Quantitative Phase Velocimetry for Label-Free Measurement of Intracellular Mass Transport Velocity

Transport of mass within cells helps maintain homeostasis and is disrupted by disease and stress. Here, we develop quantitative phase velocimetry (QPV) as a label-free approach to make the invisible flow of mass within cells visible and quantifiable. We benchmark our approach against alternative image registration methods, a theoretical error model, and synthetic data. Our method tracks not just individual labeled particles or molecules, but the entire flow of material through the cell. This enables us to measure diffusivity within distinct cell compartments using a single approach, which we use here for direct comparison of nuclear and cytoplasmic diffusivity. As a label-free method, QPV can be used for long-term tracking to capture dynamics through the cell cycle. Finally, based on the known effective particle size, we show that QPV is an accessible method to measure intracellular viscosity.

Geophysical Equatorial Edge Wave with Underlying Currents in the f-Plane Approximation

I present an exact and explicit solution to the nonlinear governing equations in the equatorial f-plane, describing geophysical edge waves propagating over a plane-sloping beach, in the presence of underlying uniform currents. I also derive the analytical expressions of geophysical edge wave dynamics and the mass transport velocity.

An inviscid analysis of the Prandtl azimuthal mass transport during swirl-type sloshing

An inviscid analytical theory of a slow steady liquid mass rotation during the swirl-type sloshing in a vertical circular cylindrical tank with a fairly deep depth is proposed by utilising the asymptotic steady-state wave solution by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645). The tank performs a periodic horizontal motion with the forcing frequency close to the lowest natural sloshing frequency. The azimuthal mass transport (first observed in experiments by Prandtl (Z. Angew. Math. Mech., vol. 29(1/2), 1949, pp. 8–9)) is associated with the summarised effect of a vortical Eulerian-mean flow, which, as we show, is governed by the inviscid Craik–Leibovich equation, and an azimuthal non-Eulerian mean. Suggesting the mass-transport velocity tends to zero when approaching the vertical wall (supported by existing experiments) leads to a unique non-trivial solution of the Craik–Leibovich boundary problem and, thereby, gives an analytical expression for the summarised mass-transport velocity within the framework of the inviscid hydrodynamic model. The analytical solution is validated by comparing it with suitable experimental data.

Mass Transport Velocity in Shallow-Water Waves Reflected in a Rotating Ocean with a Coastal Boundary

The mass transport velocity in shallow-water waves reflected at right angles from an infinite and straight coast is studied theoretically in a Lagrangian reference frame. The waves are weakly nonlinear and monochromatic, and propagate in a homogenous, viscous, and rotating ocean. Unlike the traditional approach where the domain is divided into thin boundary layers and a core region, the uniform solution is obtained here without constraints on the thickness of the bottom wave boundary layer. It is shown that the mass transport velocity is not only sensitive to topography, but depends heavily on the interplay between the vertical length scales. Similarities and differences between the cases of a constant depth, a linearly sloping bottom, and a wavy and linearly sloping bottom are discussed. The mass transport velocity can be divided into two main categories—that induced by waves with a frequency close to the inertial frequency, and that induced by waves with a much larger frequency. For waves significantly affected by rotation to first order, the cross-shore mass transport velocity is very small relative to the alongshore mass transport velocity, and the direction of the mass transport velocity is reversed relative to that in waves of much higher frequencies.

Drift velocity of spatially decaying waves in a two-layer viscous system

This paper analyses the mass transport velocity in a two-layer system induced by the action of progressive waves. First the movement inside the two layers is obtained. Next the mass transport of spatially decaying waves is calculated by solving the momentum and mass conservation equations in the Lagrangian coordinate system. Two different physical situations are analysed: the first is waves in a closed channel and the second is waves in an unbounded domain, where the steady-state mass flux may be non-zero. The influence of the viscous properties of the lower layer on the mass transport in both layers is studied. Comparison with the experiments of Sakakiyama & Bijker (1989) in a water-mud system shows good agreement. The results show that the mass transport velocity can be quite different from the velocity given by the rigid bed theory, depending on the physical properties of the lower layer.

Mass transport of interfacial waves in a two-layer fluid system

Effects of viscous damping on mass transport velocity in a two-layer fluid system are studied. A temporally decaying small-amplitude interfacial wave is assumed to propagate in the fluids. The establishment and the decay of mean motions are considered as an initial-boundary-value problem. This transient problem is solved by using a Laplace transform with a numerical inversion. It is found that thin ‘second boundary layers’ are formed adjacent to the interfacial Stokes boundary layers. The thickness of these second boundary layers is of O(ε1/2) in the non-dimensional form, where ε is the dimensionless Stokes boundary layer thickness defined as $\epsilon = \hat{k}\hat{\delta}=\hat{k}(2\hat{v}/\hat{\sigma})^{1/2}$ for an interfacial wave with wave amplitude â, wavenumber $\hat{k}$ and frequency $\hat{\sigma}$ in a fluid with viscosity $\hat{v}$. Inside the second boundary layers there exists a strong steady streaming of O(α2ε−1/2), where $\alpha = \hat{k}\hat{a}$ is the surface wave slope. The mass transport velocity near the interface is much larger than that in a single-layer system, which is O(α2) (e.g. Longuet-Higgins 1953; Craik 1982). In the core regions outside the thin second boundary layers, the mass transport velocity is enhanced by the diffusion of the mean interfacial velocity and vorticity. Because of vertical diffusion and viscous damping of the mean interfacial vorticity, the ‘interfacial second boundary layers’ diminish as time increases. The mean motions eventually die out owing to viscous attenuation. The mass transport velocity profiles are very different from those obtained by Dore (1970, 1973) which ignored viscous attenuation. When a temporally decaying small-amplitude surface progressive wave is propagating in the system, the mean motions are found to be much less significant, O(α2).

Mass transport in water waves over an elastic bed

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

Mass transport under partially reflected waves in a rectangular channel

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.