skip to main content


Title: Effect of external shear flow on sperm motility
The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.  more » « less
Award ID(s):
1700961
PAR ID:
10140853
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Soft Matter
Volume:
15
Issue:
31
ISSN:
1744-683X
Page Range / eLocation ID:
6269 to 6277
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    In this paper, we theoretically investigate the migration of a surfactant covered droplet in a Poiseuille flow by including the surface viscosities of the droplet. We employ a regular perturbation expansion for low surface Péclet numbers and solve the problem up to a second-order approximation. We represent the drop surface as a two-dimensional homogeneous fluid using the Bousinessq–Scriven law and employ Lamb's general solution to represent the velocity fields inside and outside the droplet. We obtain an expression for the cross-stream migration velocity of the droplet, where the surface viscosities are captured by the Bousinessq numbers for surface shear and surface dilatation. We elucidate the influence of the surface viscosities on the migration characteristics of the droplet and the surfactant redistribution on the droplet surface. Our study sheds light on the importance of including the droplet surface viscosities to accurately predict the migration characteristics of the droplet. 
    more » « less
  2. Microfluidic manipulation of particles usually relies on their cross-stream migration. A center- or wall-directed motion has been reported for particles leading or lagging the Poiseuille flow of viscoelastic polyethylene oxide (PEO) solution via positive or negative electrophoresis. Such electro-elastic migration is exactly opposite to the electro-inertial migration of particles in a Newtonian fluid flow. We demonstrate here through the top- and side-view imaging that the leading and lagging particles in the electro-hydrodynamic flow of PEO solution migrate toward the centerline and corners of a rectangular microchannel, respectively. Each of these electro-elastic particle migrations is reduced in the PEO solution with shorter polymers though neither of them exhibits a strong dependence on the particle size. Both phenomena can be reasonably explained by the theory in terms of the ratios of the forces involved in the process. Decreasing the PEO concentration causes the particle migration to shift from the viscoelastic mode to the Newtonian mode, for which the magnitude of the imposed electric field is found to play an important role.

     
    more » « less
  3. Abstract

    With the expansion of hydropower, in‐stream converters, flood‐protection infrastructures, and growing concerns on deltas fragile ecosystems, there is a pressing need to evaluate and monitor bedform sediment mass flux. It is critical to estimate real‐time bedform size and migration velocity and provide a theoretical framework to convert easily accessible time histories of bed elevations into spatially evolving patterns. We collected spatiotemporally resolved bathymetries from laboratory flumes and the Colorado River in statistically steady, homogeneous, subcritical flow conditions. Wave number and frequency spectra of bed elevations show compelling evidence of scale‐dependent velocity for the hierarchy of migrating bedforms observed in the laboratory and field. New scaling laws were applied to describe the full range of migration velocities as function of two dimensionless groups based on the bed shear velocity, sediment diameter, and water depth. Further simplification resulted in a mixed length scale model estimating scale‐dependent migration velocities, without requiring bedform classification or identification.

     
    more » « less
  4. This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ( $A=l/a_{0}$ ) is defined as the ratio of the particle size ( $l$ ) to the cross-sectional dimension ( $a_{0}$ ) and $\unicode[STIX]{x1D6FC}$ is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e. $\unicode[STIX]{x1D6FC}\sim O(1)$ ). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section, and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios ( ${\sim}10$ ) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers. 
    more » « less
  5. We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito ( J. Non-Newtonian Fluid Mech. , vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction. 
    more » « less