Professor Feng's general interest is in applied and computational mathematics, and mathematical modeling with a focus on vortex sheets, fast summation methods and their scalabilities, simulations in materials science, crystal growth, rheology, and Non-Newtonian fluids. His current focuses are:
Because of their long, chain-like structure, polymeric materials in flow are not described by the traditional governing equations of transport phenomena, such as the Navier-Stokes equation, or the usual Equation of Energy. Instead, these materials display a rich variety of properties that can be viscous, like Newtonian fluids, or elastic, like rubber, or something in between.
Typically kinetic theory models must be solved using computer simulation techniques. In Professor Schieber's research group, students use molecular dynamics or Brownian dynamics simulations to study the dynamics of the polymers.
Polymer Rheology Predictions
Polymeric fluids are extremely viscous. Thus, large forces and pressure drops are required to process them. These large pressure drops, combined with large viscosities, cause substantial viscous heating effects which give rise to large temperature gradients. Since the materials are very temperature sensitive, the flow field must be solved simultaneously with the temperature field for accurate predictions. By combining standard numerical techniques for macroscopic balance equations, such as finite element methods, with microscopic stochastic simulations, such as Brownian dynamics, Professor Schieber's research group uses kinetic theory models to predict flow fields, temperature fields, and concentration fields of polymeric liquids. Polymeric materials possess very interesting thermodynamic properties during flow, which lead to vastly different energy governing equations. By generalizing the traditional approaches to non-Newtonian fluid mechanics, Professor Schieber's group has made new strides in solving these problems in complex geometries.
Thermal Conductivity Measurements
When polymer melts are deformed in a flow field, the chains can change from an isotropic state to one having preferring orientation and molecular stretching. These preferred orientations are the cause of such anisotropic behavior as normal stresses. Similarly, the thermal conductivity of the polymer can be direction dependent. Professor David Venerus and Professor Schieber have jointly designed and built an optical experiment to measure the anisotropic thermal conductivity of polymer melts under deformation in all directions. The experiment utilizes an optical technique called Forced Rayleigh Light Scattering. This technique is ideal because it can nonintrusively probe the center of the sample where thermal leakage to the environment is unimportant, and it is extremely temperature sensitive.
Mechanical properties Measurements
We measure the longitudinal component of the elastic modulus of type I rat-tail collagen using laser tweezers. All experiments were performed in buffer and with freshly extracted samples to avoid structural changes due to drying or loss of proteoglycans. Keeping fibril in its natural condition, we use a combination of optical tweezers and AFM techniques on single fibrils, and exploit Euler-Bernoulli elasticity theory. With statistics of 10 measured samples we estimate the longitudinal component of Young's modulus to be 230±130MPa. We found variations in the fibril diameter of 325±40 nm. Since bending forces depend on the diameter to the fourth power, these variations are important for estimating the modulus. However, there still exist sources of variation that are not yet accounted for.
M Andreev, H Feng, L Yang, JD Schieber, "Universality and speedup in equilibrium and nonlinear rheology predictions of the fixed slip-link model", Journal of Rheology 58, 723, 2014