TECHNICAL SUMMARY: The project supports research end education in theoretical and computational modeling of complex fluids. Such fluids are common, including surfactants, to soap, emulsifies and are ubiquitous in biological systems. The fluids have resisted quantitative modeling because they spontaneously develop nanoscale and micronscale structures, e.g. micelles and lamellar structures, caused by properties of the constituent molecules which are two to four orders of magnitude smaller than the resulting mesoscale structures. The dynamic behavior of complex liquids and soft materials is studied through a combined effort of theoretical research and computational simulations. The studies expand on current capabilities in order to address the presence of disparate length and energy scales and the complicated coupling between the shape of embedded objects and the hydrodynamic flow field. In addition, the proper treatment of many of these phenomena requires a consistent description of thermal fluctuations. The project contributes to the understanding of these systems through the development and application of robust, quantitative mesoscale simulation techniques which incorporate both hydrodynamic interactions and thermal fluctuations. This project involves the development of a specific mesoscale computational and theoretical algorithm?stochastic rotation dynamics (SRD). One enhancement permits modeling multi-component amphiphilic mixtures. A second add a constrained dynamics algorithm for modeling the dynamical behavior of worm-like chains embedded in an SRD solvent. This project will achieve the goals of mesoscale modeling through two or three orders-of-magnitude enhancement of efficiency of computational algorithms by rigorously enforcing bond-length constraints permits the use of longer time steps which also eliminates high frequency degrees of freedom which often complicate comparison with theory and experiment. The the application of these algorithmic and analytic advances includes the study the dynamics of amphiphilic mixtures and non-equilibrium stress relaxation in worm-like chains. For amphiphilic mixtures, problems of interest include spontaneous emulsification and mesophase dynamics and rheology. For worm-like chains such as DNA and actin, the study addresses tension propagation and relaxation, and the influence of confinement.
Broader impacts: The project has impact within the field of complex fluids by providing substantial enhancements other research may apply to efficiently model other complex forms of soft matter. These techniques are relevant to materials used in a large range of industrial applications and the research extends these to biological systems. The engagement of students, graduate and undergraduate, in the theoretical physics behind such leading edge technology is both enlightening for undergraduates and an excellent career starting point for dissertation student.
NON-TECHNICAL SUMMARY: The project supports research and education in theoretical and computational modeling of complex fluids. Such fluids are common, including surfactants, soaps, emulsifiers and are ubiquitous in biological systems. The fluids have resisted quantitative modeling because they spontaneously develop nano-scale and micron-scale structures, e.g. micelles and lamellar structures, caused by properties of the constituent molecules which are two to four orders of magnitude smaller than the resulting mesoscale structures. Theoretical models will be constructed and computer simulations implemented to make predictions of the structures, their thermodynamic properties and the dynamical evolution in time as they are created and change under external influences. Success in this research will have direct implications to the understanding of materials as diverse as ice cream and living cells. The engagement of students, graduate and undergraduate, in the theoretical physics behind such leading edge technology is both enlightening for undergraduates and an excellent career starting point for dissertation student.
This award supports theoretical research and education in soft-condensed matter and biological physics, specifically in the fields of complex liquids and active matter. The common defining feature of a ``complex liquid'' is the presence of an internal structure that is much larger than the size of an atom but still very small compared to the size of typical fluid containers. The lengths of these so-called mesoscopic structures ranges from a dozen of nanometers to a few micrometers. Examples are the radii of microemulsion droplets in a oil-water-soap mixture or nano-particles in a sunscreen product. These structures play a key role in determining the properties of the system. Due to their tiny size they are affected by thermal motion. That is, even if the fluid appears to be at rest, a closer look under the microscope reveals an erratic motion of the mesoscopic ingredients; they are ``kicked around'' by the solvent molecules. Traditional engineering software for fluids ignores this internal random motion. Over the last 30 years, alternative, mesoscale computer methods to improve this situation have emerged. One of the objectives of this project was the further development of such an algorithm, named Stochastic Rotation Dynamics (SRD). Since calculating the path of every single molecule in a liquid is time-prohibitive, SRD makes a compromise to accelerate the calculations. Loosely speaking, it ``lumps'' more than a trillion of real particles into an artificial SRD particle and follows its time evolution and collisions with other SRD-particles.The rules about what should happen in such a collision can be designed to model a realistic fluid. In this project, fluid properties such as the viscosity of the SRD-fluid were calculated by means of statistical physics tools and compared to computer simulations. In addition, in order to model oil-water mixtures, SRD was extended to deal with two types of particles which ``do not like'' each other and the properties of such mixtures were determined theoretically. To model emulsions, a third particle type that mimics soap molecules and mediates between the two other kinds was introduced. The properties of such binary and ternary mixtures were investigated and formulas for their viscosities were derived. In the second part of the project, the experience gained with SRD and mathematical tools developed for it were transfered to study active matter. The term ``active matter'' refers to systems of many interacting units that individually consume energy and generate coherent motion. Examples are suspensions of swimming bacteria, collections of cells, flocks of birds and fish, and swarms of unmanned aerial vehicles. Mathematically, these systems can be treated as ``living fluids'', using concepts from regular fluid theory. One of the successes of this award was the rigorous derivation of the fluid dynamic equations for a particular, well-known model for active matter, the so-called Vicsek model. In addition, we found that large Tsunami-like waves that occur in this model, cannot be described by these equations but that a more sophisticated mathematical description -- kinetic theory -- borrowed from the theory of gases, leads to quantitative predictions for the wave shape. Recently, experimentalists from Italy performed a detailed analysis of real flocks of starlings and suggested modified (so-called topological) interaction rules for the Vicsek model. Using our gas-kinetic approach and performing a stability analysis we were able to show theoretically that large density waves do not occur in this modified model. This project provided training in research, statistical physics and scientific programming for a total of five undergraduate students, two graduate students and one postdoctoral fellow. Due to the multidisciplinary nature of this research in the border region of physics, chemistry, biology, applied mathematics and robotics, two of the undergraduates that participated in this project did not have majors in physics but in math and chemistry. Two of the undergraduates supported by this grant received prestigious national awards, the Astronaut Scholarship (Brandon Johnson) and the National Defense Science & Engineering Graduate Fellowship (Rylan Wolfe).
