, one of the methods to append number of the drops is increment in Ca number. According to present achievements, it was observed that in H L / H R =1.5 number of droplets was increased. To amplify generated droplet

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numbers, increment in Ca number, according to Shi [58] at density ratio unity, λ = 0.125 and Q=0.25, has been jointed to this asymetry in fig.7 and the contact angle of the all walls has been considered θ = 150 degree . In asymetric T-junction approximately a double enhancement in droplet numbers can be perceived apparently with Ca increment while the size of the droplets has declined which would be applicable in some assays such as NA (nucleic acid) or cell analysis, in which amplification of the generated droplets is desired for sample preparation. Also, Ca>0.01 contributes to dripping regime in which the dispersed phase is pulled out to the main channel and pinched off downstream in the main duct generating smaller droplets. Fig.7 not only demonstrates inlfuence of high capillary number in droplet numbers but also indicates that a specified height discrepancy can impact droplet detachment mechanism in dripping regime. In addition, in comparison with other Ca numbers, in dripping regime higher increase in droplet numbers can be observed. 11

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5.3. Effect of width ratio on droplet formation It is expected that generated droplets will be influenced by any change in the width ratio of lateral and main injection channels. To assess, various width ratios, wd / wc ,were imposed on H L / H R =1.5 in

354

which density ratio of two phases is equal to be unity, η d

355

Where wd and wc represent width of dispersed phase injection channel and continuous one

356

respectively. As fig.8 illustrates, with increment in wd / wc from 0.5 to 1.5, droplet generation can be

357

appended in terms of number and droplet length but with more augmentation to wd / wc = 2 , flow

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regime has changed to jetting one and a slug-like thread has been formed.

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For broadened assessment, a comparison has been conducted to illustrate the difference in droplet size between the unequal height T-junction and the results of Shi [49], with equal height at junction. At first step, as fig.9 indicates, a well match can be observed between the present simulation and the achievement of Shi [49], while the width ratio of the both sides is the same. At the second step,

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results of varoius width ratios in different Qd

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junction. As can be perceived, increment in width and velocity ratio can be led to increase in dimensionless droplet length. But length of droplets, in unequal height junction, indicates a little higher values at the same width ratio in comparison with the results of Shi [49]. For more observation, two different width ratios in U d /U c= 1/ 6 has been reperesented in fig.11 demonstrating

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length growth with width increment.

Qc

1 and completely hydrophobic walls. ηc = 2

has been depicted in fig.10 with unequal height at the

370 371 372 373 374 375 376 377 378 379 380 381 382

5.4. Effects of T-junction angle Low Ca number has been employed to appraise influence of junction angle on entrance of the disperse fluid in main channel at density ratio 0.1. For this purpose, two sets with two various angles 80o and 60o have been applied on the junction. Other parameters, such as volumetric flow rate ratio and Ca number have been maintaned constant. According to previous results [49,51,68], Ca<0.01 belongs to the squeezing regime and droplets should be generated consequently with lower rate. As can be seen from fig.12, not only any pinch-off did not happen in angle 80o but also a slug-like thread has been formed in main channel. This slug can provide a uniform mixing context for chemical reaction inside of the main duct without any droplet formation despite Ca=0.005. Furtheremore, higher volumetric flow rate, fig.12b can creat a thicker slug which would be favorable in chemical reactions in which a smooth combination of two involved fluids is desirable.

383 384

But as fig.13 indicates as the junction angle decreased to 60o, the dispersed phase was unable to penetrate the main duct even with higher flow rate ratio Q=1.5. The streamlines of the dispersed 12

385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424

phase for anlges 60o and 90o have been depicted in fig.14. Circulation direction of streamlines at angle 60o are the same while in angle 90 o are the opposite. In fig.13 (a) vorticities reinforce each other influence in opposite direction of the flow in main duct and consequently the to-be-dispersed phase can not permeate in continuous phase while in angle 90o influence of both vorticities supports dispersed phase to penetrate in the main duct. Therefore, it can be perceived that in despite of Ca<0.01 as the angle of junction decreased no droplet would be generated.

6. Conclusion This research has been developed to investigate some influential parameters on droplet generation in microfluidic T-junction in special purposes. It can be concluded that every change in geometry of Tjunction can influence the process of droplet formation, droplet length and its number. As it observed, difference in height of the junction can make a delay in releasing of dispersed phase into main duct. This noticeable performance can be considered as a working valve. According to the results, the certain inequality in the height of T-junction reinforced various Ca numbers effects and increased number of droplets but in smaller size. Increasing width ratios of dispersed phase injection channel represented growth in the length of droplets. Various entrance velocity ratios of dispersed phase and continuous one on unequal height junction declined the droplet size. Also, in low Ca number related to squeezing regime, specific decrease of the junction angle restrained droplet generation leading to the formation of slug thread, enhancing contact surface and providing slow and smooth mixing of the fluids.

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Fig1. Micro channels in Lab- On- a- Chip microfluidic

=30

=30

=60

=60

=150

a

=150

b

Fig2. Equilibrium profiles of a droplet on solid surfaces of (a) present study (b) reference [44]

a

b

c Fig.3 Comparison of the results of present study (a), numerical simulation of Lee [60] (b) and experimental results of Van Steijn [78] (c)

Fig.4 Comparison of the results of present study with the results of Menech [79] Ca=0.002, Q=0.25,

3

L/W

2.5

2

1.5 reference 1

shi[24] 0

0.2

0.4

0.6

Fig5. Dimensionless plug length plotted as a function of flow rate ratio

0.8

1

at Ca=0.005 and

present study

a

b

c

d

Fig.6 Comparison of the different

(b)

/

=1.5, (c)

/

/

=2, (d)

of the junction at Q=0.25,and T=1.33 (a) /

=2.5

/

=1,

b

a L/W=1.57

L/W=1.67

Ca=0.005

L/W=1.19

L/W=1.35

Ca=0.015

L/W=0.85

L/W=0.93

Ca=0.079

Fig.7 Comparison of generated droplet number and length in different Ca at [58]

/

=1.5, a) present study b) Shi

Fig.8 Droplet formation in different

at Ca=0.006

/

=1.5 and Q=0.25

a

b

Fig.9 A comparison of droplet formation at of Shi [58] (b)

and Ca=0.006 in present study (a) and study

Qd/Qc=1/3 [24]

Qd/Qc=1/3

Qd/Qc=1/6[24]

Qd/Qc=1/6

Qd/Qc=1/2[24]

Qd/Qc=1/2

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

0.2

0.4

0.6

0.8

Fig.10 A comparison of droplet size at different

1

1.2

1.4

1.6

and Ca=0.006 between the results of (a) present study at

and study of Shi [58]

a

b

,

, Fig.11 An illustration of droplet formation at

/

=1.5 and Ca=0.006 for (a )

and (b)

1.8

/

2

=1.5

a

b

Fig.12 The effect of junction angle on droplet formation process in Ca=0.005,and

junction angles

a

in different (a) Q=0.5 and (b) Q=1.5.

b

Fig.13 The effect of junction angle on droplet formation process in Ca=0.005,and

junction angles

at

in different (a) Q=0.5 and (b) Q=1.5.

at

θ = 60o

θ = 90o

Fig.14 Comparison of stream lines in Ca=0.005, Q=0.5 and ηd ηc = 0.125 at various junction angles

Highlight Research:


Inequality in junction height made a delay in releasing of dispersed phase into main duct performing like a valve.
Augmentation in entrance velocity ratio in unequal height junction enlarged size of droplets.
In lower width ratio of the channels, size and number of droplets decreased while with its increment the droplet size increased.
In low Ca number, decrease of junction angle from 900 to 800 and 600 repelled droplet formation preparing smooth mixing context.