Numerical Study on Inertial Migration of Particles in Microchannels

Abstract

Inertial migration has emerged as an interesting area of study in the area of biofluid dynamics. The particles in fluid flow move towards the wall and attain equilibrium position due to this phenomenon. This technique can help in particle separation which is highly important in biomedical engineering. Numerical study on inertial migration of non-spherical particles is a class of problem which belongs to fluid-structure interaction. Development of good numerical model to study the inertial migration will be of keen interest. The inertial migration of neutrally and non-neutrally buoyant non-spherical particles is studied with the aid of feedback forcing based immersed boundary method. The inertial migration of neutrally buoyant cylindrical particle in both Poiseuille and shear flow in straight channel are analysed first in this work. Inertial migration is characterised by equilibrium position and migration time. Particle is observed to attain equilibrium position close to 0.6 times half the channel height in case of Poiseuille flow while equilibrium position is attained at channel centre in shear flow. To understand the dependence of inertial migration dynamics on Reynolds number, particle diameter, channel height and initial position, detailed parametric study is carried out. It is observed that equilibrium position moves to lower wall with increase in Reynolds number and channel height and reduction in particle diameter in Poiseuille flow. However, it is only get affected by channel height and shear rate (shift towards channel centre) in case of shear flow. Equilibrium position stay unaffected with initial position in both flow cases. On the other hand, migration time reduces with increase in Reynolds number and particle diameter and reduction in channel height in case of Poiseuille flow. The same phenomena happen in case of shear flow except migration time increases with particle diameter rise. In the following stage, inertial migration in various non straight channels such as backward facing stepped, stepped and constricted channel are investigated. The presence of recirculation zones in these types of channels can make significant changes in inertial migration dynamics. Equilibrium position shifts towards channel centre with increase in Reynolds number, particle diameter and blockage ratio (ratio of step height to channel height) in case of backward facing stepped channel. In case of stepped channel, equilibrium position is driven towards lower wall with increase vii in depth of step whereas it remains unchanged with variation in length of step. When particle migration in constricted channel comes into picture, it is noticed that equilibrium position is unaffected by Reynolds number and constriction clearance and only slightly influenced by particle diameter. Out of all non-straight channels a common behaviour observed is that equilibrium position shifts with respect to initial position of release. Moving on, inertial migration dynamics in straight, backward facing stepped and constricted channel is compared and it is concluded that constricted channel is better for separation since equilibrium position is more predictable in the same compared to other channel configurations. Motivated by the parametric study results, artificial neural network algorithm is utilised to create a prediction model for predicting equilibrium position, and migration time of particle in both straight and constricted channel. Mass and shape of particle is another two properties which can play important part in inertial migration dynamics. Hence, in the following stage, lateral migration of various shaped particles such as circular, elliptical, square, rectangular and biconcave is addressed. It is observed that biconcave particle has equilibrium position closest to lower wall. The simulations are repeated for non-neutrally buoyant particles and it is observed that equilibrium position shifts towards lower wall when buoyancy force is taken into consideration. The model is further extended to analyse the effect of application of control force to alter the equilibrium position to centre of channel in both Poiseuille and pulsatile flows. The control force in both flows is applied in such a way that particle equilibrium position is moved to centre of channel. Magnitude of control force increases with rise in Reynolds number and reduction in particle diameter in both flow cases. However, when density ratio (particle to fluid) is increased, magnitude of control force initially rises and then reduces in both flow cases. In case of pulsatile flow, frequency of oscillation is also taken into consideration for parametric study. Control force magnitude increases with frequency of oscillation. Gaining inspiration from the parametric study results, suitable correlations are proposed for control force with the aid of linear regression algorithm in both flow cases. It is concluded that, the control of viii equilibrium position with application of external force can make significant advance in particle separation technology. The current computational model is then utilised to simulate inertial migration of multiple particles in straight, stepped and slit channels. Two particle migration in straight channel is analysed first, and it is found that equilibrium positions of both particles come closer to channel centre compared to that in single particle migration. This may be due to the reverse lift force created by secondary flow vortices interaction between the particles. This interaction can reduce with increase in initial centre-to centre distance and hence reduce migration time since time required for balancing of lifts decreases. The effect of initial orientation (horizontal, vertical and offset) is also studied and it is observed that migration time is higher for particle 2 in offset condition since it is released closer to channel centre. In the following stage, two particle migration in a stepped channel is simulated and the effect of density ratio and depth of step is studied. Equilibrium position is driven to lower wall first and then towards channel centre with increase in density ratio which can be due to the action of Saffman lift force. However, the strength of secondary flow vortices increases with depth of step and hence, equilibrium position shifts towards lower wall with it. In final step, migration of three particles in a slit channel is studied. It seems that equilibrium position stays constant with all parameters such as slit clearance, slit angle and initial orientation and only changes with initial position. The residence time increases with slit clearance and it is highest for a slit angle of π/2. For triangular orientation case, equilibrium position of particle 2 changes since its initial position is away from channel centre.