Thermal compact modeling approach of droplet microreactor based Lab-on-a-Chip devices

Highlights

• A novel compact model for thermal aware design of droplet reactor based LoC devices is presented.

• Model is applicable for various boundary conditions e.g. volumetric enzyme reaction.

• The compact model was validated by conventional CFD solver and resulted in good match.

• The compact model provided a 450 fold reduction in execution time.

• As a behavioral model it can be easily integrated into the IC-MEMS design flow.

Abstract

The paper presents a novel compact model which enables the thermal analysis of microchannels consisting of continuously moving microdroplets with biologically active content inside. The compact model utilizes the switched capacitor approach to describe the convective heat transfer and as a behavioral model, it can be easily integrated into an IC-MEMS design flow. With this novel approach the temperature profile of the channel can be calculated in minutes compared to conventional numerical techniques that requires days or weeks. The model was validated by a standard CFD solver and a good match was achieved.

Introduction

The rising complexity of Lab-on-a-Chip (LoC) devices for medical diagnostic purposes requires a multi-domain design. Sample handling is usually enabled by microfluidic techniques as the fluids are flowing in micro-sized channels where separation, mixing and bio-reactions may occur. The effects of such reactions can be detected by biosensors which provide electrical signals as output, more often required to be processed on-chip by integrated circuits. The method of co-design of MEMS and integrated circuits shown in Fig. 1 is already utilized in commercial products [1]. A MEMS device is usually modeled by numerical methods (e.g. FEM or CFD simulation) in order to generate a reduced order model (ROM). The ROM is considered as a behavioral description of the MEMS device therefore the electrical and the mechanical functionality can be handled together at a high level of abstraction. Numerical modeling usually provides high accuracy, and requires high computation times, though. In contrast, reduced order models focus on the key behavior of the device and require only moderate computation time. Therefore bypassing the numerical modeling step the design iteration time can be significantly reduced (Fig. 1). This approach can be generalized [2] especially for electro-mechanical microdevices, however the multi-physical nature of LoC devices requires special care as fluid dynamics, electrostatic/magnetic forces, chemical reactions and signal processing need to be handled at the same time. This paper introduces a reduced order thermal model for droplet microreactors which would enhance the design process of LoC devices.

The motivation for designing and manufacturing microreactors is that further reduction in sample volume can be achieved by using separate compartments e.g. liquid droplets encapsulating individual reactions.

The flow of droplets is a moving series of slugs of two phases which could be gas and liquid or two immiscible liquids. The slugs form monodisperse compartments in which species and reactions can be isolated and provide the ability to perform large numbers of experiments using extremely small sample volumes [3]. This technique enables the construction of a high throughput Lab-on-a-Chip platform. In addition to several other techniques, reaction heat measurement based biodetection seems to be one of the promising concepts in such micro-scale (chip size) laboratory devices [4].

Heat measurements constitute a direct means of determining enthalpy changes, which appear in all cases of protein–protein or protein–ligand interactions. The method referred to as calorimetry is capable of detecting antibody–antigen, protein–ligand or enzyme–ligand interactions at the bedside for any biomedically relevant case, such as cancer, neurological disorders, diabetes, and metabolic diseases. Although calorimetry is traditionally a low throughput method, the micro-scale realization enables higher reaction speeds and multiple measurements, therefore higher throughput can be achieved [5]. Continuous flow [6] and droplet calorimetry platforms are already reported [7] and demonstrated in various biological applications such as biomolecular characterization [8]. Thermal design is considered to be the key factor of sensitivity and resolution of such calorimetry based biosensors [9], [10]. The amount of thermal energy to be measured typically falls in the nano-Joule range. Lee et. al. successfully demonstrated the enthalpy measurement of urease enzyme activity with a resolution of 10 nJ in a microfluidic calorimeter with a reactor volume of 3.5 nL [10]. Their measurement results fitted very well with the simple theory of Michaelis–Menten kinetics. Droplet size, reaction kinetics, droplet velocity, material of the channel etc. affect the heat transfer from the droplet towards the ambient. These properties should be considered together with the signal processing solutions (e.g. on-chip integrated analog or digital circuits) at behavioral level. Thermal compact models are widely used in design practice, where such reduced order models (in contrast to detailed numerical models) yield results quickly in the early design phase.