Liquid Crystal Foams Generated by Pressure-Driven Microfluidic

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Liquid Crystal Foams Generated by Pressure-Driven Microfluidic Devices Shuojia Shi, and Hiroshi Yokoyama Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b00659 • Publication Date (Web): 30 Mar 2015 Downloaded from http://pubs.acs.org on April 5, 2015

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Liquid Crystal Foams Generated by Pressure-Driven Microfluidic Devices Shuojia Shi and Hiroshi Yokoyama* Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA

ABSTRACT

Thermotropic liquid crystals possess superior foaming capability without the aid of surfactants because of the anisotropic molecular structures. We developed a T-junction microfluidic device to inject gas bubbles of uniform size into a liquid crystal in the nematic and the smectic phases. The bubble size is primarily determined by the dimension of microfluidic channel regardless of the phase, and air bubbles of a few tens of micrometer diameter were stably injected at the rate up to 110Hz to the close packing density with a polydispersity less than 4%. It is shown that an efficient path to fabricate stable liquid crystal foams is to inject bubbles in the nematic phase, where the highest inject rate is possible, and promptly cool it down to the smectic phase.

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Introduction Liquid crystals are partially ordered fluids in which the constituent anisotropic molecules are preferentially oriented over a macroscopic length scale.1 When the positions of the molecules do not possess a long-range order, it is the nematic liquid crystal, which is least viscous of all liquid crystal phases and is extensively utilized as the key component of liquid crystal displays. If a long-range positional order emerges at least in one dimension, the smectic liquid crystal is formed, characterized macroscopically by a much higher viscosity and microscopically by molecular scale layered structures. For the last two decades, the liquid crystal colloid, a composite consisting of liquid crystal host and dispersed particles, has attracted considerable attention due to the intricate topological structures that the coupling between the orientational order and the particle(s) generates, as well as the unique inter-particle forces mediated by the orientational elasticity of liquid crystals.2-6 These elastic inter-particle forces are long-ranged and so strong as to overwhelm the conventional forces such as electrostatic and van der Waals forces between colloidal particles, thereby exerting a decisive impact on the stability of the colloidal structures.4 The particles can be solid,4,6 liquid2 or gas.5 This paper is concerned with a liquid crystal colloid using gas bubbles as the colloidal inclusion. Distinctive features of gas bubbles as compared with solid and liquid particles are that the gas bubbles are deformable and variable in size by means of external pressure and/or through the absorption, desorption and diffusion of the gas molecules. As the volume fraction of gas increases, the colloidal system evolves to a composite system that is more appropriately referred to as foams.7 Depending on whether the gas fraction is lower or


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higher than the volume fraction of sphere at the close packed state, c.a. 74%, foams are roughly categorized as wet and dry foams. As a foam is gradually transformed from wet to dry condition by draining the host liquid or injection of more gas bubbles, the liquid film separating the bubbles becomes thinner and eventually destabilized against spontaneous rupture that results in coalescence of bubbles. The instability of thin liquid films is a universal consequence of the van der Waals interaction,8 and hence in most cases, a foaming agent such as surfactants is employed as an additive to the host liquid in order to stabilize foam structures.7 Here we demonstrate that, because of the elasticity mediated inter-particle interactions, liquid crystals are inherently capable of foaming without any additives.5,9 In view of their possible applications in photonics and our basic interest in the structural evolution of liquid crystal foams at the microscopic scale, we aimed to develop and characterize a microfluidic device system for generation of mono-dispersed regular foam using liquid-crystal hosts. Experimental Microfluidic devices are extremely useful to efficiently process a small amount of liquid for a wide range of applications. There have been several attempts to use microfluidics to generate colloids, emulsions or foams.10-12 Detailed behaviors of liquid crystals in microfluidic devices and their utility for manipulation of liquid crystal colloids have also been recently demonstrated.13,14 Of particular interest for the current purpose is the T-junction design11,12 that allows a channel-dimension-regulated generation of liquid or gas particles at a relatively high generation rate and density in a host liquid. Despite the simple design, a few precautions about the geometry and the operation conditions are in order to obtain an optimal performance. The schematic diagram in Figure 1 illustrates the device structure consisting of the liquid channel


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running horizontally and the vertical gas channel ending at the T-junction. With the small Reynolds number, the flow rate through the channels is given by Poiseuille’s law15:

=

( − ) (1)

where , and are the width, the depth and the length of the rectangular channel, and

are the pressures at the inlet and the outlet, is the shear viscosity of the fluid, and is a

dimensionless function of /, approximately given by ≈ +

( + ).

Let us begin with the initial condition that the liquid crystal is steadily flowing from the inlet (held at a constant pressure ) to the outlet (held at a constant pressure ) at the rate given by Equation 1. The pressure inside the liquid crystal linearly varies from the inlet to the outlet; at the T-junction where the gas channel meets the liquid crystal channel, the pressure is given by = ( + )/( + ). If the pressure in the gas channel is higher than by the Lapalace pressure = 2(1⁄ + 1⁄ ) where is the surface tension of the liquid crystal, the gas blows up into the liquid crystal channel in a catastrophic manner and clogs the liquid crystal channel (Figure 1). As the gas bubble blocks the liquid crystal flow, the pressure at the Tjunction jumps up to the inlet pressure to give = . If the gas pressure is not too high to satisfy < , the gas is then pushed back into the channel to detach the gas bubble and restores the initial flow. This oscillatory behavior of the pressure at the T-junction is essential for generation of isolated gas bubbles. Therefore, if the T-junction is located close to the inlet or the outlet as depicted in Figure 1, is virtually fixed at either or , making the pressure


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oscillation impossible. Gas bubbles can be generated only when the gas pressure is at least in the range:

1 1 + 2 ! + " +

+

(2)

If the gas pressure is too high, i.e.

, only the gas flows through the channel to the outlet;

If the gas pressure is too low, only the liquid continuously flows through the channel to the outlet.

Figure 1. T-junction microfluidic device. The liquid flows from the inlet on the left to the outlet. With the use of ≈ 30mN/m as a typical value of surface tension for thermotropic liquid crystals in the nematic16.17 and smectic18 phases, the contribution of the Laplace pressure at the junction is estimated to be 2(' + ' ) ≈ 10kPa, which is large enough to have a noticeable impact on the bubble generation behaviors as will be shown below.


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Figure 2. Top view of the T-junction microfluidic device. Based on these considerations, we designed and fabricated a T-junction microfluidics with the following geometry: = = 400μm, = 40μm, = 10μm and the depth = 12μm. Figure 2 shows the optical micrograph of the microfluidic device with the T-junction at the center of the liquid crystal channel running from left to right. For both channels, filters were fabricated upstream to prevent rare but unavoidable dust particles in the flow from accidentally clogging the channels. A 12μm-thick photoresist (AZ9260,MicroChemicals) negative pattern of the device was photolithographically prepared on a glass slide by using the maskless photoexposure system developed in-house,19 which has a capability to project arbitrary computer-generated optical patterns in the near ultraviolet range on substrates with the finest resolution below 2μm. After development, the resist pattern was transferred to PDMS (Polydimethylsiloxane) by applying a vacuum-degassed 10:1 mixture of PDMS precursor and initiator (Sylgard 184, Dow Corning) and by curing it at 65/ for 2 hours. The formed PDMS was peeled off from the glass slide.

Small inlet and outlet holes were then punched in the

PDMS at the prescribed positions. The surfaces of the PDMS and a fresh glass slide were


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activated with oxygen plasma in a reactive etching chamber (RIE-1, Samco), and were bonded together to form the closed microfluidic device.

Using these design rules, the base flow rate of

the liquid crystal through the liquid channel can be estimated20 from Equation (1) to be ≈ 6 0 10' μl 0 ( − )' , which, for = 10mPa ∙ s and − = 100kPa, yields ≈ 6μl ∙ s ' .

Figure 3. Schematic illustration of the experimental setup. The outlet is open to the atmospheric pressure, while the pressure on the liquid crystal (LC) and the gas pressure are separately controlled. Figure 3 shows the overall experiment setup. Instead of the standard constant-flow operation using motorized syringes, we adopted the constant pressure mode driven by pressure-regulated air sources. Since, as indicated above, the pressure plays the primary role in the spontaneous bubble generation at the T-junction, we expect the pressure-driven system to be more stable in operation and straightforward to be analyzed. The microfluidic device was fixed in a temperature-regulated acrylic enclosure equipped with a temperature-controlled air circulator with the accuracy of 0.1/. The enclosure was fixed on the sample stage of a Nikon inverted


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microscope, and microscopic images were captured with a high-speed camera (Phantom v211, Vision Research) at a frame rate of 2000 frames/sec. As the liquid crystal host, we used 4-octyloxy-4′-cyanobiphenyl (8OCB) that is enantiotropic with the phase sequence, Solid|54.0/|Smectic A|67.5/|Nematic|80.5/|Isotropic.20 The liquid crystal was held in a clean glass syringe connected to the inlet of the microfluidic device with PTFE tubing. The other opening of the syringe was subjected to pressure-regulated air to drive the liquid crystal into the microfluidic channel. The applied pressure was limited below 110kPa, relative to the atmospheric pressure, in order to avoid structural failure of PDMS-glass microfluidics. In the present experiments, the outlet was kept open to the ambient air, i.e. = 0kPa. Results and Discussion A particularly striking observation is the ability of the T-junction microfluidic device to inject gas bubbles stably by setting proper inlet pressures even into a highly viscous smectic A liquid crystal phase as well as into the nematic phase as shown in Figure 4(a). In the smectic phase, however, the shape of the bubble is distorted from a spherical shape due to the relative weakness of the capillary force compared to the shear force; opposite is the case in the nematic phase (see below). The gas bubbles remain isolated without coalescence even in a congested state at the outlet, owing to the repulsive forces between bubbles originated in the orientational elasticity3,4 and the layered molecular structures in the smectic A phase.21,22


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(a)

(b)

Figure 4. High-speed snapshot of gas bubbles generated in the T-junction microfluidic device (a) and the flow phase diagram (b) for 8OCB in smectic A phase at 58.9/.

Figure 4(b) shows a typical flow phase diagram in the space of the liquid pressure versus the gas pressure . For a given liquid pressure, we gradually increased the gas inlet pressure from the initial state of continuous flow of liquid to the high-pressure state of continuous flow of gas, through a medium range of pressure allowing for generation of isolated gas bubbles injected in


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the liquid crystal. From the smectic A through the nematic phase, the flow phase diagram is virtually independent of temperature, and indicates that 1) bubble generation occurs only above a certain threshold pressure, 2) there is a range of gas pressure for bubble generation that grows wider as the pressure is increased, and 3) the range of gas pressure is always lower than the liquid pressure. These behaviors are universal regardless of temperature, in consistence with the expectations from the inequality in Equation 2.

The presence of a threshold pressure of about

40kPa for bubble generation can be ascribed to the maximum Laplace pressure at the T-junction for a bubble to emerge. Given the previous estimate of 10kPa, Equation 2 requires that the pressure at the liquid inlet must at least be 20kPa to overcome the Laplace pressure; furthermore, by taking into account the gradual increase of pressure at the T-junction as the bubble grows, there must be a considerable margin for the liquid inlet pressure, pushing the threshold pressure even higher.12

As a function of , the observed lower bound of the bubble

generation regime closely follows ≈ 20kPa + /2, corroborating the above arguments. The volume fraction of gas continuously increases from 0% at the lower bound gas pressure to 100% at the upper bound, and was observed to be stable at a fixed gas pressure well inside the bubble generation regime. Shown in Figure 5 is the detailed time sequence of bubble generation at the T-junction in the smectic A phase, occurring at the rate of approximately 18 bubbles/sec. An embryo of gas bubble emerging at the T-junction (c: 22ms) grew within 11ms to an extended eye-drop shape, blocking the liquid channel (d: 33ms) and was then detached from the junction to the outlet. The extended bubble shape is an indication that the flow is only partially blocked, still exerting shear stress on the gas bubble. As a result, the pressure at the T-junction cannot be the same as the liquid inlet pressure as the simple scenario predicts. This fact qualitatively accounts for the


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observation that the upper bound gas pressure is systematically lower than the liquid inlet pressure (Figure 4).

Figure 5. Sequential micrographs of gas bubble generation at the T-junction for the period of 55msec. The liquid inlet pressure was 110kPa and the gas inlet pressure was 91kPa at 62.8/ in the smectic A phase of 8OCB. The rate of bubble generation is significantly increased as the temperature is raised from the smectic A to the nematic phase as shown in Figure 6. It shows more than one order of magnitude increase to above 100Hz for 10 degrees of temperature rise. The fact that there appeared no discontinuity at the phase transition is in agreement with the continuous nature of the phase change between smectic A phase and nematic phase; however, the generation rate is enhanced at a much higher pace than the shear viscosity of the liquid crystal. Indeed, the apparent activation energy for the bubble generation rate is ca. 300kJ/mol, while the activation energy of the shear viscosity of 8OCB is on the order of 40kJ/mol.20 In contrast, the diameter of the bubble, as


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calculated from its volume assuming a sphere, exhibits only a minor decrease across the phase transition temperature. This result seems reasonable in view of the fact that the bubble size is primarily determined by the geometry of the liquid channel, except for the pressure region close to the upper bound. The slight increase toward the smectic A phase may be ascribed to the extension of the emerging bubble by the shear drag force.12 With this result in mind, the anomalous increase of bubble generation rate can be roughly understood as coming from the degree of ease of cyclic detachment of emerging bubbles at the T-junction. This is a complicated hydrodynamic nonlinear process,12 but one can notice that for a given gas inlet pressure, there always exists an upper limit for the bubble generation rate given by the continuous flow rate of gas through the T-junction divided by the volume of a bubble. Because of the weak temperature dependence of the viscosity of gas, this upper limit is virtually constant over the narrow temperature range of the present experiment. On the other hand, the time needed for the bubble detachment, regulated by the Laplace pressure, will rapidly increase with the increase in the shear viscosity, especially in the smectic phase where the capillarity is dominated by the viscosity. As the gas pressure is increased, the Laplace pressure works less favorably for the detachment action, making the detachment time even longer. At the point where the detachment time is long enough for the continuous flow to occur, the bubble generation is terminated. This scenario is qualitatively in line with the observation that the upper bound gas pressure is significantly below the liquid inlet pressure.


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Figure 6. The rate of bubble generation (a) and the bubble diameter (b) as a function of temperature. The liquid inlet pressure is 101.0kPa and the gas inlet pressure is 84.7kPa. In the nematic phase, the bubble assumes a spherical shape when it is released from the microfluidic channel into a bulk cell with a thickness much larger than the bubble size. In a previous study, Trittel et al.9 reported that larger 2D gas bubbles are unstable in the nematic phase against coalescence; in the present experiment, however, smaller bubbles with a few tens of micrometers of diameter remain mechanically stable even in the nematic phase due to the orientational elastic repulsion between curved surfaces. In the nematic phase, the orientation of the liquid crystal at the bubble surface is perpendicular, so when the liquid crystal is confined between two such spherical surfaces, an orientational distortion is induced. A simple calculation of the elastic deformation energy in the Derjaguin approximation yields the repulsive force as


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89 = 2:;(1 + ln (> ? ⁄ℎ)), where ; is the Frank elastic constant1 for bend deformations on the order of 10pN, ? and ℎ are the radius of the bubble and the separation between the bubble surfaces, and > is a constant of the order unity. This shows the repulsive force is virtually constant with a weak dependence on ? ⁄ℎ. Between the two gas bubbles there also exists a van der Waals attractive force, which is written as 8A = BC ? ⁄12ℎ with BC being the Hamaker constant.23 The attractive force increases rapidly as the two bubbles approaches closer. Using the typical value BC = 5 0 10'C J, however, we can see that the elastic repulsive force is dominant for a 10Em-radius bubble as long as the separation is larger than 30nm. Arguably, the smaller the bubble, the orientational repulsion is proportionately more dominant over the van der Waals attraction, thereby making the LC foam more stable. In practice, however, the microfluidics channel must be reduced as , ∝ ?, which results in a drastic plummet of flow rate as ? H . In order to keep the flow rate constant, the channel length has to be impractically short and/or the pressure must be intolerably high. Consequently, microfluidics generation of 1Em-radius bubbles is considered impractical, if not totally impossible. Moreover, smaller bubbles with a higher internal pressure are more prone to absorption by the host liquid crystal.5 As shown in Figure 7(a), the bubbles generated by the microfluidic device are highly uniform in size with the initial size distribution of 4% or less. At the close packing density, the spherical bubbles, subjected to a uniform flow in the cell, adopt the face-centered-cubic (FCC) structure with the (100) surface in contact with the glass substrate of the bulk cell. In Figure 7(a), the spherical bubbles on the second layer are visible through the hollow lattice spaces in the first layer. This result agrees well with the previous observation on the shear-induced self-assembly of FCC crystals in hard sphere colloids by Liu et al.24 The thickness of the nematic layer


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separating the bubbles was so small that the layer remained indiscernible even under a higher magnification with a resolution better than 1μm. The FCC structure and the spherical bubbles are highly stable under flow conditions. When the flow ceases, however, the monodispersity starts to deteriorate after a latency period of ca. 40s through the Ostwald ripening,25 resulting in the growth of certain bubbles at the sacrifice of others without coalescence over a few minutes. Figure 7(b) shows a volume (~0.1cc) of the 3D liquid crystal foam generated by the microfluidic device; here, the bubbles were injected in the nematic phase at a faster rate, and the resultant foam was immediately ejected from the outlet into the reservoir held at a lower temperature to cool it down to the smectic phase. Once the foam is in the smectic phase, the Ostwald ripening was largely suppressed, allowing for a long term stability of the liquid crystal foam structure.


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(a)

(b)

Figure 7. Nearly close-packed spherical bubbles in the nematic phase (a), and the volume of liquid crystal foam (white froth) collected and cooled to room temperature in the reservoir outside the outlet, to the right of the T-junction located at the center (b). The liquid crystal foam in the smectic A phase was found to be indefinitely stable without a noticeable change in volume over the period of weeks. In (a), the bright spots are due to optical lens effects associated with the spherical shape of gas in the liquid crystal. Conclusions


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We have demonstrated that neat thermotropic liquid crystals are capable of supporting stable 3D foam structures both in the nematic and in the smectic phases as long as the air bubbles are sufficiently small. The T-junction microfluidic devices, driven in a constant pressure mode, have proved to be a practical tool for efficient fabrication of liquid crystal foams. Finally, a word may be in order about the theoretical speed limit of the T-junction microfluidics. Since the selfregulated oscillation of pressure at the T-junction is the essential mechanism of bubble generation, the propagation of pressure wave (sound wave) from the inlet to the junction gives the upper limit. For a 400Em-long liquid channel, the propagation time is estimated to be 4 0 10' s with the sound velocity being assumed 1km/s. This is translated to the bubble generation frequency of 2.5MHz, which is comparable with the highest rate in the flow focusing device.10 This crude argument implies that there is orders of magnitude margin for improving the foam generation rate by the T-junction microfluidics, provided the pressure is proportionately increased, and the device is so made to withstand the increased pressure.

AUTHOR INFORMATION Corresponding Author *Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA. [email protected] Author Contributions


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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT Financial support by the Ohio Research Scholar Award, Ohio Third Frontier Program, the State of Ohio, USA and the grant-in-aide by Omichi Industry Co. is gratefully acknowledged.

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Langmuir

129x159mm (150 x 150 DPI)


Liquid Crystal Foams Generated by Pressure-Driven Microfluidic

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