MEAM Seminar Series Archive: Spring 2009
"Enablers for probe-based nanoscale technologies"
Speaker: Harish Bhaskaran
Probe-based technologies are gaining prominence for their projected utility in a variety of applications such as data storage, nanolithography and materials characterization. Data storage, by itself is a very interesting, large-scale application of probe-based systems and embody many of the scientific challenges associated with the commercialization of probe-based technologies. As these technologies mature, economic forces have compelled researchers to re-think the small, slow, single-probe-based, unreliable systems (such as the AFM) in terms of larger, highly functional, fast systems with longer lifetimes. These goals have seemed unachievable in probe-based systems, since key enablers for the commercialization of such technologies such as low-cost, fast nanoscale positioning as well as reduced tip wear have been elusive.
In this talk, I will give an overview of my work within IBM's probe storage project in tackling some of these interesting issues. A brief introduction to probe-based data storage will be given. A scheme for nanoscale sensing based on silicon nanowires and our progress in this direction will be discussed. Some of my work on platinum silicide tips and "encapsulated" tips for conduction-mode probe-based technologies will also be presented. The performance of the encapsulated conducting tips in sliding is shown to be several times better than commercial conducting probes. Both these technologies have enabled us to perform phase transformations in chalcogenide-based phase change materials. In addition, I shall present some preliminary results of the IBM/Univ. of Pennsylvania/Univ. of Wisconsin at Madison collaboration that has culminated in ultra-sharp, nanoscale, diamond-like-carbon tips.
Kathleen J. Stebe
"Oriented assembly of anisotropic particles by capillary interactions"
Speaker: Kathleen J. Stebe
Chair, Department of Chemical and Biomolecular Engineering
Goodwin Professor of Engineering and Applied Science
University of Pennsylvania
Particles at fluid interfaces occur in nature, with the particles ranging from pollen to insects which walk on water. Particles at interfaces are exploited in classical applications like Pickering emulsions, in which particles stabilize emulsions, and froth flotation, in which ore particle adsorption to fluid interfaces is used to separate and recover metal ores. Particles at interfaces also occur in emerging applications in which nanomaterials are organized at interfaces.
The assembly of particles into ordered structures via capillary interactions is studied. Early work in this field focused primarily on spherical particles that distort fluid interfaces and create excess area. The particles assembled by capillary interactions which occur because the excess area created by the particles decreases as the particles approach each other. Here, particles with shape anisotropy are studied. Such particles create undulations with excess area that can be locally elevated at certain locations around the particle. The local elevation of excess area makes these sites locations for preferred assembly. Hence, particles orient and aggregate in preferred orientations. Such self assembly is often termed directed assembly. Three key issues in directed assembly are means of controlling the object orientation, alignment, and the sites for preferred assembly, including means of promoting registry of features on particles. Each of these issues is addressed in detail in for the example of a right circular cylinder using analysis, experiment and numerics. A series of other shapes are then studied to illustrate the generality of the concepts developed.
"Nanomechanics of biological systems: What can we learn from nature about the principles of hierarchical materials?"
Speaker: Huajian Gao
Walter H. Annnenberg University Professor
The importance of mechanics and mechanical properties in biological functions has been widely recognized. The study on nanomechanics of biological systems is partly motivated by the observation that multi-level structural hierarchy is a rule of nature. Hierarchical structures/materials can be observed in all biosystems from chromosome, protein, cell, tissue, organism, to ecosystems. Mechanics of hierarchical materials inspired by nature may provide useful hints for materials engineering. Some questions of interest include: what are the roles and principles of structural hierarchy? what determines the size scales in a hierarchical material system? is it possible to design hierarchical materials with designated mechanical and other properties/behaviors? Specifically, natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures which seem to primarily serve their mechanical functions. The present talk will therefore be focused on the basic mechanics principles behind these hierarchical materials, including the principle of multiscale flaw insensibility. We perform detailed analyses on two idealized, self-similar models of hierarchical materials (“fractal bone” and “fractal gecko hair”), one mimicking the mineral-protein composite structure of bone and bon-like materials, and the other mimicking gecko’s attachment system, to demonstrate that structural hierarchy leads to simultaneous enhancement/optimization of multiple mechanical properties/functions such as stiffness, toughness, flaw tolerance and work of adhesion. In conventional homogeneous materials, the fracture energy is a material constant. In contrast, hierarchical materials do not have a unique fracture resistance, rather their fracture toughness depends on length scale: the bigger the scale, the larger the fracture resistance. This has been demonstrated by determining the traction-separation laws (cohesive laws) at different length scales in a hierarchical material.
Yucun Lou, PhD Candidate
"Guided assembly of nanostructures"
Speaker: Yucun Lou
Advisor: John L. Bassani
Mechanical Engineering and Applied Mechanics, University of Pennsylvania
A solid solution can spontaneously separate into phases, e.g. spinodal decomposition, that self assemble into patterns. This process can be guided via external fields to form ordered micro- and nano-structures, e.g., nanodots and nanowires. A Cahn-Hilliard type phase field model is developed that incorporates chemical, interfacial, and elastic energies, including heterogeneous elastic properties, and that couples naturally to externally-imposed mechanical fields. Aggregation in bulk and in thin films under patterned external stress fields are investigated through detailed simulations, which includes a systematic variation of transformation strain, elastic contrast and the magnitude of external load. The patterned external stress fields are shown to directly affect the kinetics and morphology of aggregation through interacting with internal elastic properties. A major contribution of this thesis is the demonstration that the trends observed from simulations can be qualitatively interpreted through Eshelby-type asymptotic estimates for interaction energies.
Neelesh A. Patankar
"Fully resolved simulation of immersed bodies: Macro to micro scales"
Speaker: Neelesh A. Patankar
Associate Professor of Mechanical Engineering
The primary goal of this work is to develop a general purpose numerical tool for the motion of immersed bodies in fluids. The immersed bodies could be rigid or deforming, and the length scales could range from sub-micron to meter or larger. To that end, this talk will proceed in three parts: 1. solving rigid motion in a fluid, 2. simulating freely swimming bodies with specified deformations, and 3. incorporating thermal fluctuations to resolve Brownian motion. To simulate freely moving rigid bodies, the key idea is to assume that the entire fluid-particle domain is a ‘fluid’ and then to constrain the particle domain to move with a rigid motion. This algorithm is then modified to fully resolve the swimming motion of an organism as a result of its prescribed deformations. In this case we first solve the Navier-Stokes equations in the entire fluid-organism domain. In the next fractional step, the fluid velocity in the organism domain is corrected by a “momentum redistribution” scheme. This imposes the prescribed deforming velocity in the frame of reference of the organism. The resulting solution gives the swimming velocity of the organism and the surrounding flow field. Lastly, to include the effect of thermal motion we develop an approach named Fluctuating Immersed MATerial (FIMAT) dynamics. In this approach the algorithm, to resolve the motion of immersed bodies, is identical to that described above. The only difference is that thermal fluctuations are included in the fluid equations via additional random stress terms. Solving the fluctuating hydrodynamic equations coupled with the immersed body results in the Brownian motion of that body. Applications of this numerical tool are wide ranging and include modeling sediment transport, aquatic locomotion and aerial flight, evolution of aquatic life forms, animation, and biological problems such as understanding the binding pathways of ligands and function of motor proteins.
George G. Adams
"Contact and adhesion in a microswitch: Ductile and brittle separation"
Speaker: George G. Adams
College of Engineering Distinguished Professor
Professor of Mechanical and Industrial Engineering
We present the results of an experimental investigation and numerical modeling of microscale adhesive contacts with emphasis on the contacts which occur in a MEMS switch. Particular attention is devoted to the transition between ductile and brittle separation modes and on the contact evolution of gold-on-gold microcontacts.
A specially designed SPM contact test station has been constructed to conduct cycling tests. The contact evolution is studied by observing the characteristics of the pull-off force. The magnitude of the pull-off force, the force vs. displacement curves, and the rate-dependent pull-off force are all sampled during cycling. It is found that ductile separation causes significant modification of the contact surfaces. This deformation can contribute to a higher pull-off force when the contacts are cycled at 300Hz compared with cycling at 0.5Hz.
Three parameters describing contacts with adhesion were identified in our numerical modeling. A series of finite element simulations of a single load/unload cycle of an elastic/plastic contact are performed to study the impact of each of these parameters. A brittle separation is said to occur if little or no plastic deformation occurs on unloading. A ductile separation is characterized by large unloading plastic deformation, often at constant contact radius. The results show which parameters are most important in producing ductile and brittle separation.
Zdenek P. Bazant
"Size and risk: Scaling of quasibrittle structure strength and lifetime based on atomistic fracture mechanics"
Speaker: Zdenek P. Bazant
McCormick Institute Professor
W.P. Murphy Professor of Civil Engineering and Materials Science
After introductory historical comments, the lecture reviews the main aspects of quasibrittle fracture mechanics with the related size effects. Until the 1980s, all the observed size affects of structural strength were modeled by Weibull’s statistical theory. Beginning in 1983, researches conducted primarily at Northwestern University have shown that structures made of quasibrittle (or brittle heterogeneous) materials exhibit strong non-statistical size effects caused by energy release associated with the stress redistribution engendered by stable growth of a large fracture or a large fracture process zone. The main results for quasibrittle materials such as concrete and laminated, woven and braided fiber-polymer composites are summarized. Attention is then focused on multiscale modeling of strength statistics and size effect. Based on activation energy controlled propagation of atomic lattice cracks, it is shown that the probability distribution (pdf) of strength of a representative volume element (RVE) of a quasibrittle material consists of a Gaussian core with a Weibull tail grafted on the left at the failure probability of about 0.001. The strength distribution of structures failing at macro-fracture initiation from one RVE is modeled by a weakest-link model of finite size. This model implies nonlocal behavior and reveals that the Weibull tail of pdf spreads into the Gaussian core as the size increases. It also implies that the safety factors must be considered to depend on the structure size (and shape). Further it is shown how the empirical Evans law for the dependence of the subcritical crack growth rate on the applied stress can be analytically derived from atomistic fracture and multiscale transition indicated by damage mechanics. Combining this law with statistics reveals that the structure lifetime is strongly size dependent and the type of lifetime pdf varies with the structure size. In closing, some consequences for the design of large concrete structures, and of fiber composites for large load-bearing parts of fuel efficient aircraft, ships and automobiles, are pointed out.
Michael G. Schrlau, PhD Candidate
"Carbon-based nanoprobes for cell nanosurgery and biological applications"
Speaker: Michael G. Schrlau
Advisor: Haim H. Bau
Mechanical Engineering and Applied Mechanics, University of Pennsylvania
Since their discovery, researchers have been intrigued by the possibility of using carbon nanotubes and nanopipes for, among other uses, intracellular delivery and sensing of cellular signals. However, the inability to efficiently interface these nanostructures with larger, maneuverable probes has hindered their use as cell probes. To overcome these issues, I have developed multifunctional, carbon-based cell nanoprobes, called carbon nanopipettes (CNPs). CNPs integrate carbon nanopipes, with diameters ranging from tens to hundreds of nanometers, into the tips of pulled glass capillaries. Since CNPs are made from glass capillaries, they readily interface with standard cell physiology equipment such as micromanipulators, injection systems, and electrophysiology amplifiers. CNP technology establishes a viable means of utilizing carbon nanotubes and nanopipes for cell probing, intracellular injection, and cell electrophysiology.
I will describe the fabrication methods used to efficiently manufacture large quantities of CNPs without the need for assembly and discuss their resultant properties. I will then present a study where CNPs were used to inject calcium-mobilizing second messengers into cells to identify previously unknown intracellular signaling pathways in breast cancer cells. Next, I will demonstrate the multifunctional capability of CNPs by electrically measuring the changes in cell membrane potential in response to pharmacologic agents. I will conclude by briefly covering the future opportunities and potential biological applications for CNP technology.
"Field directed assembly for nanomanufacturing and nanoscale device integration"
Speaker: Benjamin Yellen
Mechanical Engineering and Materials Science Department
Over the last few decades, a new nanomanufacturing paradigm based on “bottom up” self-assembly strategies has emerged as a viable method for integrating nanoscale optical, electronic, and biological components into useful microsystem architectures. The main advantage of self-assembly techniques is that the device components can be fabricated separately and then placed into desired geometric arrangements, as opposed to the current paradigm based on monolithic integration strategies. Not only does this self assembly technique enable the integration of a broader class of materials into useful systems than do monolithic strategies, it can also significantly reduce the costs due to the self-guiding placement of materials onto various 2-D and 3-D substrates. However, the inherently stochastic characteristics of self-assembly present a significant engineering challenge in how to deal the variability of the starting material, as well as the variability in the assembly process itself. Thus, there remains an urgent need to develop techniques for sorting colloidal particles, such as nanotubes/nanowires, biological components, and other active materials, and for uniformly placing them into precise patterns.
In the course of this talk, I will present my recent and future work on magnetically guided self-assembly systems, and I will point out critical differences between molecular and mesoscale self-assembly mechanisms. I will show why magnetic forces, which are considered too weak for molecules, are capable of overcoming hydrodynamic forces and the effects of Brownian motion on mesoscale objects. I will also demonstrate how novel self-assembly mechanisms can be designed to take advantage of the long-range nature of attractive and repulsive magnetic forces. Throughout this talk, I will introduce potential applications for these techniques in cell printing, microarrays, and biomedical implants, as well as for other lab-on-a-chip applications. Finally, I will outline my future work and goals to apply the techniques I have previously developed to new fields in electrochemical energy production and nano-patterning.
Jonathan A. Malen, PhD Candidate
"Energy transport and conversion in organic-inorganic hybrid materials"
Speaker: Jonathan A. Malen
University of California, Berkeley
Organic-inorganic hybrid materials aim to combine the manufacturability of plastics with the transport properties of semiconductors. Over the last twenty years researchers focused on electronic applications, but the field is now expanding to address the challenges of energy demand and climate change. Organic-inorganic hybrids are promising replacements for bulk semiconductor photovoltaic and thermoelectric materials because they self-assemble with controllable feature sizes at length scales characteristic of transport processes. Metal-molecule-metal junctions are the building blocks for such hybrid materials. Prior measurements of conductance on single molecule junctions left several questions unanswered, e.g., is conductance p or n type, what is the origin of transport fluctuations, and can hybrid materials be used for efficient energy conversion? To answer these questions we measured junction thermopower, an alternative property to conductance that uniquely distinguished between p or n type transport in molecular junctions. A modified scanning tunneling microscope (STM) was used to make repeated junctions containing one or a few molecules. Statistical analysis of the data spread between measurements provided insight to the nature and origin of electronic transport fluctuations in conductive molecular junctions. Recent thermopower measurements of C60 (buckminsterfullerene) indicate a ~100 fold increase in the thermoelectric figure of merit, ZT, relative to previously measured conductive molecules. These results evoke hope for efficient energy conversion using organic-inorganic hybrid materials.
Jaydev P. Desai
"Image-guided surgical robotics: From macro-scale to meso-scale"
Speaker: Jaydev P. Desai
Director, Robotics, Automation, Manipulation, and Sensing (RAMS) Laboratory
Department of Mechanical Engineering
University of Maryland, College Park
Magnetic resonance imaging (MRI) provides excellent soft tissue contrast and has become a standard tool of physicians in several image-guided interventions. The American Cancer Society estimates one in eight women born today is likely to be diagnosed with breast cancer during their lifetime. Although these statistics are discouraging, positive trends are evident as a result of innovations in diagnosis and treatment over the past decade. Recent, large scale studies reported in The Lancet and The New England Journal of Medicine demonstrate the value of MRI as an effective tool in the diagnosis of breast cancer. Hence, coupling diagnosis with MRI based biopsy (Bx) will lead to better delineation of the tumor margin. For breast cancer treatment, radiofrequency ablation (RFA) has emerged as a promising approach for early stage breast cancer with maximum effectiveness and conservation of healthy breast tissue without full surgical intervention. Since Bx and RFA are both needle-based procedures, advancements in robotic systems for Bx/RFA of breast tumors will potentially improve targeting accuracy and improve the outcome of the procedure. Hence, the first part of the talk will discuss our efforts on the development of the macro-scale robotic system for Bx/RFA of breast tumors under continuous MRI.
In the second part of the talk, we will discuss our progress in the development of meso-scale robotic system operating under MRI for neurosurgical interventions. As a background, brain tumors are among the most feared complications of cancer. Whether a primary (intrinsic) malignancy, or a secondary (metastatic) malignancy, involvement of the brain in a cancer patient is devastating because it threatens the very personality and identity of the individual. Currently, the optimal treatment for most brain tumors involves primary surgical resection. Unfortunately, many patients cannot undergo primary surgical resection of their brain tumor due to either poor general health or an unfavorable location of the lesion, usually deep or otherwise inaccessible to conventional neurosurgical techniques. As a result, our efforts have targeted towards the development of a MRI compatible meso-scale “minimally invasive” neurosurgical intracranial robot (MINIR).
Haizhen Pan, PhD Candidate
"Problems of orthotropic plastic constitutive models: Non-associated flow and evolution of anisotropy"
Speaker: Haizhen Pan
Advisor: John L Bassani
Mechanical Engineering and Applied Mechanics
University of Pennsylvania
In this thesis two main topics are addressed: i) non-associated plastic flow for anisotropic materials, e.g., textured polycrystals; and ii) deformation-induced evolution of anisotropy for materials with microstructure. We consider a class of elastic-plastic materials that possess local orthotropic symmetry that is naturally represented in terms of second-order orientation tensors.
Recent developments in multiscale modeling have unequivocally demonstrated that plastic flow a wide range of crystalline materials is non-associative (i.e., district yield and flow functions) due to the effects of non-glide stresses on the motion of dislocations. To describe orthotropic non-associated behavior for polycrystals, new yield functions admitting tension and compression asymmetries are proposed by utilizing representation theory for the functions of tensors (Wang, 1969, 1971; Smith, 1969, 1971). A bifurcation calculation from uniform states described by constitutive models for orthotropic, non-associated flow is carried out, demonstrating a strong effect on strain localization.
The second part of work focuses on the development of anisotropic elastic-plastic constitutive models to account for microstructural evolution. Examples of material systems of interest include polycrystals, whisker-reinforced composites, polymers, as well as complex viscoplastic fluids. The evolution of microstructure, e.g. of crystallographic texture or short-fiber orientations, leads to generally anisotropic material response. In this thesis, the microstructures of interest are represented by orthonormal vectors. These vectors are assumed to spin with the microstructure, which is characterized as the difference between the material and plastic spins. A flow rule is proposed for plastic part of velocity gradient in the intermediate configuration that is represented in terms of a non-symmetric stress tensor and two second-order orientation tensors. The theory of invariants (Spencer, 1971) coupled with representations for tensor-valued functions (Wang and Smith, 1969-1971) are utilized to derive the general forms for yield and flow functions and to develop phenomenological constitutive relations for the plastic part of stretching rate and plastic spin. Comparisons with experimental data about the rotation of these vectors for textured polycrystals under uniaxial tension and simple shear loading are very promising. Furthermore, the evolution of microstructure is predicted to have significant effects on overall material response including on strain localization, in the form of sheet necking.
To investigate the full three dimensional nature of instabilities in sheet deformation, the constitutive models for non-associated flow with microstructural evolution have been implemented in a finite element program (Abaqus). Three-dimensional simulation are carried out to study sheet necking and shear localization in detail. From these simulations, both the anisotropic non-associated flow and microstructural evolution are shown to have significant effects on the onset of localization and post-bifurcation deformation.
Kamil L. Ekinci
"Progress towards a functional NEMS sensor: Understanding NEMS dissipation in fluids"
Speaker: Kamil L. Ekinci
Mechanical Engineering Department, Boston University
Center for Nanoscale Science and Technology, NIST
One of the most promising applications of nanoelectromechanical systems (NEMS) is sensing. In resonant sensing, one usually measures a small resonance frequency shift, which results from an attached mass or an applied force to the resonator. With their small masses, high frequencies and small force constants, NEMS resonators are expected to emerge as new tools for sensing a variety of analytes, probing biological entities and measuring molecular forces. Along these lines, several groups have shown that a NEMS resonator operating in vacuum is sensitive enough to weigh a single molecule. However, there remain significant roadblocks in this line of work. In this talk, I will give a brief introduction to the potential of NEMS based mass sensors and to the major challenges in front of realizing functional NEMS sensors. The challenge, which I will discuss in depth, is the operation of a NEMS resonator in a fluid: the fluid, literally and figuratively, dampens the NEMS resonator and reduces its exquisite sensitivity. I will describe the new physics that we have observed in studying NEMS dissipation in fluids and suggest possible remedies to the dissipation problem. Time permitting, I will present other progress from my group in the area of optical and electronic transducers, read-out of NEMS arrays, and so on.
Kevin T. Turner
"Interface mechanics of microtransfer printing and direct bonding processes"
Speaker: Kevin T. Turner
Department of Mechanical Engineering
University of Wisconsin-Madison
The transfer and bonding of layers of high quality semiconductor materials provides new routes to realize a range of micro- and nanosystems. Applications include the fabrication of advanced optoelectronics, the intentional introduction of strain in electronic devices to enhance performance, and the construction of complex micromechanical devices. Microtransfer printing and direct wafer bonding are two manufacturing approaches that enable this type of the materials integration. Microtransfer printing provides a route to transfer thin (0.1-10 µm) semiconductor layers using soft polymer stamps and direct wafer bonding is frequently employed to join thicker layers (0.1-1 mm). While these two methods allow the integration of layers with very different dimensions, both processes can be analyzed using a similar mechanics framework and both rely on room temperature adhesion driven by van der Waals forces and hydrogen bonding.
In order to design and expand the capabilities of microtransfer printing and direct bonding for materials integration, an understanding of the underlying mechanics of these processes is essential. In this talk, models that describe these processes as well as a new experimental technique that permits detailed characterization of the adhesion and separation behavior of room temperature-bonded interfaces will be presented. The process models are based on a fracture mechanics framework and provide the ability to quantify the role of key manufacturing parameters. A specific example of the mechanics of a method for introducing elastic strain in a thin device layer through bonding will be used to illustrate the utility of the models. In order to ensure an accurate description of the interface behavior in the process models, a new experimental technique for characterizing surface force-mediated adhesion has been developed. In this technique, the adhesion and separation behavior of the interface is measured by monitoring the deflection of a thin microscale cantilever that is controllably cycled in and out of contact with a thicker test surface. The technique as well measurements of the adhesion and separation behavior of smooth Si-Si and Si-PDMS interfaces will be presented.
"Modeling soft multifunctional materials"
Speaker: Luis Dorfmann
Associate Professor of Civil and Environmental Engineering
The lecture begins with an overview of experimental results that characterize the elastic behavior of rubberlike solids. This is followed by illustrations of how the behavior departs from the purely elastic; we examine stress softening associated with the Mullins effect, and the different degrees of stress softening for different rubbers are highlighted. The main part of the seminar focuses on recent theoretical work concerning the coupling of mechanical and magnetic effects in so-called magneto-sensitive elastomers, which are being used as active components in various applications where the mechanical stiffness of the material can be changed rapidly by the application of a suitable magnetic field. These smart materials typically consist of an elastomeric matrix and a distribution of ferromagnetic particles. We summarize the relevant equations and propose a coupled free-energy formulation, which depends on the deformation gradient and on the magnetic induction. Finally, we discuss how constitutive equations are specialized to isotropic incompressible magneto-sensitive elastomers in either Lagrangian or Eulerian form.
L. B. Freund
"Characterizing the resistance generated by a molecular bond as it is forcibly separated"
Speaker: L. B. Freund
Division of Engineering, Brown University
One goal of measurements of the resisting force generated by a molecular bond as it is being forcibly separated under controlled conditions is to determine values of physical parameters thought to be responsible for its functional characteristics. In this work, we establish the dependence of force history during unbinding on both the characterizing measures and the controllable loading parameters. This is pursued for the practical range of behavior in which unbinding occurs diffusively rather than ballistically, building on the classic work of Kramers. For a bond represented by a one-dimensional energy landscape, modified by to account for time-dependent applied loading, we present a mathematical analysis showing the statistical dependence of the resistance of the bond on bond well shape, general time dependence of the imposed loading, and stiffness of the loading apparatus. The quality of the result is established through comparison of its implications with the results of full finite element solutions of the equivalent boundary value problems for the Smoluchowski partial differential equation.
Arne J. Pearlstein
"Steady shapes, speeds, and internal circulation of small water drops falling through air"
Speaker: Arne J. Pearlstein
Professor of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
For steady axisymmetric motion of water drops falling through air, previous experimental, computational, and approximate analytical work has found or predicted only oblate drop shapes. Here, we present numerical solutions of the full Navier-Stokes equations for water drops falling through air, accounting for interfacial deformation and flow in the two Newtonian fluids, with the only assumptions being that the flow is isothermal and that there is no interphase mass transfer by evaporation or condensation. Slightly prolate drop shapes are predicted for water drops with equivalent diameters up to 700 µm falling through air. Larger drops are predicted to be oblate, with the transition from prolate to oblate behavior corresponding to the axis ratio passing smoothly through unity without the drop becoming spherical. We also show that the internal recirculation flow in the drop is significantly more vigorous than measured by Beard and Pruppacher for drops "suspended" in a vertical wind tunnel. An explanation is proposed to reconcile previous experimental results and the approximate theoretical results with which they agree, and the present computational results. Implications for scavenging of particluate and trace gases by falling raindrops are discussed.