Date

2015

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Mechanical Engineering

First Adviser

Liu, Yaling

Other advisers/committee members

Rockwell, Donald; Webb, Edmund; Oztekin, Alparslan; Spear, Michael; Liu, Yaling

Abstract

Transport phenomena in biological flow and soft matter is very important in understanding human disease and health. The interaction between cells and blood plasma is important because it not only shows complex mechanical behavior but also advance our knowledge in medical research. This dissertation presents modeling work in drug carrier delivery in blood suspensions and early detection of circulating tumor cells. Methodologically, the Lattice Boltzmann method was employed as Navier-Stokes fluid solver due to its competence in modeling single phase and multiphase flow, handling complex geometries, and the capacity in parallel computing. A significant part of the work was devoted to the theory, algorithm, boundary conditions, and code implementations. The cells were implemented using a coarse grained molecular dynamics model because of its capacity in modeling solid nonlinear large deformations. Besides the suspending fluid and cells, nanoparticles (drug carriers) were also introduced into the system. The coupling fluid and solid was based on the Immersed Boundary Method which removes the burden of expensive mesh updating in traditional Arbitrary Lagrangian Eulerian approach. The developed code was validated for lid driven cavity flow, cell stretching test, and sphere dropping test in a quiescent fluid. Numerical models were created to study nanoparticle transport in blood cell suspensions. Nanoparticle (NP) dispersion rate is found to be strongly influenced by Red blood cell (RBC) motion, and to have an approximately linear relationship with shear rate in the RBC tumbling ( shear rate< 40 1/s) and RBC tank treading (shear > 200 1/s) regions of the flow regime. Between these two regions, there is a transition region where cell gradually transit from a tumbling motion initially into a tank treading motion eventually. From NP dispersion rate under different shear rate, a general formula to estimate NP dispersion rate was developed as D=k*shear+D0 where D0 is the thermal diffusion coefficient, k is a constant that depends on the hematocrit and cell capillary number. The formula was extended to predict NP dispersion with cell suspensions in channel flows. The formula relates the normalized NP dispersion rate with hematocrit levels, shear rate, thermal diffusion rate and cell size. The predictions given by the proposed empirical formulae agree well with data reported in the literature. Thus, these simple predictive analytical formulae provide an efficient approach for assessing NP dispersion under various flow conditions and hematocrit levels, thereby facilitating practical modeling of NP transport and distribution in large scale vascular systems. That is the novelty of this work compared to other studies in literature. The general formula was also much needed in NP transport and distribution prediction in a large scale vascular network. Another contribution of the work is the systematic parametric study of the cell translocation through a micropore under different pressure difference and micropore size. The goal of the study is to optimize the microfluidic design so that it can efficiently separate cancer cells from other blood cells. Different cell deformability characterized by membrane compressibility modulus were selected to represent cancer cells and white blood cells. We found that the cell translocation time increases with the cell membrane compressibility modulus, but not very sensitive to the membrane compressibility. However, the cell translocation time grows exponentially as the pressure or micropore diameter decreases. Thus, the pressure difference and the size of the micropore become the key parameters in microfluidic design. Traditionally the Laplace-Young equation was widely used to analyze the cell shape and the pressure difference and tension balance. We found that the tension of the cell membrane during the cell squeezing process is not uniform, with high stress at the leading membrane or at the membrane contacting the wall. This is contradictory to the uniform tension distribution assumption in the Laplace-Young equation. However, when the bending is relatively small, and a local averaged tension is used, the Laplace-Young equation can still provide a rough prediction for the minimum required pressure.

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