2.1.1. Newtonian flow systems

Under this system, interfacial tension between two liquid phases becomes dominant above all physical forces such as gravitational forces, viscous forces and inertia forces as the interest of dimension gets smaller due to the existence of a high surface-to-volume ratio within a microscale device. With that, an approximation of the magnitude of surface tension force, which has the stabilizing effect on the emerging tip [13], arising from

$$
\Delta P\_L = \sigma \left(\frac{1}{r\_\alpha} + \frac{1}{r\_\gamma}\right) \tag{4}
$$

and (II). The influence of two phase flow rates and viscosities on the size of water-in-oil emulsion study at a T-shape microfluidics concluded that the relationship between shear stress and flow rate of continuous phase, thus quantifies the magnitude of shear stress (τ∝ ηcQoil, where η<sup>c</sup> is the viscosity of continuous phase) acting on the interface [13]. As Qwater, the volumetric flow rate of dispersed phase increases, the shear stress exerted on the droplet is increased due to the difference of the flow rate of the two fluids decreases with increasing

permission from [38], Copyright 2015, Elsevier.

Figure 2. Passive Newtonian droplet generation with microfluidics. (I). Oleic acid droplet production at aqueous glycerol solution with varying flow rate ratios: (1) 0.16, (2) 0.8, (3) 0.667, (4) 0.11, (5) 0.1 (6) 0.2. (II) Drop images at different values of continuous phase viscosity in Newtonian System. The images a–d are μCP = 0.00332, 0.008, 0.01 and 0.018 Pa.s, respectively. (III) The effect of interfacial tension on droplet breakup dynamics with experimental and numerical justification: (a) 8.2 mN/m, (b) 10 mN/m, (c) 15 mN/m, (d) 20 mN/m, (e) 25 mN/m and (f) 29.8 mN/m. (IV) The impact of different inlet channel geometries and angle on microfluidic drop formation. (V) Droplet formation mode under various contact angles. I is reproduced with permission from [36], Copyright 2015, Royal Society of Chemistry. II is reproduced with permission from [37], Copyright 2009, Springer. III is reproduced with permission from [31], Copyright 2011, Springer. IV is reproduced with permission from [21], Copyright 2009, American Physical Society. V is reproduced with

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where r<sup>a</sup> and r<sup>r</sup> are the radii of axial and radial curvature across the interface in a squeezing regime.

Much studies were conducted in particular on the predominance of interfacial tension on characters of microfluidic Newtonian droplet formations [8, 9, 28, 29] and its changes in presence of surfactants in microfluidic systems [30, 31]. Surface flows of surfactant can induce variations in surface tension, i.e. Marangoni effect, which can substantially alter the interfacial morphology and resulting droplets size [32]. Apart from the presence of surfactant, depending on the fluid viscosity or concentration [12, 33], temperature [34] and the presence of micro- or nanoparticles in the fluid [34, 35] can modify considerably the value of surface tension of the fluid in nature and thus tailor the two-phase flow behavior within the microfluidic system. The effect of aforementioned is summarized in Figure 2.

The interaction between the solid surface and fluid in a microchannel has also been a major research focal point as the interaction impacts the dynamics of the droplet formation process. Figure 2 (V) illustrates the flow patterns for different wetting conditions in a T-shaped microchannel. Most studies of droplet generation in microfluidic devices involve the numerical studies of the contact angle effect on the shape, size, the distance between two neighboring droplets, detachment point and the generation frequency of droplets in microfluidic system [12, 29], in which the channel wall surface plays significant role in generating larger droplets with smaller contact angle provide longer contact time with the surface, especially for small values of capillary number, in consistent with the numerical results.

The flows in a microscale or nanoscale device naturally emphasize phenomena associated with interfacial tension and wetting properties. In addition, inertial and viscosity effects are two important parameters in characterizing the role of the shear-stress exerted from the continuous phase acts to deform the interface during the microdroplet breakup process, i.e. Figure 2 (I)

Microdroplets Advancement in Newtonian and Non-Newtonian Microfluidic Multiphase System http://dx.doi.org/10.5772/intechopen.75358 147

[25–27]. For most microfluidic applications, the Reynolds number is much smaller than 1, indicating the effects of volume-based inertia and gravity are not as significant as that in macroscale. The surface-based interfacial tension, flow rates, surface chemistry, and the viscosity become more significant and play in controlling flow behavior of multiphase flow in microscale. Moreover, the degree of confinement, channel aspect ratio, and geometrical structure also significantly induce the impact on capillary pressure, which promote the destabiliza-

Under this system, interfacial tension between two liquid phases becomes dominant above all physical forces such as gravitational forces, viscous forces and inertia forces as the interest of dimension gets smaller due to the existence of a high surface-to-volume ratio within a microscale device. With that, an approximation of the magnitude of surface tension force, which has

> 1 rα þ 1 rγ

where r<sup>a</sup> and r<sup>r</sup> are the radii of axial and radial curvature across the interface in a squeezing

Much studies were conducted in particular on the predominance of interfacial tension on characters of microfluidic Newtonian droplet formations [8, 9, 28, 29] and its changes in presence of surfactants in microfluidic systems [30, 31]. Surface flows of surfactant can induce variations in surface tension, i.e. Marangoni effect, which can substantially alter the interfacial morphology and resulting droplets size [32]. Apart from the presence of surfactant, depending on the fluid viscosity or concentration [12, 33], temperature [34] and the presence of micro- or nanoparticles in the fluid [34, 35] can modify considerably the value of surface tension of the fluid in nature and thus tailor the two-phase flow behavior within the microfluidic system. The

The interaction between the solid surface and fluid in a microchannel has also been a major research focal point as the interaction impacts the dynamics of the droplet formation process. Figure 2 (V) illustrates the flow patterns for different wetting conditions in a T-shaped microchannel. Most studies of droplet generation in microfluidic devices involve the numerical studies of the contact angle effect on the shape, size, the distance between two neighboring droplets, detachment point and the generation frequency of droplets in microfluidic system [12, 29], in which the channel wall surface plays significant role in generating larger droplets with smaller contact angle provide longer contact time with the surface, especially for small

The flows in a microscale or nanoscale device naturally emphasize phenomena associated with interfacial tension and wetting properties. In addition, inertial and viscosity effects are two important parameters in characterizing the role of the shear-stress exerted from the continuous phase acts to deform the interface during the microdroplet breakup process, i.e. Figure 2 (I)

(4)

ΔPL ¼ σ

tion of the interface and the drop formations.

the stabilizing effect on the emerging tip [13], arising from

effect of aforementioned is summarized in Figure 2.

values of capillary number, in consistent with the numerical results.

2.1.1. Newtonian flow systems

146 Microfluidics and Nanofluidics

regime.

Figure 2. Passive Newtonian droplet generation with microfluidics. (I). Oleic acid droplet production at aqueous glycerol solution with varying flow rate ratios: (1) 0.16, (2) 0.8, (3) 0.667, (4) 0.11, (5) 0.1 (6) 0.2. (II) Drop images at different values of continuous phase viscosity in Newtonian System. The images a–d are μCP = 0.00332, 0.008, 0.01 and 0.018 Pa.s, respectively. (III) The effect of interfacial tension on droplet breakup dynamics with experimental and numerical justification: (a) 8.2 mN/m, (b) 10 mN/m, (c) 15 mN/m, (d) 20 mN/m, (e) 25 mN/m and (f) 29.8 mN/m. (IV) The impact of different inlet channel geometries and angle on microfluidic drop formation. (V) Droplet formation mode under various contact angles. I is reproduced with permission from [36], Copyright 2015, Royal Society of Chemistry. II is reproduced with permission from [37], Copyright 2009, Springer. III is reproduced with permission from [31], Copyright 2011, Springer. IV is reproduced with permission from [21], Copyright 2009, American Physical Society. V is reproduced with permission from [38], Copyright 2015, Elsevier.

and (II). The influence of two phase flow rates and viscosities on the size of water-in-oil emulsion study at a T-shape microfluidics concluded that the relationship between shear stress and flow rate of continuous phase, thus quantifies the magnitude of shear stress (τ∝ ηcQoil, where η<sup>c</sup> is the viscosity of continuous phase) acting on the interface [13]. As Qwater, the volumetric flow rate of dispersed phase increases, the shear stress exerted on the droplet is increased due to the difference of the flow rate of the two fluids decreases with increasing Qwater. These numerical and experimental results imply that the flow rate of the both phases considerably alter the microdroplet formation mechanisms under laminar flow in different microfluidic configurations. Apart from the effect of two phase flow rates or flow rate ratio, Q = Qd/Qc, the length of the microdroplet formed is also depending on the viscosity ratio (λ = ηd/ηc). Previous investigations reported that an increase of the viscosity of continuous phase gives rise to the viscous stress added on the dispersed phase, and thus decreasing the microdroplet size and alter the flow pattern [11, 20, 39]. This was further validated by a numerical study on the microdroplet detachment mechanism for Newtonian fluids that subjected to cross-flow drag, continuous phase inertia, interfacial tensions, and viscosity ratio, which are shown by the following equations

$$\text{Interfocal tension force}, F\_{\sigma} = \frac{\pi \sigma w\_d^2}{d} \tag{5}$$

$$\text{Cross} - \text{Flow drag force},\\ F\_D = 3\pi \eta\_c (\upsilon^\* - \upsilon\_d) df\left(\lambda\_\eta\right) \tag{6}$$

where d is the droplet diameter, v\* is the continuous phase velocity at the height of the microdroplet center, vd is the microdroplet velocity, λη <sup>¼</sup> ηd=η<sup>c</sup> is the viscosity ratio and f λη <sup>¼</sup> <sup>2</sup> <sup>3</sup> þ λη <sup>=</sup> <sup>1</sup> <sup>þ</sup> λη captures the effect of the disperse phase viscosity on the microdroplet drag. When λη ≫ 1, the disperse phase viscosity is sufficiently high that the microdroplet is solid-like and the interfacial tension force reduces to the drag from Stokes flow around a solid sphere. On the contrary, internal flow within the microdroplet becomes possible and this acts to reduce the drag on the microdroplet from the continuous phase for smaller values of λη [40]. Meanwhile, a detailed studies of droplet microfluidics performance as function of flow conditions as it is crucial when designing the geometry of the microchannel, particularly is one of the major parameter which can be very sensitive to flow conditions and drop properties [41]. Specifically, the cross-sectional area of the main channel can influence the volume of microdroplets detached significantly in both the squeezing regime as well as in the dripping regime as presented here.

#### 2.1.2. Non-Newtonian flow systems

Although there are many methods of producing monodispersed microdroplets, controlling the size of the droplets within the range of 1–100 μm remains to be a challenge that has yet to be fully resolved. Non-Newtonian fluids have far more complex rheological properties that are normally physical and chemical conditions dependent. It also exhibits more complex behaviors in terms of its dynamics in comparison to its Newtonian counterpart, particularly in the field of microfluidics [17]. This is due to the non-linear relationship between the shear rate of the fluid and its viscosity as compared to Newtonian fluids, whose viscosities remain constant regardless of the shear rate. Generally, non-Newtonian fluid can be classified into three general groups in shear flow, which are shown in Table 2.

In an attempt to develop an efficient and reliable drug delivery system, researches have been carried out using various types of non-Newtonian fluids in order to determine which materials would yield the most desirable results. Of all, shear thinning fluids are the most commonly encountered fluids in our everyday lives, many existing as ordinary fluids such

as paints and blood. Due to the rheological property of the latter, the common rule of thumb in designing and developing drug delivery system usually consider shear thinning approach as working mechanism. A mathematical model to simulate the deformation of droplets

Fluids Description Fluid type Model Constitutive equations

Pseudoplastics (Shear-Thinning)

Thixotropy Rheopexy

Viscoplastics Bingham

Ostwald Waele

Carreau-Yasuda

Plastics

Herschel-Bulkley

Generalized Herschel-Bulkley

Viscoelastic Oldroyd-B <sup>τ</sup><sup>1</sup> <sup>þ</sup> <sup>λ</sup><sup>1</sup> <sup>τ</sup>

Giesekus-Leonov

Phan-Thien-Tanner <sup>τ</sup>

White-

Upper-Convected Maxwell

\*Note: Most common models for viscoelastic fluids.μ denotes the shear viscosity; γ denotes the shear rate; f denotes the fiber volume fraction; d and L are the diameter and fiber length; n is the number of the suspension; h is the average distance from a given fiber to its nearest neighbor; τ<sup>p</sup> denotes the shear stress for the polymer; λ denotes relaxation times

and Gk denotes relaxation moduli; N denotes the number of relation modes; Ct

stress tensor; D denotes the strain rate tensor; ξ denotes the adjustable parameters of the model.

Table 2. Comparison of non-Newtonian power-law model fluid behavior [18, 24, 42, 43].

<sup>2</sup>denotes first and second invariants; H is the strain memory function; τ

Cross <sup>μ</sup>�μ<sup>∞</sup>

Ellis <sup>μ</sup> <sup>¼</sup> <sup>μ</sup><sup>o</sup>

Microdroplets Advancement in Newtonian and Non-Newtonian Microfluidic Multiphase System

Casson ð Þ j j <sup>τ</sup> <sup>1</sup>=<sup>2</sup> <sup>¼</sup> <sup>τ</sup><sup>o</sup>

<sup>μ</sup> <sup>¼</sup> <sup>m</sup> ð Þ <sup>γ</sup>\_ <sup>n</sup>�<sup>1</sup>

n

<sup>1</sup>þð Þ <sup>τ</sup>=τ1=<sup>2</sup> α�1

▽

<sup>τ</sup><sup>p</sup> <sup>þ</sup> <sup>λ</sup>1τ<sup>p</sup> � αλ<sup>1</sup>

τ¼τ<sup>1</sup> þ τ<sup>2</sup> τ<sup>2</sup> ¼ 2μ2D

Metzner <sup>τ</sup><sup>1</sup> <sup>þ</sup> λ γð Þ<sup>τ</sup>

K-BKZ <sup>τ</sup><sup>f</sup> <sup>¼</sup> μ γð Þ nL<sup>3</sup>

<sup>τ</sup><sup>p</sup> <sup>¼</sup> <sup>Ð</sup><sup>t</sup> �∞ PN k¼1 Gk <sup>λ</sup><sup>k</sup> exp � <sup>t</sup>�<sup>t</sup>

τ þ λ<sup>1</sup> τ

<sup>D</sup> <sup>¼</sup> <sup>1</sup>

<sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>B</sup> <sup>þ</sup> <sup>μ</sup>ð Þ <sup>γ</sup>\_ for j j <sup>τ</sup> <sup>&</sup>gt; <sup>τ</sup><sup>B</sup> �

<sup>γ</sup>\_ <sup>¼</sup> 0 for j j <sup>τ</sup> <sup>&</sup>lt; <sup>τ</sup><sup>B</sup> �

<sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>H</sup> <sup>þ</sup> <sup>m</sup>ð Þ <sup>γ</sup>\_ <sup>n</sup> for j j <sup>τ</sup> <sup>&</sup>gt; <sup>τ</sup><sup>H</sup> �

<sup>γ</sup>\_ <sup>¼</sup> 0 for j j <sup>τ</sup> <sup>&</sup>lt; <sup>τ</sup><sup>H</sup> �

<sup>τ</sup> <sup>¼</sup> ð Þþ <sup>τ</sup><sup>o</sup> <sup>þ</sup> <sup>τ</sup><sup>1</sup> ð Þ mo <sup>þ</sup> <sup>ξ</sup>m<sup>1</sup> ð Þ <sup>γ</sup>\_ <sup>n</sup>

<sup>1</sup> � 2μ<sup>1</sup> D � λ2D ▽ � �

<sup>2</sup> <sup>þ</sup> μγ\_ <sup>¼</sup> <sup>0</sup>

<sup>μ</sup> τ<sup>p</sup>

▽ <sup>¼</sup> <sup>2</sup>μ γð Þ<sup>D</sup>

u1, <sup>2</sup>S12Sij

0 λk

24ln <sup>2</sup><sup>h</sup> ð Þ<sup>d</sup>

<sup>2</sup> ð Þþ <sup>∇</sup><sup>u</sup> ð Þ <sup>∇</sup><sup>u</sup> <sup>T</sup> h i

▽ <sup>¼</sup> <sup>2</sup>μ<sup>D</sup>

▽ <sup>þ</sup> <sup>ξ</sup> <sup>D</sup> � <sup>τ</sup> � <sup>τ</sup> � <sup>D</sup><sup>T</sup> � � <sup>þ</sup> <sup>Y</sup>

� � �

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149

� � �

> � � �

� � �

¼ 0

<sup>λ</sup> � τ ¼ 2GD

� �H Ið Þ <sup>c</sup>�<sup>1</sup>; IIc�<sup>1</sup> <sup>C</sup>�<sup>1</sup>

�<sup>1</sup> denotes finger strain tensor; Ic-1and IIc-

▽ denotes upper convected time derivative of the

<sup>t</sup> t � �<sup>0</sup> dt0

<sup>c</sup> ð Þ j j <sup>1</sup>=<sup>2</sup> <sup>þ</sup> <sup>μ</sup>j j <sup>γ</sup>\_ � �<sup>1</sup>=<sup>2</sup> for j j <sup>τ</sup> <sup>&</sup>gt; <sup>τ</sup><sup>c</sup> j j <sup>γ</sup>\_ <sup>¼</sup> <sup>0</sup> for j j <sup>τ</sup> <sup>&</sup>lt; <sup>τ</sup><sup>c</sup> j j

<sup>¼</sup> <sup>1</sup> <sup>þ</sup> ð Þ λγ\_ <sup>2</sup> � oð Þ <sup>n</sup>�<sup>1</sup> <sup>=</sup><sup>2</sup>

μ�μ<sup>∞</sup> μo�μ<sup>∞</sup>

μo�μ<sup>∞</sup> <sup>¼</sup> <sup>1</sup> <sup>1</sup>þkð Þ <sup>γ</sup>\_ <sup>n</sup>

Dilatant (Shear-Thickening)

The rate of shear at any point is determined only by the value of the shear stress at that point at that instant; can be known as timeindependent fluids/ generalized Newtonian fluids (GNF).

The relation between shear stress and shear rate further dependence on the duration of shearing and their kinematic history.

characteristics of both viscous fluids and elastic solids and showing partial elastic recovery after deformation.

Viscoelastic\* Substances exhibit

Purely viscous/Time-Independent

Timedependent


Qwater. These numerical and experimental results imply that the flow rate of the both phases considerably alter the microdroplet formation mechanisms under laminar flow in different microfluidic configurations. Apart from the effect of two phase flow rates or flow rate ratio, Q = Qd/Qc, the length of the microdroplet formed is also depending on the viscosity ratio (λ = ηd/ηc). Previous investigations reported that an increase of the viscosity of continuous phase gives rise to the viscous stress added on the dispersed phase, and thus decreasing the microdroplet size and alter the flow pattern [11, 20, 39]. This was further validated by a numerical study on the microdroplet detachment mechanism for Newtonian fluids that subjected to cross-flow drag, continuous phase inertia, interfacial tensions, and viscosity ratio,

Interfacial tension force, F<sup>σ</sup> <sup>¼</sup> πσwd

Cross � Flow drag force, FD <sup>¼</sup> <sup>3</sup>πη<sup>c</sup> <sup>v</sup><sup>∗</sup> ð Þ � vd df λη

where d is the droplet diameter, v\* is the continuous phase velocity at the height of the microdroplet center, vd is the microdroplet velocity, λη <sup>¼</sup> ηd=η<sup>c</sup> is the viscosity ratio and

microdroplet drag. When λη ≫ 1, the disperse phase viscosity is sufficiently high that the microdroplet is solid-like and the interfacial tension force reduces to the drag from Stokes flow around a solid sphere. On the contrary, internal flow within the microdroplet becomes possible and this acts to reduce the drag on the microdroplet from the continuous phase for smaller values of λη [40]. Meanwhile, a detailed studies of droplet microfluidics performance as function of flow conditions as it is crucial when designing the geometry of the microchannel, particularly is one of the major parameter which can be very sensitive to flow conditions and drop properties [41]. Specifically, the cross-sectional area of the main channel can influence the volume of microdroplets detached significantly in both the squeezing regime as well as in the

Although there are many methods of producing monodispersed microdroplets, controlling the size of the droplets within the range of 1–100 μm remains to be a challenge that has yet to be fully resolved. Non-Newtonian fluids have far more complex rheological properties that are normally physical and chemical conditions dependent. It also exhibits more complex behaviors in terms of its dynamics in comparison to its Newtonian counterpart, particularly in the field of microfluidics [17]. This is due to the non-linear relationship between the shear rate of the fluid and its viscosity as compared to Newtonian fluids, whose viscosities remain constant regardless of the shear rate. Generally, non-Newtonian fluid can be classified into three general

In an attempt to develop an efficient and reliable drug delivery system, researches have been carried out using various types of non-Newtonian fluids in order to determine which materials would yield the most desirable results. Of all, shear thinning fluids are the most commonly encountered fluids in our everyday lives, many existing as ordinary fluids such

captures the effect of the disperse phase viscosity on the

2

<sup>d</sup> (5)

(6)

which are shown by the following equations

f λη <sup>¼</sup> <sup>2</sup>

<sup>3</sup> þ λη <sup>=</sup> <sup>1</sup> <sup>þ</sup> λη

148 Microfluidics and Nanofluidics

dripping regime as presented here.

2.1.2. Non-Newtonian flow systems

groups in shear flow, which are shown in Table 2.

\*Note: Most common models for viscoelastic fluids.μ denotes the shear viscosity; γ denotes the shear rate; f denotes the fiber volume fraction; d and L are the diameter and fiber length; n is the number of the suspension; h is the average distance from a given fiber to its nearest neighbor; τ<sup>p</sup> denotes the shear stress for the polymer; λ denotes relaxation times and Gk denotes relaxation moduli; N denotes the number of relation modes; Ct �<sup>1</sup> denotes finger strain tensor; Ic-1and IIc-

<sup>2</sup>denotes first and second invariants; H is the strain memory function; τ ▽ denotes upper convected time derivative of the stress tensor; D denotes the strain rate tensor; ξ denotes the adjustable parameters of the model.

Table 2. Comparison of non-Newtonian power-law model fluid behavior [18, 24, 42, 43].

as paints and blood. Due to the rheological property of the latter, the common rule of thumb in designing and developing drug delivery system usually consider shear thinning approach as working mechanism. A mathematical model to simulate the deformation of droplets through an axisymmetric contraction using shear thinning fluids. When the dispersed phase was a shear thinning fluid and the continuous phase was a Newtonian fluid, the local viscosity of the microdroplet decreased upon entering the contraction, remained at a low viscosity within the contraction and increased upon exiting, resulting in a compact bulletshaped microdroplet at the exit. In contrast, when the continuous phase was shear thinning and the dispersed phase was Newtonian, the microdroplet exited the contraction with a very irregular shape [44, 45].

when the viscosity of the power law fluid is increased with lower behavior index. In the case of CMC, the frequency of microdroplet formation increased when viscosity of dispersed phase is increased (0.02 wt% (w/w)) at each constant rate of Qd; however, the reduction in frequency of droplet formation was observed when the viscosity of CMC polymer fluid is further increased to 0.04% (w/w) where power-law index (n) is smaller than unity contributes to significant effect of shear thinning behavior. This was explained by the other non-Newtonian fluid when the fluid elasticity also plays a key role in resisting the drop pinch off contributes an increase in droplet

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While shear thinning fluids are described as the most commonly encountered non-Newtonian fluid, viscoelastic fluids take the center stage in the synthesis of microdroplets. Such microdroplets are often produced using polymer solutions, such as alginate compounds [47] and polyethylene glycol [48], which have viscoelastic characteristics. This phenomenon was clearly observed in the multiple beads-on-a-string formation. It is determined that for polymer solutions that have high elasticity and extensibility, an extensional response was obtained, even at very low viscosities [49]. An observation on viscoelastic polymers that have larger molecular weight result in a higher elasticity number, El, which consequently increases the pinch-off times of the microdroplets. It was found that the size of the aperture affects the pinch-off times, whereby increasing the size of the apertures increases the pinch-off times [50]. This was validated by a demonstration on the production of monodisperse double emulsion microparticles from various non-Newtonian polymer solutions, one of which exhibited viscoelastic characteristics [21]. It was determined that when the viscoelastic solution was used as the inner fluid, the viscoelasticity of the fluid prevented microdroplets from pinching off from the orifice. This resulted in oscillations that are brought downstream by the continuous phase, which consequently brought about the

The development of emulsification via microfluidic in the past decades is embodied in various fields. In the aspect of system design and fabrication, continuous reports with regards to new material development coupled with creative, novel fabrication techniques, enable evolutional microfluidic system from conventional two-dimensional (2D) straight microchannel to multifunctional three-dimensional (3D) systems [51]. In the aspect of theory and applications, in-depth understanding of the flow dynamic as mentioned in the previous section leads to much unique systems design for generation and manipulation of droplets with diverse behaviors and surface morphologies in various applications being reported [52–54]. Although the encapsulation process may seem straightforward, there are few considerations need to be noted. One common technique used is the addition of surface active agent to either continuous or dispersed phase. Such addition can create distinctive microdroplets formation, but not always an ideal solution to the development of more complex microfluidic systems with

breakup time.

beads-on-a-string phenomenon [49].

3. Microdroplets formation

3.1. Microdroplets encapsulation

The influence of the dispersed phase viscosity between Newtonian and shear-thinning fluid on generated droplet size in microfluidic T-junctions are illustrated in Figure 3. The experimental results indicate that the larger viscosity of dispersed phase fluid brings the significant effect on reducing the size of generated microdroplet at each constant value of Qd. Also, when the concentration of dispersed fluid is increasing from 0 to 60 wt% at constant value of Qd of 0.6 mL/h; there will be a reduction in microdroplet size formed due to the change in the viscosity from 0.928 to 8.406 cP. Nevertheless, the similar phenomenon is not found when Qd exceeds 1.2 mL/h in the condition of 60 wt%, viscosity of 8.406 cP for dispersed fluid. At Qd of 1.2 mL/h, for the lower dispersed fluid viscosity ranging from 0.928 to 3.191 cP, the microdroplet volume is decreased. However, it is increased for the higher viscosity dispersed fluid (8.406 cP) due to a convectively unstable jetting regime that took place in which microdroplet formation lacks both periodicity and size uniformity therefore highly polydispersed in size were produced. When Qd is further increased to a high relatively flow rate, a transition between convectively unstable flow and droplet breakup begins to prevail. This can be explained by the instabilities of microdroplets due to the inertia effects at the T-junction, begin to dominate in the dispersed phase and then evolve in the microchannel which is characterized by long instability wavelengths [46]. The behavior of the perturbations propagates in the direction of the flow and the dispersed phase does not break into microdroplet which is also defined as convective instability or unstable stratified flow. In contrast, reduction in carboxymethylcellulose (CMC) microdroplet size relative to drop volume was observed in larger power-law index; however, the size of droplet shrinks


Figure 3. Representative outcomes for the effect of Newtonian (water-glycerol) and non-Newtonian CMC dispersed phase viscosity on droplet generation frequency in microfluidics T-junction.

when the viscosity of the power law fluid is increased with lower behavior index. In the case of CMC, the frequency of microdroplet formation increased when viscosity of dispersed phase is increased (0.02 wt% (w/w)) at each constant rate of Qd; however, the reduction in frequency of droplet formation was observed when the viscosity of CMC polymer fluid is further increased to 0.04% (w/w) where power-law index (n) is smaller than unity contributes to significant effect of shear thinning behavior. This was explained by the other non-Newtonian fluid when the fluid elasticity also plays a key role in resisting the drop pinch off contributes an increase in droplet breakup time.

While shear thinning fluids are described as the most commonly encountered non-Newtonian fluid, viscoelastic fluids take the center stage in the synthesis of microdroplets. Such microdroplets are often produced using polymer solutions, such as alginate compounds [47] and polyethylene glycol [48], which have viscoelastic characteristics. This phenomenon was clearly observed in the multiple beads-on-a-string formation. It is determined that for polymer solutions that have high elasticity and extensibility, an extensional response was obtained, even at very low viscosities [49]. An observation on viscoelastic polymers that have larger molecular weight result in a higher elasticity number, El, which consequently increases the pinch-off times of the microdroplets. It was found that the size of the aperture affects the pinch-off times, whereby increasing the size of the apertures increases the pinch-off times [50]. This was validated by a demonstration on the production of monodisperse double emulsion microparticles from various non-Newtonian polymer solutions, one of which exhibited viscoelastic characteristics [21]. It was determined that when the viscoelastic solution was used as the inner fluid, the viscoelasticity of the fluid prevented microdroplets from pinching off from the orifice. This resulted in oscillations that are brought downstream by the continuous phase, which consequently brought about the beads-on-a-string phenomenon [49].
