Mathematical Modeling of Chemotaxis and Fluid Dynamics
Summary
Mathematical models of chemotaxis coupled with fluid dynamics seek to describe how mobile organisms or cells navigate chemical gradients while interacting with a surrounding fluid medium. Classical chemotaxis models, typified by the Keller–Segel system, capture the evolution of cell density under random motility and directed movement towards higher concentrations of a chemoattractant. When embedded in a fluid environment, one augments these equations with the incompressible Navier–Stokes system to account for advection of both cells and chemicals by the flow. Such coupled models feature nonlinear cross-diffusion, chemo-sensitivity terms and hydrodynamic pressure effects. Key analytical questions concern global existence versus finite-time blow-up of solutions, uniform boundedness, asymptotic convergence to homogeneous states and the influence of fluid viscosity and advection on pattern formation. From a practical standpoint, these models illuminate processes as diverse as bacterial aggregation in microfluidic channels, tumour invasion in interstitial flow, and pollutant degradation by microbial consortia in porous media. The global significance of this field lies in its capacity to predict and control biofilm formation, optimise bioreactor design and understand the self-organisation of active suspensions in environmental and biomedical contexts.
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Mathematical Modeling of Chemotaxis and Fluid Dynamics publication trend
The graph below shows the total number of articles in mathematical modeling of chemotaxis and fluid dynamics across all publications each year (not limited to Nature Index journals).
Technical terms
C chemotaxis: Directed movement of cells or organisms up a chemical concentration gradient.
Navier–Stokes equations: System of partial differential equations governing the motion of incompressible viscous fluids.
Advection: Transport of a substance by the bulk motion of the fluid.
Logistic damping: Nonlinear term limiting population growth, typically of the form μ u (1–u/K).
Viscosity: Measure of a fluid’s resistance to gradual deformation by shear stress.
Blow-up: Phenomenon where solution norms become unbounded in finite time.
Boundedness: Property that solution norms remain finite for all time.
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