Mass transfer dynamics in the dissolution of Taylor bubbles.

The knowledge of thermodynamic and mass transfer parameters in gas-liquid systems is critical for the design of macroscale units for separation and reaction processes. The phenomenon of shrinkage of Taylor bubbles upon dissolution has the capability of supplying these design parameters, provided a reliable mathematical model is available for data deconvolution. Unfortunately, the existing models in the literature suffer from at least one of the following three major limitations. First, mass transfer between the bulk liquid segment and the surrounding liquid film has been incorrectly estimated. Second, the liquid segment is assumed to be well mixed, even though there is clear evidence of the contrary in the literature [Yang et al., Chem. Eng. Sci., 2017, 169, 106]. Third, an average mass transfer coefficient is assumed to be valid throughout the dissolution process, despite the fact that bubble velocities can change significantly during dissolution. In this work, we have rectified these limitations and developed a detailed model that takes into account the local concentration gradients and the flow profiles, without resorting to the computationally expensive, full numerical simulations of the fluid flow and concentration distribution equations. To validate the model, experiments were carried out in circular, silica capillaries of different radii by generating segmented flow of CO2 in physical solvents, and the diffusivity and the solubility were subsequently extracted with an error of less than 5%. This work can be extended to the study of gas-liquid-solid reactions in the Taylor flow configuration, and applied to the design of catalyst-coated monolithic reactors.

The hydrodynamics of segmented two-phase flow in a circular tube with rapidly dissolving drops.

This article discusses boundary integral simulations of dissolving drops flowing through a cylindrical tube for large aspect ratio drops. The dynamics of drop dissolution is determined by three dimensionless parameters: λ, the viscosity of the drop fluid relative to the suspending fluid; Ca, the capillary number defining the ratio of the hydrodynamic force to the interfacial tension force; and k, a dissolution constant based on the velocity of dissolution. For a single dissolving drop, the velocity in the upstream region is greater than the downstream region, and for sufficiently large k, the downstream velocity can be completely reversed, particularly at low Ca. The upstream end of the drop travels faster and experiences greater deformation than the downstream end. The film thickness, δ, between the drop and the tube wall is governed by a delicate balance between dissolution and changes in the outer fluid velocity resulting from a fixed pressure drop across the tube and mass continuity. Therefore, δ, and consequently, the drop average velocity, can increase, decrease or be relatively invariant in time. For two drops flowing in succession, while low Ca drops maintain a nearly constant separation distance during dissolution, at sufficiently large Ca, for all values of k, dissolution increases the separation distance between drops. Under these conditions, the liquid segments between two adjacent drops can no longer be considered as constant volume stirred tanks. These results will guide the choices of geometry and operating parameters that will facilitate the characterization of fast gas-liquid reactions via two-phase segmented flows.

Transport of biomolecules to binding partners displayed on the surface of microbeads arrayed in traps in a microfluidic cell.

Arrays of probe molecules integrated into a microfluidic cell are utilized as analytical tools to screen the binding interactions of the displayed probes against a target molecule. These assay platforms are useful in enzyme or antibody discovery, clinical diagnostics, and biosensing, as their ultraminiaturized design allows for high sensitivity and reduced consumption of reagents and target. We study here a platform in which the probes are first grafted to microbeads which are then arrayed in the microfluidic cell by capture in a trapping course. We examine a course which consists of V-shaped, half-open enclosures, and study theoretically and experimentally target mass transfer to the surface probes. Target binding is a two step process of diffusion across streamlines which convect the target over the microbead surface, and kinetic conjugation to the surface probes. Finite element simulations are obtained to calculate the target surface concentration as a function of time. For slow convection, large diffusive gradients build around the microbead and the trap, decreasing the overall binding rate. For rapid convection, thin diffusion boundary layers develop along the microbead surface and within the trap, increasing the binding rate to the idealized limit of untrapped microbeads in a channel. Experiments are undertaken using the binding of a target, fluorescently labeled NeutrAvidin, to its binding partner biotin, on the microbead surface. With the simulations as a guide, we identify convective flow rates which minimize diffusion barriers so that the transport rate is only kinetically determined and measure the rate constant.

Mass transfer in the biomolecular binding of a target against probe molecules on the surface of microbeads sequestered in wells in a microfluidic cell.

Diagnostic tools which screen the binding interactions of a protein target against a display of biomolecular probes to identify molecules which bind the target are central to cell proteomic studies, and to diagnostic assays. Here, we study a microfluidic design for screening interactions in which the probe molecules are hosted on microbeads sequestered in wells arranged at the bottom of a microfluidic flow channel. Assays are undertaken by streaming an analyte solution with a fluorescently labelled target through the cell, and identifying the fluorescing beads. Numerical simulations are first constructed for the analyte flow over the microbeads in the well array, and the increase in the target concentration on the microbead surface. The binding profile is expressed as a function of the ratio of the convective to the diffusive transport rates (Peclet number or Pe), and the ratio of the kinetic to the diffusive rates (Damkohler number, Da). For any Pe, as Da becomes small enough, the transport is determined by the intrinsic kinetic binding rate. As Pe increases, a thin concentration boundary layer develops over the top surface of the microbead because of the convective flow, and target binds more rapidly. However, the relatively stagnant layers of liquid in the well provide a diffusion barrier which slows the target transport, and for any Da and Pe the transport is slower than equivalent patches of probes arranged on the channel wall. Experiments are also undertaken at high Pe, using the binding of fluorescently labelled NeutrAvidin as a target to probes of its binding partner, biotin, on the microbead surface. The binding profile is compared to the simulations to measure the kinetic rate constant, and this comparison shows that the transport in the cell is not kinetically limited because of the diffusion barriers created by the stagnant liquid layer in the well. Simulations and experiments on microbeads which are only partially recessed in the well demonstrate an increase in the mass transfer rate as more of the microbead surface intersects the flow and the diffusion limitation due to the stagnant layer of liquid surrounding the bottom part of the microbead is minimized.