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Molecular Communication in Ducts in the Presence of Gravity

Recently, the application of communication engineering principles to biomedical problems has spawned the emerging interdisciplinary research field of molecular communication (MC). MC is ubiquitous in natural biological systems and has a high potential for bio-medical applications such as targeted drug delivery, health monitoring, and micro-fluidic channel design. Besides medical applications, MC may be applied in industrial settings, e.g., for monitoring of chemical reactors and pipelines. While classical communication systems rely on transport by electro-magnetic or acoustic wave propagation, in MC, information is encoded into the type or concentration of signaling particles that are transported from a transmitter (TX) to a receiver (RX) by diffusion, flow or combinations thereof. For the extreme cases, namely, the nondispersive and the dispersive regime, there exist insightful closed-form expressions for the particle motion within a duct channel. In the nondispersive or flow-based regime, particles do not appreciably diffuse over the cross section of the duct while being transported by advection over the TX-RX distance. Therefore, the laminar flow velocity profile determines the particle motion. In the dispersive or Aris-Taylor regime, particles fully diffuse over a length greater than the radius of the duct while being transported over the TX-RX distance. As a consequence, particles get transported by different flow velocities in different time instances.

In this project, the effect of gravity that changes the transport characteristics of the particles next to diffusion and laminar flow will be considered. Gravity is modeled by a constant acceleration or, for special cases, by a constant velocity, both pointing in negative y-direction. The focus lies on extenting the solution for the Aris-Taylor regime. In the Aris-Taylor model, diffusion is assumed to be high enough to average out the different velocities of the laminar flow velocity profile, leading to a tractable 1-D model with effective flow speed and effective diffusion coefficient. The main objective of this project is to gain insight under which conditions this simplification is still valid in the presence of gravity and to investigate how the effect of gravity can be incorporated into the mathematical solution.

Tasks:

  • Literature review on advection-diffusion equations and the derivation of the Aris-Taylor regime solutions
  • Mathematical modelling of the advection-diffusion process with gravity
  • Derivation of an analytical solution similarly to the Aris-Taylor solution whereby suitable simplifications can be applied
  • Evaluation based on comparisons to particle-based simulations