Dr. Manish Kumar - Research

I use theory, computation, and data-driven methods to study the dynamics of complex fluids and soft matter relevant to energy, biological, and environmental applications:

1. Data-driven methods

Data-driven methods enable us to get physical insights from data, which are otherwise challenging or even inaccessible. My research focuses on two aspects of data-driven methods:

Reduced-order model: Investigation of chaotic flows in complex fluids is computationally expensive due to the requirement of very high degrees of freedom to perform direct numerical simulations (DNS). However, the dynamics of chaotic flows often lie on invariant manifolds with far fewer degrees of freedom, which allows the development of reduced-order models by evolving dynamics in the manifold coordinates. I have introduced the Viscoelastic Data-driven Manifold Dynamics (VEDManD) framework to develop reduced-order models for turbulence in viscoelastic flows. The VEDManD framework integrates a viscoelastic variant of proper orthogonal decomposition (VEPOD), advanced autoencoders, and neural ODEs to develop reduced-order models. Using this framework I have developed a reduced-order model of elastoinertial turbulence which accurately captures its dynamics roughly a million times faster than the DNS. The reduced-order models can accelerate the investigation of the dynamics of complex systems and they can also facilitate the design of strategies to control these systems.

Data-assimilation: Data-assimilation technique combines mathematical models and partial measurement to access the physical parameters that are challenging to measure in experiments. It provides a great opportunity to obtain high-quality parameters for physics-based models. My research uses the data assimilation technique to extract the concentration-dependent diffusion coefficients of Li-ions in highly non-ideal solutions from noisy measurements of concentration profiles, which deepens our understanding of lithium ion flux in battery electrolytes and contributes to the development of next-generation Li-ion batteries. I also use data assimilation to extract the stress field from the velocity measurement in complex fluids, which is essential to develop quantitative predictive constitutive models of complex fluids.

Collaborator: Matthew Gebbie (University of Wisconsin-Madison)

2. Elastoinertial turbulence

The presence of a tiny amount of polymers (a few parts per million) dramatically reduces turbulent drag. Therefore, Polymer additives are commonly used in the pipeline transport of liquids such as crude oil transport, water heating and cooling systems, and airplane tank filling to reduce turbulent drag, which leads to reduced pumping costs and liquid transfer time. Polymer additives also have been envisioned to be used in sewer systems to improve drainage capacity, which could mitigate the problems of flooding and water clogging. Due to global warming, we see more and more frequent extreme weather events resulting in unexpected heavy rain in unexpected places. It is neither feasible nor economical to replace drainage systems in a short time. Therefore, the temporary enhancement of drainage capacity using polymer additives could prevent/mitigate the catastrophic damage resulting from unexpected heavy rain. I study the effects of polymer additives on the flow dynamics in open and closed channels. Elastoinertial turbulence (EIT) is a chaotic state resulting from the interplay between inertia and elasticity and sets a limit on the achievable drag reduction through polymer additives in turbulent flows. I have developed numerical tools to simulate and investigate the dynamics of EIT including Coherent Structures underlying its dynamics. I have pioneered the use of spectral proper orthogonal decomposition (spectral POD) to investigate the dynamics of elastoinertial turbulence (EIT) and discovered that its chaotic dynamics are predominantly composed of a collection of self-similar, nested traveling waves.

EIT_website.mov

nested_traveling_EIT_v2.mp4

3. Viscoelastic flows through porous media

elastic_turbulence_v1.mov

Viscoelastic flows through porous media are common in industrial applications such as enhanced oil recovery, soil & groundwater remediation, and microbial mining. Such flows are also relevant for biological processes such as targeted drug delivery, biofilm transport inside the body during bacterial infection, and transport of particles in the lung airway. Large elastic stresses induced by confinement in the porous media lead to elastic instabilities in the viscoelastic flows. The polymeric stresses can also lead to chaotic flows even at negligible inertia. I study viscoelastic instabilities in confined geometries and the effects of pore-scale instabilities on the sample-scale transport of fluids and particles in porous media. The dynamic flow patterns and the material transport in viscoelastic flows are ultimately controlled by the topology of the polymeric stress field. However, the measurement of the polymeric stress field is extremely challenging, often inaccurate, and limited to simple geometries and steady flows. Using the concept of Lagrangian Coherent Structure (LCS), I have developed a framework to determine the polymeric stress field directly from the readily measured velocity field, which is applicable even for complex geometries and unsteady flows. This framework opens the door to understanding the intricate roles of the stress fields in the dynamics and transport of viscoelastic flows.

Collaborators: Sujit S. Datta (California Institute of Technology) , Jeffrey S. Guasto (Tufts University)

two_cylinder_video.mp4

multistaility_video.mp4

4. Flagellated cells in complex flows

sperm_traj_straight.mp4

Microorganisms affect our lives daily in both good and bad ways. Beneficial microorganisms help in waste treatment, environmental remediation, and food production, whereas detrimental microorganisms lead to human and animal infections, product contamination, and membrane biofouling. Many microorganisms and motile cells use long, thin elastic structures to propel themselves through viscous fluids, generally called flagella or cilia. Sperm cells are single flagellated cells and they travel a distance of more than a thousand times their body length to reach the eggs through highly chaotic flows and complex geometries for successful fertilization. The elastohydrodynamic interaction between the elastic flagella and background flows leads to rich buckling dynamics of flagella, which ultimately affects the motility of the microorganisms. My research investigates flagellar dynamics and the motility of microorganisms in nontrivial background flows.

Collaborator: Jeffrey S. Guasto (Tufts University)

sperm_traj_circle.mp4

buckling_exp.mp4

buckling_sim_nonmotile.mp4

motile_buckling.mp4

5. Membrane filtration

Membrane-based devices are widely used in chemical, food processing, and pharmaceutical industries to remove impurities, increase the concentration of solutions, and buffer exchange. There is a need to concentrate protein to a high concentration (>200 mg/ml) to achieve therapeutic concentration and reduce dosage volume. The emergence of a concentration boundary layer close to the membrane induces gel formation on its surface, which has an undesirable impact on device performance and it also limits the maximum achievable concentration. I have developed numerical tools to study the evolution of the gel layer inside filtration devices and the effect of the gel on device performance. Membrane fouling is another major challenge in membrane-based devices as it limits the permeate flux through the membrane. I investigate the properties of the membrane made of piezo-fibers, which have the potential to mitigate fouling. The vibration of piezo-fibers creates traping zones close to the fibers, where the particles get trapped instead of colliding and sticking with the fibers.

Collaborators: David Warsinger (Purdue University) , Michael Ladisch (Purdue University)

TFF.avi

pizofiber_traping.avi

Page updated

Google Sites

Report abuse