Laminar Liquid Flow Research Articles

Chemotactic separation of enzymes.

We demonstrate a procedure for the separation of enzymes based on their chemotactic response toward an imposed substrate concentration gradient. The separation is observed within a two-inlet, five-outlet microfluidic network, designed to allow mixtures of active (ones that catalyze substrate turnover) and inactive (ones that do not catalyze substrate turnover) enzymes, labeled with different fluorophores, to flow through one of the inlets. Substrate solution prepared in phosphate buffer was introduced through the other inlet of the device at the same flow rate. The steady-state concentration profiles of the enzymes were obtained at specific positions within the outlets of the microchannel using fluorescence microscopy. In the presence of a substrate concentration gradient, active enzyme molecules migrated preferentially toward the substrate channel. The excess migration of the active enzyme molecules was quantified in terms of an enrichment coefficient. Experiments were carried out with different pairs of enzymes. Coupling the physics of laminar flow of liquid and molecular diffusion, multiphysics simulations were carried out to estimate the extent of the chemotactic separation. Our results show that, with appropriate microfluidic arrangement, molecular chemotaxis leads to spontaneous separation of active enzyme molecules from their inactive counterparts of similar charge and size.

Physical phenomena occurring in the process of physical–mechanical degumming of fiber from flax straw

The study presents physical phenomena that occur in the physical–mechanical process of degumming of fiber from flax straw. Moreover, the effect of liquid flow through the straw has been determined by analysis of the mass exchange (motion) according to the principles of fluid mechanics. It was shown that conditions of the degumming process, especially the temperature, have a significant effect on acceleration of the mass exchange. The analyses of the results indicated that the developed model laboratory device allowed for evaluation of the mechanism of mass exchange by slow laminar liquid flow. The evaluation of the degumming process with convective mass motion at a higher speed of liquid flow was based on model tests of hydrodynamic washing of three types of gels: fruit pectin, animal gelatin and starch from linen fabrics. It was shown that temperature is a decisive factor affecting the washing out of gels. Better washing out was achieved by using diffusive penetration of water into the gel structure at the initial phase of the process. Using the dynamic washing out of the gels with a water stream of high flow speed (at the m/s range) shortened considerably the washing time.

Entrance and temperature dependent property effects in the laminar forced convection in straight ducts with uniform wall temperature

The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. Uniform temperature boundary conditions are specified at the duct walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat ducts, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number are presented for different values of the entrance Prandtl number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the local Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity.

An enhanced transmission line method for modelling laminar flow of liquid in pipelines

The transmission line method is a very efficient method for dynamic modelling of flow in pipelines and uses delay elements to represent wave propagation. In this article, an existing transmission line method model is investigated and shown to have some deficiencies. An alternative technique is introduced to enhance the transient and steady-state accuracy. Extremely good agreement is obtained between this new transmission line method and an analytical model. The model has been implemented in simulation of a number of highly dynamic systems and has been found to be robust and reliable.

Laminar and transitional liquid metal duct flow near a magnetic point dipole

AbstractThe flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centred in spanwise direction. Our model uses the quasistatic approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers $\mathit{Re}$ as well as the transitional time-dependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes and their dependence on $\mathit{Re}$ and on the Hartmann number $\mathit{Ha}$, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared: streamwise-, spanwise- and wall-normal-oriented dipole axes. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation, which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. The enstrophy in the turbulent wake grows linearly with $\mathit{Ha}$ which is connected with a dominance of the wall-normal derivative of the streamwise velocity.

A Numerical Study of the Thermal Performance of Microchannel Heat Sinks with Multiple Length Bifurcation in Laminar Liquid Flow

A rectangular, straight microchannel heat sink with multiple length bifurcation has been designed, and the corresponding laminar flow and thermal performance have been investigated, numerically. Five different cases with multiple length bifurcation and various arrangements are investigated, as well as one case without bifurcations. All laminar fluid flow and surface heat transfer results are obtained using computation fluid dynamics, and a constant heat flux thermal boundary condition is applied to the heated surfaces. The inlet velocity ranges from 0.6 m/s to 1.4 m/s, with the corresponding Reynolds number from 220 to 520. The local pressure, velocity, temperature distributions, and averaged heat transfer coefficient are presented. The overall thermal resistances subjected to inlet Reynolds number are evaluated and compared for six different microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with bifurcation flow is better than that of the corresponding straight microchannel heat sink, especially the heat sink with longer length bifurcation. The usage of multiple length bifurcated plates in microchannel heat sink can reduce the overall thermal resistance by a factor of up to 2, and make the temperature of a heated surface more uniform, especially for the heat sink having a short bifurcation in the center and two bifurcations near the sides (case 4). It is suggested that proper design of the multiple length bifurcation could be employed to improve the overall thermal performance of microchannel heat sinks.

Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

A parametric investigation is carried out on the effects of temperature dependent viscosity and thermal conductivity and of viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Uniform heat flux boundary conditions are specified at the heated walls. A superposition method is proved to be applicable in order to predict the value of the Nusselt number by considering separately the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. In addition, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the viscosity and thermal conductivity Pearson numbers and of the Brinkman number.

Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow

This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum, pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress. The problem is solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity, pollutant concentration, polymer stress components, skin friction and wall mass transfer rate. The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into, say, water bodies. The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.

Enhancement Factor for Gas Absorption in a Finite Liquid Layer. Part 4: Influence of Gas‐Phase Mass Transfer during a Second‐Order Reaction in a Liquid in Laminar Flow

AbstractNumerical analysis is presented for gas absorption accompanied by a second‐order reaction into a liquid layer of finite thickness in laminar flow, with the gas‐phase mass transfer resistance and the axial decrease of the gas‐phase solute concentration due to absorption being taken into account. Both cocurrent and countercurrent flow modes are analyzed, where the presence of significant resistance or axial decrease of the solute concentration in the gas phase can lead to substantially lower rates of gas absorption than those found when the influence of gas‐phase mass transfer is not considered. Approximate expressions describing the exact numerical solution to the enhancement factor in the cocurrent flow mode are developed and can be extrapolated for estimating the enhancement factor in a more general case of a (1, n)‐th‐order reaction in which the influence of gas‐phase mass transfer cannot be neglected.

Homogeneous Flow of Hydraulic Fluid Retaining Gap

This paper presents the laminar flow of homogeneous liquids in crevices of smooth hydraulic resistance. The paper presents a theoretical model for the distribution of pressure in the gap and the flow rate through the slot hydraulic. The presented theoretical models for the distribution of pressure and flow in the gap on conventional hydraulic resistance of hydraulic joints, whose shape is related to the errors of their execution. In deriving the theoretical models, by introducing a variable height of the gap in the initial episode, was founded stream velocity profile variability in the hydraulic fluid retaining gap and zero values of local losses at the entrance to the slot. An analysis of the validity of the simplifications adopted in the given formulas for the distribution of pressure and flow in the hydraulic gap and on the basis provides guidelines for estimating the energy losses that occur cracks in the hydraulic resistance.

Melting phenomenon in magneto hydro-dynamics steady flow and heat transfer over a moving surface in the presence of thermal radiation

The Lie group method is applied to present an analysis of the magneto hydro-dynamics (MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation. By using the Lie group method, we have presented the transformation groups for the problem apart from the scaling group. The application of this method reduces the partial differential equations (PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations (ODEs) with appropriate boundary conditions. The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method (FDM). The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.

Rate of gas absorption on a slippery bubble mattress

We investigate the absorption of a pure gas into a liquid in laminar flow past a superhydrophobic surface consisting of alternating solid walls and micro-bubbles. We experimentally measure and numerically estimate the dynamic mass transfer of gas absorption at stable gas–liquid interfaces for short contacting times. We study the net rate of gas absorption experimentally by in situ measurements of dissolved oxygen concentration profiles in aqueous solutions flowing over oxygen bubbles by fluorescence lifetime imaging microscopy. We numerically analyze the dynamics of interfacial mass transfer of dissolved oxygen by considering (i) kinetic equilibrium conditions at bubble surfaces that are conventionally described by Henry's Law and (ii) non-equilibrium conditions at bubble surfaces using Statistical Rate Theory (SRT). Our experimental results show that kinetic equilibrium is not established for short contact times. Mass transfer of gas into liquid flow past micro-bubbles can be well described by our simulations performed with the non-equilibrium theory for a short exposure time (∼180 μs) of liquid with a microbubble, deviating from the commonly accepted Henry's Law.

Local Nusselt number enhancement during gas–liquid Taylor bubble flow in a square mini-channel: An experimental study

Taylor bubble flow takes place when two immiscible fluids (liquid–liquid or gas–liquid) flow inside a tube of capillary dimensions within specific range of volume flow ratios. In the slug flows where gas and liquid are two different phases, liquid slugs are separated by elongated Taylor bubbles. This singular flow pattern is observed in many engineering mini-/micro-scale devices like pulsating heat pipes, gas–liquid–solid monolithic reactors, micro-two-phase heat exchangers, digital micro-fluidics, micro-scale mass transfer process, fuel cells, etc. The unique and complex flow characteristics require understanding on local, as well as global, spatio-temporal scales. In the present work, the axial streamwise profile of the fluid and wall temperature for air–water (i) isolated single Taylor bubble and, (ii) a train of Taylor bubbles, in a horizontal square channel of size 3.3 mm × 3.3 mm × 350 mm, heated from the bottom (heated length = 175 mm), with the other three sides kept insulated, are reported at different gas volume flow ratios. The primary aim is to study the enhancement of heat transfer due to the Taylor bubble train flow, in comparison with thermally developing single-phase flows. Intrusion of a bubble in the liquid flow drastically changes the local temperature profiles. The axial distribution of time-averaged local Nusselt number (Nu¯z) shows that Taylor bubble train regime increases the transport of heat up to 1.2–1.6 times more as compared with laminar single-phase liquid flow. In addition, for a given liquid flow Reynolds number, the heat transfer enhancement is a function of the geometrical parameters of the unit cell, i.e., the length of adjacent gas bubble and water plug.

An exact solution for laminar, unidirectional flow of Houska thixotropic fluids in a circular pipe

Laminar flow of an incompressible thixotropic liquid which obeys the Houska model as its constitutive equation is investigated theoretically in a circular pipe under equilibrium (steady) conditions. Having derived the single differential equation governing fully-developed, unidirectional, pipe flow of this fluid model, it is shown that an analytical solution is possible for the linear case of the Houska model. The existence and uniqueness of the analytical solution so-obtained is examined theoretically. For the more general nonlinear case of the Houska model, the trust region algorithm is used to obtain numerical results for the flow characteristics. The effects of thixotropic parameters such as breakdown-to-rebuild ratio, viscosity ratio, and Bingham number are investigated on the structural parameter and velocity profiles. As a special case, pipe flow of a thixotropic fluid obeying the Moore model is addressed and a correct boundary condition is proposed at the pipe centerline for this particular fluid model.

First-harmonic balance for fast evaluation of power-law fluid flow enhancement under periodic pressure gradient

This work considers rectilinear laminar flow of power-law liquids under a periodic pressure gradient. In contrast to Newtonian flow, previous studies have shown that the interaction between nonlinearities by non-Newtonian rheology and exogenous periodic forcing can yield important changes in the flow patterns, such as mean flowrate enhancement for shear-thinning fluid whereas flowrate reduction for shear-thickening fluid relative to non-forcing conditions. The aim of this work was to evaluate the ability of first-harmonic approximation for estimating mean flowrate enhancement/reductions under periodic pressure gradient oscillations. The first-harmonic balance involves the projection of nonlinearities on a first-harmonic Fourier basis, which reduces the governing partial differential equation into three ordinary boundary-value problems that should be solved numerically. The results showed that the predictions from the first-harmonic balance were in good agreement, both qualitative and quantitative, with direct numerical simulations of the governing partial differential equation. The advantage of the former over the latter is the computational burden since numerical computations for the first-harmonic equations does not depend of the forcing frequency.

Enhancement Factor for Gas Absorption in a Finite Liquid Layer. Part 3: Instantaneous and Second‐Order Reactions in a Liquid in Laminar Flow

AbstractNumerical analysis on gas absorption accompanied by an instantaneous reaction or a second‐order reaction into a liquid layer of finite thickness in laminar flow is presented. A similar influence of the reactant diffusivity ratio, the Fourier number, and the Hatta number on the enhancement factor is reported compared to the ideal situation in which the liquid layer is in plug flow motion. Approximate enhancement factor expressions are developed for both reaction cases by analogy to the plug flow situation, where the predictions according to the original penetration theory tend to give erroneous results in the enhancement factor at Fourier numbers above 0.1. The developed expressions in the case of a second‐order reaction can be extrapolated for estimating the enhancement factor in the more general case of a (1, n)‐th‐order reaction.

Numerical Investigation on Laminar Microconvective Liquid Flow With Entrance Effect and Graetz Problem due to Variation in Thermal Properties

This work deals with the analysis of forced convection in single-phase laminar flow of liquid through microsized circular geometry with a diameter of 100 × 10−6 m. The problem with hydrodynamically and thermally developing flow in the entrance region with no-slip, no-temperature jump and constant wall heat flux boundary condition is numerically studied. Two-dimensional (with axisymmetry) simulation is carried out to understand the effect of fluid property variations on flow development and heat transfer. Pure continuum-based governing equations are solved to predict the significance of momentum and energy transport due to temperature-dependent viscosity and thermal conductivity variation, respectively. The radial inward flow is induced due to temperature-dependent density variation that sharpens the axial velocity profile. The investigation also analyzes the change in Nusselt number with locations in the channel for Graetz problem with uniform heating condition. The flattening of axial velocity profile, radial temperature profile, and inward radial flow influences the heat flow characteristics. The investigations in computational domain show that Nusselt number in thermal entrance region deviates from constant properties solution due to scaling effects.

Hydrodynamic and thermal transport characteristics of swirling flows through microchannels with interfacial slip

Fluid flow and heat transfer characteristics of decaying laminar swirling flow of liquids in microchannels have been theoretically investigated, with the consideration of interfacial slip. The effects of slip–swirl interactions on friction factor and Nusselt number have been investigated. The effect of swirl is found to increase the friction factor, while the velocity slip tends to decrease the same, and the combined effect could either result in an increase or a decrease in the friction factor as compared to that in case of flow without slip and without swirl depending upon the situation. It has been recognized that, for a given slip length, there is a threshold inlet swirl number S0 above which the average friction factor over the entrance length (f¯SS) is higher than that in case of flow with no slip and no swirl (f¯), while, below the threshold swirl number S0, f¯SS<f¯. The threshold inlet swirl number S0 is found to be almost independent of the Reynolds number and the critical radius of inlet Rankine vortex profile for the swirl. It has also been revealed that both the inlet swirl and velocity slip effectively increase the Nusselt number.

Research of laminar liquid flow in asymmetric narrow channels

Purpose – The purpose of this paper is to find a solution of laminar liquid flow in asymmetric narrow channels. In many cases, an intuitive solution is much more useful and necessary for engineering applications, although numerical solutions can be obtained.Design/methodology/approach – The Navier‐Stokes equations of laminar liquid flow in asymmetric narrow channels are simplified based on geometric characteristics of narrow channels, physical characteristics of liquid and boundary conditions. The simplified Navier‐Stokes equations are solved theoretically. Verification of the obtained results is carried out based on comparing with the Jeffery‐Hamel flow, which is an exact solution of liquid flow in convergent or divergent channels proposed by Jeffery.Findings – This paper proposed an intuitive solution of laminar liquid flow in asymmetric narrow channels. Obtained results show that the solution can provide a fairly precise flowrate, when a ratio between the width of the channel and the curvature of the b...

Hydrodynamic Swirl Decay in Microtubes with Interfacial Slip

The decay of swirl in a laminar swirling flow of liquid through a microtube is numerically investigated. The Navier-Stokes equations are solved with velocity slip at the wall. The influences of swirl–slip interactions on swirl decay are investigated. The decay of swirl is quantified by the variation in the ratio of swirl number at a section with that at the inlet (S/S0) along the flow. A mathematical expression of S/S 0 with nondimensional distance along the flow from the inlet is developed in terms of the pertinent flow parameters like Reynolds number, inlet swirl number, dimensionless slip length, and dimensionless critical radius of inlet Rankine vortex profile for the swirl. Such a functional relationship may act as an elegant design tool for microtubes characterized with swirling flows in presence of interfacial slip.