Hindered diffusion of nanoparticles
Doktorsavhandling, 2020

Brownian theory provides us with a powerful tool which can be used to delve into a microscopic world of molecules, cells and nanoparticles, that was originally presumed to be beyond our reach. Consequently, modeling the inherent dynamics of a system through a Brownian transport equation is of relevance to several real-word problems that involve nanoparticles including, the transport and mitigation of particulate matter (PM) generated though fossil fuel combustion and nanocarrier mediated drug delivery. Experimentally forecasting these systems is challenging due to the simultaneous prevalence of disparate length and time scales in them. Correspondingly, an in-silico driven assessment at such nanoscales can complement existing experimental techniques.

Hence, in this thesis, a novel multiphase direct numerical simulation (DNS) framework is proposed to address the transport at these nanoscales. A coupled Langevin-immersed boundary method (LaIBM), that solves the fluid as an Eulerian field and the particle in a Lagrangian basis, is developed in this thesis. This framework is unique in its capability to include the resolved instantaneous hydrodynamics around the Brownian nanoparticle (without the need for an a-priori determination of the relevant mobility tensors) into the particle (Langevin) equation of motion. The performance of this technique is established and validated using well-established theoretical bases including the well-known theories for unbounded and hindered diffusion (wherein hydrodynamic interactions mediated by the fluid such as particle-particle or particle-wall influence the governing dynamics) of Brownian particles in a liquid. Correspondingly, it is shown that directional variations in mean-squared displacements, velocity auto-correlation functions and diffusivities of the Brownian nanoparticle correspond well with these standard theoretical bases. Moreover, since the resolved flow around the particle is inherently available in the proposed DNS method, the nature of the hydrodynamic resistances (on the particle) including the inherent anisotropies and correlated inter-particle interactions (mediated by the fluid) are further identified and shown to influence particle mobility. Furthermore, this framework is also extended towards Brownian transport in a rarefied gas using first order models to account for the non-continuum effects. Thus, the utility of this novel method is established in both colloids and aerosols, thereby aiding in modeling the transport of a fractal shaped PM (in the latter) and a spherical nanocarrier in a micro-channel (in the former).



Hydrodynamic interactions

Nanoscale and Rarefied gas.

Multiphase DNS

Langevin-immersed boundary method

Brownian motion


Virtual defence in Zoom
Opponent: Prof. Efstathios (Stathis) Michaelides W.A. "Tex" Moncrief, Jr. Founding Chair of Engineering, Department of engineering, College of science and engineering, Texas Christian University


Ananda Subramani Kannan

Chalmers, Mekanik och maritima vetenskaper, Strömningslära

A continuum-based multiphase DNS method for studying the Brownian dynamics of soot particles in a rarefied gas

Chemical Engineering Science,; Vol. 210(2019)

Artikel i vetenskaplig tidskrift

Assessment of hindered diffusion in arbitrary geometries using a multiphase DNS framework

Chemical Engineering Science,; Vol. 230(2021)

Artikel i vetenskaplig tidskrift

A. S. Kannan, A. Mark, D. Maggiolo, G. Sardina, S. Sasic, and H. Ström.A hydrodynamic basis for off-axis Brownian diffusion under intermediate confinements in micro-channels. International Journal of Multiphase Flow (Submitted December 2020)

A. S. Kannan, A. Mark, D. Maggiolo, G. Sardina, S. Sasic, and H. Ström. Hindered diffusion of nanoparticles in a liquid re-visited with a continuum based direct numerical simulation framework. To be submitted to a journal (2021)

The Knudsen Paradox in Micro-Channel Poiseuille Flows with a Symmetric Particle

Applied Sciences,; Vol. 11(2021)p. 1-13

Artikel i vetenskaplig tidskrift

"In this thesis we try and tame chaos using determinism."
                                                   - Ananda S. Kannan, 

Brownian motion, or the chaotic dance of molecules/nanoparticles due to incessant collisions with the constituent elements of a fluid, has been an integral part of modern day science. This characteristic random behavior, named after Robert Brown, has been the subject of extensive research since the 17th century. From understanding the complex behavior of micro-organisms, to forecasting the next stock market crash, to studying the dynamics of super-massive black holes and to modern day artificial intelligence -- understanding chaos through the lens of Brownian theory has been the approach of choice for a generation's worth of research. In fact, the significance of Brownian theory in modern day science is unmistakable, as this core idea is the subject of Albert Einstein's famed dissertation and many would argue that it is his biggest contribution (to science) along with the theory of relativity. Thus, Brownian theory is touted to be that elusive window into a microscopic world of molecules, cells and nanoparticles that was presumed to be beyond our reach.

Consequently, the primary objective of this thesis is to facilitate an in-silico based foray into this 'Brownian' world by developing novel strategies to study these complex phenomena at both molecular and continuum scales of abstraction. In this process, the existing collection of routinely used numerical tools are improved and further extended, thereby complementing and in some cases replacing experimental based efforts. This is accomplished by first developing a novel multiphase direct numerical simulation (DNS) framework that leverages a resolved solution of the continuum hydrodynamics (around the particle) and couples this with Einstein's Brownian theory. In addition, a direct simulation Monte-Carlo (DSMC) method is also used to further probe these phenomena at a molecular scale of abstraction. All these assessments combined provide a description that spans across molecular and continuum scales, thereby resolving the Brownian transport problem from two opposing perspectives i.e. building up from a molecular basis or alternately projecting down from continuum theory. These frameworks are used to evaluate both gas-particle (aerosols) and liquid-particle (colloids) systems, probing certain aspects of the Brownian transport problem relevant to a wide range of applications including (but not limited to) evaluating nano-carrier mediated drug delivery and particulate emission dispersion and mitigation. Thus, the next generation of technologies which are needed to tackle some of the common problems that plague our society today can be developed and optimized by employing the novel in-silico based strategies discussed and developed in this thesis.


Teknisk mekanik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4894


Chalmers tekniska högskola

Virtual defence in Zoom


Opponent: Prof. Efstathios (Stathis) Michaelides W.A. "Tex" Moncrief, Jr. Founding Chair of Engineering, Department of engineering, College of science and engineering, Texas Christian University

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