[Paper Review] Concentration banding instability of a sheared bacterial suspension

Laxminarsimharao, Piyush Garg+1 more|arXiv (Cornell University)|Aug 23, 2018

Micro and Nano Robotics3 citations

TL;DR

This paper proposes a shear-induced instability in bacterial suspensions driven by long-ranged hydrodynamic interactions, leading to exponential growth of concentration and velocity layering perturbations under shear. Non-linear simulations confirm the formation of gradient-banded velocity profiles with local bacterial depletion at band interfaces, explaining recent experimental observations of shear-banding without requiring additional mechanisms.

ABSTRACT

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bacterial suspensions.

Motivation & Objective

• To identify the physical mechanism behind shear-banding in bacterial suspensions observed experimentally.
• To determine whether long-ranged hydrodynamic interactions alone can drive the formation of concentration and velocity bands.
• To analyze the linear stability of a sheared bacterial suspension and identify the growth of layering perturbations.
• To simulate the non-linear evolution of the instability and predict the resulting flow and concentration structures.
• To explain the local depletion of bacteria at band interfaces observed in experiments.

Proposed method

• Conduct a linear stability analysis on a homogeneously sheared bacterial suspension to identify exponentially growing perturbations in shear-rate and concentration.
• Model the system using hydrodynamic interactions that are long-ranged, consistent with the Stokeslet approximation for low-Reynolds-number flows.
• Derive and solve the linearized equations of motion and continuity for the fluid and bacterial concentration fields under shear.
• Perform non-linear simulations to track the evolution of perturbations beyond the linear regime.
• Analyze the resulting flow profiles to identify the formation of gradient-banded structures with distinct velocity and concentration gradients.
• Examine the spatial distribution of bacteria at band interfaces to quantify local depletion.

Experimental results

Research questions

• RQ1 Can long-ranged hydrodynamic interactions alone induce shear-banding in bacterial suspensions?
• RQ2 What is the nature of the instability mechanism driving concentration and velocity layering under shear?
• RQ3 How do the linear growth rates of perturbations relate to the observed banding patterns?
• RQ4 What is the role of bacterial depletion at band interfaces in the non-linear regime?
• RQ5 How do the simulated velocity and concentration profiles compare to experimental observations?

Key findings

• The linear stability analysis reveals exponentially growing layering perturbations in both shear-rate and bacterial concentration fields.
• Non-linear simulations show the instability evolves into stable, gradient-banded velocity profiles with distinct concentration gradients.
• A local depletion of bacteria is consistently observed at the interfaces between bands, consistent with experimental observations.
• The instability is driven solely by long-ranged hydrodynamic interactions, without requiring additional forces or interactions.
• The mechanism explains recent experimental reports of shear-banding in bacterial suspensions without invoking complex rheological or colloidal effects.
• The system transitions from homogeneous shear to a heterogeneous, band-separated state due to the intrinsic instability of the suspension under shear.