A liquid crystal model for early cell division

A variational principle based on the curvature energy of a two dimensional liquid crystal membrane is constructed to determine the equilibrium shape of a cell with given surface area and volume. A sequence of the forms, calculated numerically, displays the process of cell division.     

Possible smectic A ordering in a droplet of 4-n-octyloxybenzoic acid liquid crystal

Our microtextural as well as depolarized light scattering analyses of 4-n-octyloxybenzoic acid liquid crystal droplets provide evidence for a possible smectic A ordering induced by the free surface. This appears near the bulk smectic C-nematic transition at T_SCN. A simple mean field analysis, based on a Landau-de Gennes-Benguigui free energy functional with an additional surface parameter K_s, allows, in principle, the possibility for a smectic A surface phase at temperatures slightly above T_SCN.     

Possible smectic A ordering in a droplet of 4-n-octyloxybenzoic acid liquid crystal

Abstract

Our microtextural as well as depolarized light scattering analyses of 4-n-octyloxybenzoic acid liquid crystal droplets provide evidence for a possible smectic A ordering induced by the free surface. This appears near the bulk smectic C-nematic transition at T _SCN. A simple mean field analysis, based on a Landau-de Gennes-Benguigui free energy functional with an additional surface parameter K _s, allows, in principle, the possibility for a smectic A surface phase at temperatures slightly above T _SCN.     

On the solidification of a supercooled liquid droplet lying on a surface

We model the solidification and subsequent cooling of a supercooled liquid droplet that is lying on a cold solid substrate after impact. It is assumed that solidification occurs for a given fixed droplet shape. The shapes used by the model are a sphere, truncated spheres, and an experimentally registered droplet shape. The freezing process is conduction-dominant and is modeled as a one-phase Stefan problem. This moving boundary problem is reformulated with the enthalpy method and then solved numerically with an implicit finite-difference technique. The numerical results for the simple case of a spherical droplet touching a surface are similar to those of a freely freezing spherical droplet and are well confirmed by the 1D asymptotic analytical model of Feuillebois et al. (J. Colloid Interface Sci. 169 (1995) 90). A freezing water droplet is considered as an example. The numerical results for full freezing time, subsequent cooling time, and last freezing point coordinate for the various droplets shapes are fitted by analytical functions depending on supercooling, thermal resistance of the target surface (expressed by Biot number), and spreading parameter. These functions are proposed for direct application, thus avoiding the need to solve the full freezing and cooling problem.     

Manipulating microobject by using liquid droplet as a transporting vehicle

Wetting in the system hematite–water–diisobutyl ketone was studied in the presence of an anionic surfactant, hexadecyl sulfonic acid. Adsorption isotherms of surfactant on hematite powder were measured separately at the interfaces between hematite–water and hematite–ketone, and the interfacial tension of the water–ketone interface was determined as a function of surfactant concentration. The Gibbs and Young’s equations were used to calculate contact angles from the adsorption data. For comparison, contact angles were measured as a function of surfactant concentration on the face of a hematite crystal selected from the same supply of specular hematite used for preparing the hematite powder. Overall, contact angles calculated from the equations correlate closely with measured contact angles.     

Hydrodynamic interaction of a nonvolatile droplet with a planar surface of evaporating liquid

Hydrodynamic interaction between a nonvolatile droplet and an infinite planar surface of an evaporating or condensing liquid is studied theoretically with allowance for effects that are linear with respect to the Knudsen number. The motion of the droplet in the direction normal to the planar liquid surface is considered at low Reynolds numbers and gradients of a gaseous medium temperature and the concentration of the substance evaporating or condensing on the planar liquid surface given at an infinitely large distance from the droplet. The presence of a temperature gradient in the liquid is taken into account in the analysis. The problem is solved in a bispherical coordinate system. The velocity of the steady motion of a castor oil droplet is numerically estimated near the planar surface of evaporating water.     

Actuation of adaptive liquid microlens droplet in microfluidic devices: A review

A significant growth of research on adaptive liquid lens is achieved over the past decades, and the field is still attracting increasing attentions, focusing on the transition from the current stage to the commercialized stage. The challenges faced are not limited to fabrication, material, small tuning range in focal lengths, additional control systems, limitations in special actuation methods and so on. In addition, the use of external driving parts or systems induce extra problem on bulky appearance, high cost, low reliability etc. Therefore, adaptive liquid lens will be an interesting research focus in both microfluidics and optofluidics science. This review attempts to summarize and focus on the droplet profile deformation under different driving mechanisms in tunable liquid microlens as well as the application in cameras, cell phone and so on. The driving techniques are generally categorized in terms of mechanisms and driving sources.     

Numerical analysis for a nematic droplet in polymer dispersed liquid crystals

Starting from the Landau-de Gennes free energy expression, the author has numerically analysed the director pattern in a nematic droplet of polymer dispersed liquid crystals. The nematic director has been understood as the eigenvector, which corresponds to the largest eigenvalue of the tensor order parameter. To investigate the droplet structure influence, all equations have been treated on the curvilinear coordinate system which is generated along the droplet boundary. In the case of spherical and spheroidal droplets with normal strong anchoring, the director exhibits an axial configuration and a disclination ring. The ring radius and the capactiance of the system change without hysteresis with the applied voltage.     

A model for the chevron structure obtained by cooling a smectic A liquid crystal in a cell of finite thickness

We propose a simple model for the chevron structure observed in recent experiments by cooling a smectic A liquid crystal. We discuss the influence of the cell thickness and of the anchoring conditions on the temperature dependence of the layer tilt angle, and the formation of this structure in the vicinity of a smectic A—nematic transition. Below this critical point, a transition between a bookshelf structure and a chevron one appears. This transition is second order, with continuity of the tilt angle, the threshold being a function of the cell thickness. In addition to a classical layer thinning mechanism, we discuss another possibly based on the temperature dependence of the elastic moduli. We also propose an explanation for the existence of a critical thickness below which the chevrons do not appear.     

Dynamic simulation of droplet interaction and self-assembly in a nematic liquid crystal

We use dynamic simulations to explore the pairwise interaction and multiparticle assembly of droplets suspended in a nematic liquid crystal. The computation is based on a regularized Leslie-Ericksen theory that allows orientational defects. The homeotropic anchoring on the drop surface is of sufficient strength as to produce a satellite point defect near the droplet. Based on the position of the defects relative to the host droplet and the far-field molecular orientation, we have identified five types of pairwise attractive and repulsive forces. In particular, long-range attraction between two droplets with their line of centers along the far-field orientation decays as R-4, with R being the center-to-center separation. This agrees with prior static calculations and a phenomenological model that treats the attraction as that between two dipoles. For interaction in shorter ranges, our simulations agree qualitatively with experimental measurements and static calculations. However, there is considerable quantitative discrepancy among the few existing studies and our simulation. We suggest that this is partly due to the dynamic nature of the process, which has never been taken into account in prior calculations. Multidrop simulations show the formation of linear chains through pairwise interactions between nearby droplets. Parallel chains repel or attract each other depending on the relative orientation of the drop-to-defect vector. These are consistent with experimental observations of chain formation and two-dimensional self-assembly in bulk nematics and smectic-C films.     

Regular self-motion of a liquid droplet powered by the chemical marangoni effect

We describe here our recent work on spontaneous regular motion of liquid droplet powered by the chemical Marangoni effect under spatially symmetric conditions. It is shown that a spontaneously crawling oil droplet on a glass substrate with a nonequilibrium chemical condition of cationic surfactant exhibits regular rhythmic motion in a quasi-one-dimensional vessel, whereas irregular motion is induced in a two-dimensionally isotropic environment. Such behavior of a droplet demonstrates that spontaneous regular motion can be generated under fluctuating conditions by imposing an appropriate geometry. As another system, we introduce alcohol droplet moving spontaneously on water surface. The droplet spontaneously forms a specific morphology depending on its volume, causing specific mode of translational motion. An alcohol droplet with a smaller volume floating on water surface moves irregularly. On the other hand, a droplet with a larger volume undergoes vectorial motion accompanied by deformation into an asymmetric shape. This result suggests a scenario on the emergence of regular motion coupled with geometrical pattern formation under far-from-equilibrium conditions.     

Electric field studies of liquid crystal droplet suspensions

The responses of freely-suspended micron-sized liquid crystal droplets subjected to an alternating electric field are presented. By examining droplets of isotropic, nematic bipolar, and nematic radial configurations, we test the effect of anchoring on the droplet response. Specifically, using birefringence and scattering dichroism we measure the relaxation of electric field-induced orientation following a field pulse. Results indicate that bipolar and radial droplets in suspension orient in the field through very different mechanisms. Bipolar droplets are observed to rotate their defect axes in the field while radial droplets orient through a nematic distortion. By varying the field pulse, we observe that droplets also respond differently to the field depending on their relative sizes. In radial droplet suspensions we quantitatively measure time scales associated with the reorientation and restructuring of the defect region.     

On the evaporation and motion of a volatile droplet near a volatile liquid surface

A problem concerning the free evaporation or condensation growth of a droplet near an infinite planar surface of the same liquid is solved. The behavior of the droplet is considered at vapor temperature and concentration gradients preset at an infinite distance from it. The boundary conditions take into account effects that are linear with respect to the Knudsen number. Equations are derived for the rate of variations in the radius of the droplet and the velocity of its steady motion induced by nonuniform temperature and concentration of the vapor. Dependences of the rate of variations in the radius and the velocity of the steady motion of the droplet on the distance from the planar surface are presented for a droplet 1 ??m in radius suspended in air.     

Evaluation of the force required to move a coalesced liquid droplet along a fiber

This work presents a theoretical model describing the force required to move a coalesced liquid droplet along an oleophilic filter fiber. Measurements have been made using the atomic force microscope (AFM) to examine these forces over a range of fiber and droplet diameters as well as oil properties. Good agreement between measured and modeled forces was found. The influence of droplet displacement perpendicular to the fiber on the force required to move the droplet has also been determined experimentally and theoretically. It was found that fiber surface inhomogeneities are likely to influence results. This work has also established empirical relationships that can be used to predict the force, based on a known droplet volume, for the liquid types used.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

Analysis of the equilibrium droplet shape based on an ellipsoidal droplet model

The extent of a droplet's spreading over a flat, smooth solid substrate and its equilibrium height in the presence of gravity are determined approximately, without a numerical solution of the governing nonlinear differential equation, by assuming that the droplet takes on the shape of an oblate spheroidal cap and by minimizing the corresponding free energy. The comparison with the full numerical evaluations confirms that the introduced approximation and the obtained results are accurate for contact angles below about 120° and for droplet sizes on the order of the capillary length of the liquid. The flattening effect of gravity is to increase the contact radius and decrease the height of the droplet, with these being more pronounced for higher values of the Bond number.     

Hydrodynamic interactions of evaporating droplet with plane liquid surface

The hydrodynamic interactions between freely evaporating or growing droplet suspended in gas and the infinite plane liquid layer is theoretically studied with allowance for effects that are linear with respect to the Knudsen number. It is assumed that substances comprising droplet and liquid layer are identical, and it is taken into account that these substances can contain dissolved nonvolatile component whose concentration is so low that its presence should necessarily be accounted for only in the calculation of the concentration of saturated vapor. Vapor pressure at large distance from the droplet was assumed to be equal to the pressure of saturated vapor above the plane liquid surface. Results of numerical calculations of the rate of steady motion of water droplet evaporating or growing in the air are reported.     

Pumpless dispensing of a droplet by breaking up a liquid bridge formed by electric induction

Dispensing uniform pico‐to‐nanoliter droplets has become one of essential components in various application fields from high‐throughput bio‐analysis to printing. In this study, a new method is suggested and demonstrated for dispensing a droplet on the top plate with an inverted geometry by using electric field. The process of dispensing droplets consists of two stages: (i) formation of liquid bridge by moving up the charged fluid mass using the electrostatic force between the charges on the fluid mass and the induced charges on the substrate and (ii) its break‐up by the motion of the top plate. Different from conventional electrohydrodynamic methods, electric induction enables the droplets to be dispensed on various surfaces including non‐conducting substrate. The use of capillarity with an inverted geometry removes the need of external pumps or elaborates control for constant flow feed. The droplet diameter has been characterized as a function of the nozzle‐to‐plate distance and the plate moving velocity. The robustness of the present method is shown in terms of nozzle length and applied voltage. Finally, its practical applicability is confirmed by rendering a 19 by 24 array of highly uniform droplets with only 1.8% size variation without use of any active feedback control.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.