Michael D. Graham

2022 Julian C. Smith Lectures

Michael D. Graham
Steenbock Professor of Engineering
Harvey D. Spangler Professor
University of Wisconsin - Madison

Dynamics and distributions of cells in blood flow

Monday, May 2nd - 4:00 PM - 155 Olin Hall

As they flow, red blood cells migrate toward the center of a blood vessel, leaving a cell-free layer at the vessel wall, while white blood cells and platelets are preferentially found near the walls, a segregration phenomenon called margination. We present direct simulations of blood flow as well as mechanistic theory that aim to describe and understand these phenomena. We also describe collaborative work with the laboratory of Wilbur Lam that demonstrates the importance of these phenomena in medicine.

To disentangle effects of shape, size, and deformability, with first describe direct simulations of multicomponent suspensions of deformable capsules. Observations indicate that margination can be driven by contrasts of size, stiffness or shape – for example, a trace component of stiff or small particles will marginate in a suspension whose majority component is large and soft.  A mechanistic theory predicts, in good agreement with experiments and our simulations, that the cell-free layer thickness follows a master curve with confinement ratio and volume fraction.It also predicts several regimes of segregation, depending on the value of a dimensionless “margination parameter” that quantifies the effect of cell-cell collisions as well as hydrodynamic migration of particles away from walls. 

These segregation phenomena have important physiological and clinical consequences. Treatment of patients with drugs such as dexamethasone or epinephrine lead to softening of white blood cells, and thus to their demargination. In blood disorders such as sickle cell disease and iron deficiency anemia, the diseased cells are smaller and stiffer than heathy red blood cells, and our simulations predict that these cells will strongly marginate. We also predict that that these marginated cells generate large shear stress fluctuations on the vessel walls, a phenomenon that may explain clinical observations of vascular inflammation in persons with these disorders. 


Complex flows of complex fluids -- dynamics of polymer and surfactant solutions in flow

Tuesday, May 3rd - 3:30 PM - 155 Olin Hall

Addition of a small amount of a long-chain polymer to a liquid or a micelle-forming surfactant can result on dramatic effects on flow processes. These additives alter drop breakup processes, the stability of coating flows, the behavior of particle-laden fluids such as blood and the dynamics of turbulence. This presentation focuses on the role that polymer additives play in reducing drag in turbulent flows, with a brief discussion at the end on new models for the rheology of wormlike micelle solutions. 

The flow of a liquid is smooth and steady at low speeds, as if thin layers of fluid were sliding over one another. At higher speeds, this laminar flow becomes turbulent — the steady flow gives way to fluctuating eddies that hinder the motion of the fluid and dramatically increasing energy consumption relative to the laminar flow. The processes that drive these fluctuations become self-sustaining during the transition from laminar to turbulent flow, so this transition is a window into the origins of fully developed turbulence.We study this transition using direct simulations of a flowing dilute polymer solution. If the Reynolds number (dimensionless flow rate) is sufficiently low, a turbulent channel flow will laminarize as polymer concentration increases, but then become turbulent again at higher concentration. Direct simulations of flow in the latter regime yield a surprising result: the turbulent fluctuations strongly resemble so-called Tollmien-Schlichting (TS) waves. Although these patterns are found in Newtonian flows, they do not play a role in fully-developed Newtonian turbulence.In the polymeric case, however, polymer stresses suppress the normal turbulent structures while amplifying the TS modes, consistent with experimental observations. 

Flows of surfactant solutions are much less well-understood than polymer solutions, because their rheology is substantially more complex. We have developed a model of wormlike micelle solutions that predicts flow induced structure formation and reproduces the steady and transient shear and extensional rheology of a number of experimental surfactant systems. The aim of this work is to have a model that can be used in complex flow simulations to understand and predict phenomena such as vorticity banding and turbulent drag reduction.