## About

63

Publications

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Introduction

We are interested in modeling natural phenomena using equations and solving those equations by analytical and numerical methods. Currently, we are modeling heat and mass transfer in flat heat pipes.

Education

August 1985 - May 1992

August 1982 - May 1985

## Publications

Publications (63)

Flat heat pipes have been used in cooling computer chips. However, previous models impose heat rate through the pipe as an input parameter, preventing optimization of heat transfer. We consider a hori- zontal flat heat pipe with an idealized porous wick on either one or both walls. A constant temperature difference is imposed across the two ends of...

In solving the coupled vapor and liquid unidirectional flows in micro heat pipes, we discovered numerically an integral identity. After asymptotic and polynomial expansions, the coupled flows yield two reciprocal systems of equations. In system A, a vapor velocity UA obeys the Poisson equation and drives, through an interfacial boundary condition,...

A flat heat pipe is a thin rectangular sealed duct with the inner wall typically covered by a porous structure. The pores are filled with a liquid and its vapor occupies the rest of the pipe. As one end of the pipe is heated, the liquid evaporates and increases the local vapor pressure that pushes the vapor to the cooler end, where the vapor conden...

Hyperbolic functions do not form a complete set and in general it is not possible to expand a given function as an infinite series of hyperbolic functions. Here, we take the classical problem of steady laminar flow in a rectangular duct and turn the duct 90°. The maximum velocity in the duct should remain unchanged if the flow is driven by the same...

We take the classical problem of laminar flow in a rectangular duct and turn the duct 90°. Driven by the same pressure gradient, the volume flow rate should remain the same. This leads to an identity that relates a polynomial to infinite series of tanh functions. We discuss the mathematical properties of this identity and verify it by two different...

The human body contains approximately 20 billion individual blood vessels that deliver nutrients and oxygen to tissues. While blood flow is a well-developed field of research, no previous studies have
calculated the blood flow rates through more than 5 million connected vessels. The goal of this study was to test if it is computationally feasible t...

Drop flow in rectangular microchannels has been utilized extensively in microfluidics. However, the pressure-gradient versus flow-rate relation is still not well understood. We study the motion of a long drop in a rectangular microchannel in the limit the capillary number Ca→0 (Ca=μU/σ, where U is the constant drop velocity, μ is the viscosity of t...

Fluid flow in microchannels has wide industrial and scientific applications. Hence, it is important to explore different driving mechanisms. In this paper, we study the net transport or fluid pumping in a two-dimensional channel induced by a travelling temperature wave applied at the bottom wall. The Navier–Stokes equations with the Boussinesq appr...

Heat pipes are efficient in transferring heat and have been applied in various thermal systems. Previous models of heat pipes use the heat rate through the pipe as an input parameter, and therefore lack predic-tive capabilities. Here, we demonstrate, using a simple heat pipe, that if the evaporation and condensing kinetics are properly modeled, the...

Micro heat pipes have been used to cool microelectronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. We model heat and mass transfer in triangular, square, hexagonal, and rectangular micro heat pipes under small imposed temperature differences. A micro heat pipe is a closed microchannel fille...

Micro heat pipes have been used to cool microelectronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. A typical micro heat pipe has a long and narrow cavity of polygonal cross section sealed at both ends. A long vapor bubble occupies the center of the cavity, while the liquid fills the rest. A...

Micro- and nanowires are commonly used in biological sciences, micro- and nanoelectronics, and optoelectronics, and their morphological stability needs to be understood and controlled. We study the linear stability of equilibrium circular wires with length to diameter ratio of 1, 2, 3.5, 6, and 11, assuming that the wire surface can deform by capil...

Micro- and nanowires are commonly used in biological sciences, micro- and nanoelectronics, and optoelectronics, and their morphological stability needs to be understood and controlled. Previous linear-stability analyses of infinitely-long circular wires have shown that the critical wavelength for instability approaches infinity if the wire surface...

Spatially periodic systems with localized asymmetric surface structures (ratchets) can induce directed transport of matter
(liquid/particles) in the absence of net force. Here, we show that propulsion for the directed motion of water droplets levitating
on heated ratchet surfaces in the Leidenfrost (film boiling) regime is significantly enhanced as...

Micro heat pipes have been used to cool microelectronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. A typical micro heat pipe has a long and narrow cavity of polygonal cross section. A long vapor bubble occupies the center of the cavity, while the liquid fills the rest. As one end of the pip...

We introduce a marker-particle method for the computation of three-dimensional solid surface morphologies evolving by surface diffusion. The method does not use gridding of surfaces or numerical differentiation, and applies to surfaces with finite slopes and overhangs. We demonstrate the method by computing the evolution of perturbed cylindrical wi...

A micro- and nanoscale asymmetric potential enhances propulsion of liquid drop motion in the Leidenfrost (film boiling) regime. However, the requirement of high operation temperature to levitate a liquid droplet is a critical drawback for practical application of micro- and nanosystems. In this study, we show that the threshold temperature for the...

A surface free energy polar plot contains two possible sources of singularity: the cusps that give facets on an equilibrium crystal, and the circular arcs connecting the cusps that can lead to missing orientations. Instead of specifying surface free energy, we model the surface stiffness so that both singularities can be treated precisely. Here, we...

Ratcheted structures with superhydrophobicity have potential to drive motion of liquid drops in microfluidic devices. We report development of a new process to integrate microscale pillars with varied periods of ratchets from sub-micrometer to 1.5 mm in SU-8. For the fabrication, an hierarchical mixed process of thermal imprint lithography and opti...

Ratchets provide directionality in the motion of matter. We report motion of liq- uid droplets in the Leidenfrost regime whose directionality is rectified by topological ratchets. Topologically ratcheted gratings with the period ranging from millimeter down to sub-micrometer were fabricated using micromachining techniques. Water droplets dispensed...

Micro heat pipes have been used to cool micro electronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. In this work, a dual-wet pipe is proposed as a model to study heat transfer in micro heat pipes. The dual-wet pipe has a long and narrow cavity of rectangular cross-section. The bottom-half o...

A liquid film of thickness h<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Pi=Pi(h). This solution has been applied recently to non-uni...

A surface energy polar plot contains two possible singularities: the cusps that give facets on an equilibrium crystal, and the circular arcs connecting the cusps that can lead to missing orientations. The common approach of specifying the surface energy usually cannot handle both singularities simultaneously. We model the surface stiffness to avoid...

Grain growth during material processing and synthesis is controlled by grain-boundary migration. When a grain boundary ends at a free surface, a groove will develop at the tip to reduce the combined surface and grain-boundary energies. This groove may hinder the movement of the grain boundary and its effect needs to be understood. Previous studies...

A liquid thread of radius R will break up into drops if the axial wavelength of the surface perturbation L>2 pi R. If L < 2 pi R, the thread is stable and will remain intact. This is Rayleigh's stability criterion that was derived using a continuum model. We use molecular dynamics to simulate the evolution of Lennard-Jones liquid threads with R=S,...

Grain-boundary migration controls grain growth, which is important in material processing and synthesis. When a vertical grain boundary ends at a horizontal free surface, a groove forms at the tip to reduce the combined grain-boundary and surface energies. The groove affects the migration of the grain boundary, and its effect must be understood. Th...

The oscillating drop/bubble technique is increasingly popular for measuring the interfacial dilatational properties of surfactant/polymer-laden fluid/fluid interfaces. A caveat of this technique, however, is that viscous forces are important at higher oscillation frequencies or fluid viscosities; these can affect determination of the interfacial te...

A thin gold film under annealing on a silica substrate can develop “fingers” at the perimeter of the film. The perimeter retracts to leave behind longer fingers, which eventually pinch off to reduce the surface energy of the system. New fingers then form at the film edge and the process continues until the entire film disintegrates. To maintain the...

A thin liquid film experiences additional intermolecular forces when the film thickness h is less than roughly 100 nm. The effect of these intermolecular forces at the continuum level is captured by disjoining pressure P. Since P dominates at small film thicknesses, it determines the stability and wettability of thin films. To leading order, P = P(...

Micro heat pipes have been used in cooling micro electronic components. However their effective thermal conductivity is low compared with that of conventional heat pipes. Due to the complexity of the coupled heat and mass transport, and to the complicated three-dimensional bubble geometry inside micro heat pipes, there is a lack of rigorous analysi...

A thin liquid film experiences additional intermolecular forces when the film thickness h is less than roughly 100nm. The effect of these intermolecular forces at the continuum level is captured by the disjoining pressure Π. Since Π dominates at small film thicknesses, it determines the stability and wettability of thin films. To leading order, Π =...

Facets appear often on crystalline solids and affect surface evolution. Previous models of facets prescribe the surface energy γ as a function of crystallographic orientation θ. However, when the anisotropy is strong, the reduced surface energy γ+d2γ/dθ2 can become negative, which may make surface-evolution problems ill-posed. Recently, a new model...

A vertical grain boundary intercepting a horizontal free surface forms a groove to reduce the combined surface energy of the system. The groove grows with time and is commonly used for measuring surface diffusion coefficients. This work studies grooving by capillarity-driven surface diffusion with strong surface energy anisotropy and finds that fac...

Grain-boundary migration controls grain growth and is important in materials processing and synthesis. The mobility of grain boundaries is usually measured by the “quarter-loop” and Sun–Bauer methods. In these methods, a grain boundary migrates and its tip position along a free surface is recorded to infer the mobility. At the tip, a groove develop...

Micro heat pipes have been used in cooling micro electronic components. However their effective thermal conductivity is low compared with that of conventional heat pipes. Due to the complexity of the coupled heat and mass transport, and to the complicated three-dimensional bubble geometry inside micro heat pipes, there is a lack of rigorous analysi...

The diffusion-controlled growth of multiple compound phases is studied with the nonlinear Kirkendall effect included. Previous work [1] has analyzed the growth of one compound layer. In that analysis, the nonlinear, time-dependent diffusion equation with two free boundaries is reduced by a self-similar transformation into an ordinary differential e...

This work studies the coupled grooving and migration of an initially straight, inclined grain boundary ending at a horizontal free surface with an inclination angle β⪡1. The coupled motion is separated into two time regimes. In Regime I, the grain boundary turns vertically at the groove root. In Regime II, the turning relaxes following two differen...

Grain-boundary migration controls the growth and shrinkage of crystalline grains and is important in materials synthesis and processing. A grain boundary ending at a free surface forms a groove at the tip, which affects its migration. This coupled grooving and migration is studied for an initially straight, inclined grain boundary intercepting a ho...

Thin solid films are the basic structure in most microelectronic and optoelectronic devices. This is a direct result of the layer-by-layer manufacturing technique, which involves roughly a hundred steps of successive material deposition and patterning. During these processes, the device is often heated to high temperatures, and the solid components...

Facets or planar surfaces appear often on crystalline solids, and need to be accurately modeled in studying surface evolution. Previous models of facets prescribe the surface free energy γ as a function of crystallographic orientation θ. However, when the anisotropic is strong, the reduced surface energy γ+d2γ/dθ2 can become negative, which may ind...

Facet formation and evolution are important in many processes, such as crystal growth, solidification, and grain growth during annealing. Current models of facets usually choose a particular form of anisotropic surface energy and then compute the interfacial profile. This approach works fine if the surface energy anisotropy is weak and the interfac...

A semi-infinite, uniform film on a substrate tends to contract from the edge to reduce the surface energy of the system. This work studies the two-dimensional retraction of such a film step, assuming that the film evolves by capillarity-driven surface diffusion. It is found that the retracting film edge forms a thickened ridge followed by a valley....

The diffusion controlled growth of a compound phase AnB between two thin films of material A and B is studied with the nonlinear Kirkendall effect included. This growth process is important in electronic materials processing and in synthesis of high-temperature materials using multilayer films. Previous models of the growth rate do not solve the di...

The diffusion controlled growth of a compound phase AnB between two thin films of material A and B is studied with the nonlinear Kirkendall effect included. Previous models of the growth rate do not solve the diffusion equation, and thus do not fully utilize the predictive capability. This paper describes a self-similar transformation that reduces...

This work studies the motion of an expanding or contracting bubble
pinned at a submerged tube tip and covered with an insoluble Volmer surfactant. The motion is driven by constant flow rate Q into or out of the tube tip. The purpose is to examine two central assumptions commonly made in the bubble and drop methods for measuring dynamic surface tens...

Interfacial energy is a central factor in setting the morphology of phases and in determining the stability of equilibrium morphologies. here the authors examine the morphological evolution of a rod via capillary-driven surface diffusion as it both approaches and departs the topological singularity of pinch off. During the final stages of pinching...

Capillarity-driven morphological evolution of axisymmetric rods, as they snap off into two bodies, is examined. Surface diffusion is taken as the dominant mechanism for mass transport. It is found that during pinching the surface profile locally near the pinchoff point is self similar. This local solution asymptotes far from the neck to two opposin...

A solid film freshly deposited on a substrate may form a non-equilibrium contact angle with the substrate, and will evolve. This morphological evolution near the contact line is investigated by studying the motion of a solid wedge on a substrate. The contact angle of the wedge changes at time t = 0 from the wedge angle α to the equilibrium contact...

Holes formed in a solid film during annealing can grow and lead to the formation of many isolated islands. The morphological evolution of holes is thus of primary importance in the production of planar films. This work studies the linear instability of a stationary axisymmetric hole in a film with zero surface mean curvature. At the hole, the film...

The exposed part of the eyeball is covered by a tear film, which is vital for the proper function of the eye. The film thickness has been measured to be roughly 10 μm; however, how a tear film of this thickness is generated has not been clearly explained. It is proposed that the tear film is deposited analogous to a coating process by the rising me...

The amount of surfactants (surface active agents) adsorbed onto a fluid interface affects its surface tension. Thus the distribution of surfactants must be determined to find the jump in the normal and tangential stresses across the interface. Scriven uses differential geometry to derive the correct surface balance equation for an arbitrary surface...

The linear morphological instability of a line of film on a substrate has been examined for contact angles between 0 and π. The base state of the line is an infinitely long cylinder with cross‐sectional shape a segment of a circle. We assume that mass flows by diffusion along the film surface and that local equilibrium holds. We find that for non‐z...

We study the motion of pendant bubbles expanding or contracting with constant volume flow rate at the end of a capillary tube. We focus on the effect of viscous forces by deforming the bubble at order one capillary numbers and small Reynolds number. The liquid flow therefore obeys the Stokes equation and the corresponding boundary integral equation...

Foam in porous media exhibits an unusually high apparent viscosity, making it useful in many industrial processes. The rheology of foam, however, is complex and not well understood. Previous pore-level models of foam are based primarily on studies of bubble flow in circular capillaries. A circular capillary, however, lacks the corners that characte...

This work determines the pressure–velocity relation of bubble flow in polygonal capillaries. The liquid pressure drop needed to drive a long bubble at a given velocity U is solved by an integral method. In this method, the pressure drop is shown to balance the drag of the bubble, which is determined by the films at the two ends of the bubble. Using...

Understanding the role of thin films in porous media is vital to elucidate wettability at the pore level. The type and thickness of films coating pore walls determine reservoir wettability and whether or not reservoir rock can be altered from its initial state of wettability. Pore shape, especially pore wall curvature, is important in determining w...

Understanding the role of thin films in porous media is vital if wettability is to be elucidated at the pore level. The type and thickness of films coating pore walls determines reservoir wettability and whether or not reservoir rock can be altered from its initial state of wettability. Pore shape, especially pore wall curvature, is an important fa...

The motion of a long bubble in various regular-polygonal and rectangular capillaries is solved by a singular perturbation method in the limit Ca->0 (Ca = μU/σ, where μ is the liquid viscosity, U the bubble velocity, and σ the surface tension). The purpose is to study the effects of capillary corners on the motion of the bubble. In the outer problem...

The shapes of gravity-free, three-dimensional menisci are computed from the augmented Young-Laplace equation. Incorporation of disjoining thin-film forces in the Young-Laplace relation eliminates the contact line, thereby eliminating the free boundary from the problem. To calculate a meniscus with finite contact angles, the conjoining/disjoining pr...

Calculation of meniscus shapes is often difficult because the contact line is usually a free boundary. We describe a method which avoids this difficulty by using a disjoining force to eliminate the free contact line. Thus, a free-boundary problem is converted to a problem with a known domain boundary. We solve numerically the augmented Young—Laplac...

The driving force for morphological evolution of thin films increases as the size of the films decreases. Thus, to further miniaturize microelectronic and optoelectronic devices, the morphological instability and evolution of thin films need to be understood. We study the linear instability of two film shapes commonly encountered in experiment: a s...