1 Introduction

Haptics, as one of the most essential sensations, plays a crucial role in the perception and comprehension of objects’ properties, such as temperature, texture, shape, etc. (Baumgartner et al. 2013). Humans are able to interact and operate with surrounding objects through tactile and kinesthetic sensations (Bremner and Spence 2017). Beyond its ubiquity in daily life, haptics is of considerable significance in diverse fields, including engineering (Giri et al. 2021), medical science (Khaled et al. 2004), biology (Kern 2009), and many other domains. Virtual reality (VR) presents the user with a rendered digital environment for an immersive experience as if he/she was in a real world (Fox and Felkey 2017). Virtual environment has the potential of providing the user with simulations and sensory feedback such as vision, hearing, and haptics through different display modalities. As a typical example, in the realm of medical training, novice physicians can benefit from haptic and visual feedback when manipulating surgical tools and interacting with organs in simulated surgical scenarios (Basdogan et al. 2004). The incorporation of haptic feedback can significantly contribute to the development of diagnostic skills and reduce the risk in real surgical conditions (Coles et al. 2011; Ribeiro et al. 2016).

In recent years, haptic perception and its associated technologies have attracted considerable interest from research communities. Despite great advancements in haptic technologies, most research has primarily focused on interactions with rigid or deformable bodies, while studies on haptic interaction with fluids remain relatively scarce. Fluid haptics has great potential in various applications such as surgical training, entertainment, rehabilitation (Lledo et al. 2014) and education (Qi et al. 2020).

Some studies in the literature have attempted to review haptic interaction techniques in virtual reality. Xia (2018) provided a detailed review of the paper working on the haptic rendering technique spanning from the year 2010 to 2015. However, this review mainly delved into haptic rendering for rigid-rigid and rigid-deformable interactions, and haptic interaction with fluids was only briefly reviewed without systematic analysis. Hamza-Lup et al. (2011) reviewed haptic and visual simulation technologies applied in surgical training. Their focus primarily lied on the techniques relating to the medical domain in existing Application Programming Interfaces (APIs) and frameworks. Huang et al. (2022) reviewed wearable haptic devices from the perspective of haptic feedback modes. Tong et al. (2023) surveyed hand-based haptic interaction and the key components of hand-based haptic simulation. Despite various reviews on haptic techniques, there is still a significant gap in the literature concerning systematic reviews that specifically address haptic interactions with fluids in virtual environment. Therefore, it is essential to conduct a thorough and systematic review that provides comprehensive insights into the current state-of-the-art techniques. Such a review would help to advance the understanding of haptic perception in virtual fluid interactions and address the challenges inherent in this domain.

The scope of this systematic review is not confined to a specific application or a particular type of haptic device. Instead, this paper aims to provide a comprehensive overview of the latest developments in haptic technologies for the interaction with fluids in virtual environment. This review is specifically focused on the current state-of-the-art of both haptic rendering methods and haptic devices designed for simulating fluid interactions. Furthermore, existing research was analyzed across multiple dimensions, including fluid simulation methods, haptic feedback, evaluation techniques, and applications, to identify the current limitations.

The structure of this systematic review is organized as follows: Sect. 2 outlines the methodology employed for conducting the literature review; Sect. 3 presents an overview of the reviewed studies focusing on haptic rendering methods; Sect. 4 highlights haptic devices designed for fluid interaction; Sect. 5 provides an analysis of current research across multiple aspects; and Sect. 6 concludes this review by summarizing key findings and offering directions for future research.

2 Methodology of the literature review

This section outlines the methodology used to conduct this analytical review, following the PRISMA framework (Page et al. 2021) and the guidance from Xiao and Watson (2019), as shown in Fig. 1. Firstly, research motivations and questions were formulated to guide the systematic review. Keywords were defined for the initial screening of relevant works. Then, the collected papers were filtered according to inclusion criteria and their accessibility. A forward and backward search approach (Webster and Watson 2002) was applied to ensure comprehensive coverage of relevant literature. Finally, the full-text papers that met the inclusion criteria were retained for qualitative and quantitative analysis.

Fig. 1
figure 1

PRISMA flow diagram of the paper selection process

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A total of three keyword sets were defined for the search process, as presented in Table 1. Different combinations of keywords were used to identify relevant publications. After an initial search, 289 potential studies were identified based on the keyword sets. The abstract of each study was reviewed to further assess its relevance to the research topic based on inclusion criteria. The main inclusion criteria for this review are as follows:

  1. (1)

    Papers should be published between 2004 and 2024, as the research of haptic interaction with fluids is a relatively new field.

  2. (2)

    The study should include haptic technologies specifically developed for interacting with fluids.

  3. (3)

    The study should involve immersive interactions with user tests that provide insight into user experience and feedback.

Table 1 Keyword sets used for the searching process
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After applying these inclusion criteria, a total of 59 papers were selected for review. These papers cover various topics in haptic interaction with fluids, including rendering methods, the design of haptic devices, and the optimization of fluid haptic simulation techniques. The following sections will present a detailed review of these studies, analyze the current status and limitations of the research, and suggest directions for future work.

3 Haptic rendering for the perception of fluid properties

As one of the key technologies in computer haptics, haptic rendering enables users to perceive the physical properties of virtual objects through haptic interaction in a virtual world. This is achieved by calculating the corresponding force or tactile feedback and transmitting it to the haptic device (Salisbury et al. 2004). While this technology has been researched for decades, the study of haptic rendering for the perception of fluid properties has emerged more recently. Different from rigid body simulations, which require high haptic update rates up to 1000 Hz to maintain realistic feedback, fluid haptics requires lower update rates since the change of interaction forces is slower and smoother over time (Cirio et al. 2011a). Table 2 summarizes existing research on haptic rendering for interactive fluids, including the rendering modalities, haptic update rates, fluid simulation methods, haptic devices and evaluation methodologies.

Table 2 Summary of the existing research on haptic rendering for interactive fluids
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Baxter and Lin (2004) were among the first researchers who delved into the integration of haptic feedback with interactive fluid simulation. They developed a paint model (Baxter et al. 2004) based on the Navier–Stokes (N–S) equations and demonstrated its capability to simulate the fluid viscosity in a 2D interactive painting system.

Gosline et al. (2004a, b) presented a method for the rendering of fluid-filled objects in medical simulators. They utilized fluid pockets enclosed within elastic bodies for haptic simulation and simplified the fluid pressure as a constant distributed force to achieve haptic update rates of over 500 Hz.

Dobashi et al. (2006, 2007) introduced a precomputed approach for estimating and rendering haptic feedback in a virtual canoe simulator. In their method, the water’s behavior was decomposed into linear and non-linear components. The non-linear flow was simulated using the finite difference method, and the friction and pressure were precomputed and stored in a fluid resistance map. However, the precomputation limited the flexibility of the simulation, as any change in the environment, such as variations in fluid properties or interaction scenarios, required recalculating and storing new data.

Mora and Lee (2007, 2008) proposed a multimodal system that integrated both haptic and visual feedback to create an immersive VR experience for interacting with fluids. They incorporated Stam’s 2D method (Stam 1999) into a deformable surface by using a mass-spring system with depth effect and force feedback in three-dimensional space (Vines et al. 2009a, b). When the user stirs the virtual fluid with a haptic probe, the system generates deformation of the fluid surface, allowing changes in fluid properties to be perceived through force feedback.

Höver et al. (2009) proposed a data-driven method to directly synthesize haptic feedback by interpolating raw measured data. They measured and recorded the velocity and corresponding forces along the trajectory of the haptic probe. Then, they utilized the Maxwell model (Shaw and MacKnight 2005) to determine the dimensions of the interpolated force field.

Fluid–structure coupling phenomena are common when interacting with fluids. Yoo et al. (2010a, b) developed an energy-based approach using bond graphs to model the coupling between fluids and deformable objects. They represented the fluid flow and deformable objects as separate bond graph models and coupled them by merging these models. Although this approach proposed a unified model for fluid–structure interaction (FSI), it was only validated for one-dimensional fluid flow.

To achieve more realistic haptic feedback, Cirio et al. (2011a) incorporated Smoothed-Particle Hydrodynamics (SPH) (Monaghan 2005) into their haptic rendering method and validated the method in a virtual cooking application (Cirio et al. 2011b). By using a unified SPH-based model, the forces between fluid and rigid particles can be directly calculated without requiring extra collision detection. Then, they extended their approach to interactions with multistate media, including fluids, deformable bodies as well as rigid bodies (Cirio et al. 2011c). The extended model enabled flexible modification of particle states by introducing fluid and deformable state coefficients that describe the motion of each particle (Cirio et al. 2013b). Cirio’s team also developed a vibrotactile rendering method for perceiving the splashing fluids in a virtual foot-water pool or a hand-water basin (Cirio et al. 2013a) by utilizing sound generation mechanisms. As the one of earliest works focusing on multisensory fluid interaction, they provided a novel solution for haptic interaction techniques.

Building on Cirio’s work, Liang et al. (2016) incorporated interactions between solid bodies while simulating the fluid–structure interaction (FSI) by using a unified SPH method. They believed that by adding force feedback for solid collisions when a haptic proxy was in contact with the vessel wall, this could enhance the realism of the interaction with virtual environment.

Mandal et al. (2018) incorporated the texture changes on the surface of a solid object caused by contact with fluids into force feedback. Recognizing that the solid surface would feel slipperier when submerged in water, the authors rendered the haptic feedback by creating a friction map. The proposed method was compared with the work of Cirio et al. (2013b) and Liang et al. (2016) and a user test involving ten subjects was conducted to evaluate its effectiveness.

Wang and Wang (2014) proposed a hybrid model for FSI in virtual environment, where the fluid was modeled by the SPH method, and the haptic proxy was modeled by the finite element method (FEM). To address the problem of the size difference between fluid particles and solid meshes, they developed a contact detection algorithm to reduce omissions.

Cheng and Liu (2019) developed a multisensory VR system that integrated acoustic and haptic feedback. A novel sound synthesis method was proposed based on the guidance from haptic force feedback. The SPH haptic rendering method was employed to calculate several forces in rigid-fluid interaction and then results were transferred to the sound synthesis module to guide the generation of the synchronized sound.

Li et al. (2023) introduced a fast search algorithm that could detect the rigid-fluid collision by dividing the space into uniform grids to reduce the search cost. They also introduced a new force model that consisted of pressure, viscous force, friction and buoyancy to render the haptic feedback. The results of the cell injection experiment verified the effect of buoyancy in their force model.

Sirwal et al. (2024) attempted to utilize a low-cost commercial haptic device to render the interaction between the fluid and the tool. The potential of deformable models was explored by creating a virtual environment where a deformable membrane cylinder is immersed in viscous fluids.

For haptic interaction with the fluid and the deformable object, Liu et al. (2019) employed a different particle-based approach named the position-based dynamics (PBD) method (Müller et al. 2007). Considering the inhomogeneity of deformable objects, they developed a force model including the combination of buoyance, pressure, viscosity and elastic force to compute haptic force coupled between the fluid and deformable particles. They compared the proposed method with previous work (Cirio et al. 2013b) in the experimental design and verified the effect of elastic force in deformable-fluid interaction.

Different from the research focusing on the interaction with one type of fluid, Zhang and Liu (2017) were the first to address the issue of multiple-fluid interaction in virtual reality by using an SPH-based mixture model (Ren et al. 2014). In their approach, diffusion was not considered for immiscible fluids. For mixable flows, the volume fraction of each SPH particle changed due to the non-uniform distribution of velocity fields.

Recent studies have suggested that the perception of wetness can be understood as a combination of thermal and other tactile sensations (Filingeri et al. 2014). Peiris et al. (2018) explored this aspect by utilizing thermal changes and vibration mechanisms to create a haptic illusion of wetness on the face. This kind of illusion mechanism was validated through an initial user study proposed by Youssef et al. (2024)

In addition to these contact-based haptic rendering methods for fluid interaction, methods based non-contact devices have also been explored to provide tactile feedback. Ultrasound haptics is one of the popular non-contact haptic technologies using ultrasonic waves to create pressure points in mid-air. Amplitude modulation (AM) and spatiotemporal modulation (STM) are the two metaphors that control the arrays of ultrasound transducers to aggregate pressure at special focal points in space (Hoshi et al. 2010). Barreiro et al. (2019, 2020) rendered the pressure distribution on the hand by dynamically optimizing the actuation of transducers using these two metaphors respectively. 3D smoke scenarios were developed for the comparison of produced pressure fields on the skin, and the results demonstrated that STM could deliver more detailed information with smoother and larger coverage. Jang and Park (2020) proposed an AM-based tactile rendering method to achieve vibrotactile sensations when interacting with virtual fluids from a faucet. The developed method applied the Lagrangian fluid simulation approach for the computation of pressure distribution and a hill-climbing method to obtain the local extrema of the pressure field.

4 Haptic devices for interaction with fluids

Haptic devices for interacting with fluids can be broadly categorized into two categories: contact-based and non-contact devices. Contact-based haptic devices deliver feedback through direct physical contact with the user, such as wearable gloves (Liu et al. 2020), exoskeletons (Schmidt et al. 2020), handheld controllers (Cheng et al. 2018; Sagheb et al. 2019, 2023), etc. Non-contact haptic devices, on the other hand, utilize technologies such as ultrasound or air jets to simulate the sensation of touch without direct physical contact. This section will introduce the haptic devices designed or adopted for VR-based fluid interaction.

Some researchers have developed liquid-based haptic interfaces by using the natural feel of liquid dynamics. Yoshimoto et al. (2010) developed a painting interface with dilatant fluid to simulate different tactile properties, such as stickiness, hardness, and roughness. Users can feel different paints through the haptic glove and then mix them in a shallow pool filled with dilatant fluid. Peiris et al. (2018) presented LiquidReality, a wearable system that can simulate the sensation of wetness on the user’s face through thermal and vibrotactile stimuli. Liao et al. (2019) also developed a wearable LiquidMask that can simultaneously produce thermal changes and vibration responses. Different from LiquidReality, the thermal change of LiquidMask was generated by the exchange of real hot and cold water.

GravityCup (Cheng et al. 2018) is a liquid-based handheld haptic device that could provide the user with a weight and inertia sensation when moving virtual objects. Water is pumped into or out of the cup-shaped handheld bag from a wearable device on the waist, creating the sensation of liquid weight increase and decrease.

Sagheb et al. (2019) introduced a non-liquid interface, named SWISH, to provide the gravity of the virtual fluid. This device utilizes a rack-and-pinion mechanism inside the vessel to relocate the center of gravity when the fluid moves inside the vessel, thus affording users a kinesthetic sensation of the virtual fluid behavior. Sagheb’s team also developed another weight-shifting handheld device, Geppetteau (Sagheb et al. 2022, 2023). Different from their previous work, the whole system leverages the inherent slack of the string and four motors to drive the active mass within the vessel in three dimensions. By dynamically altering the center of gravity of the virtual fluid inside the vessel, the users could perceive the volumes and viscosities of virtual fluids.

Liu et al. (2020) focused on the perception of the hand by developing a liquid-based wearable device that provided tactile sensation in underwater VR scenes. Their system enabled the user to perceive pressure, vibration and temperature when interacting with ocean creatures.

Schmidt et al. (2020) explored the combination of simplified fluid dynamics and haptic rendering using high dexterity hand exoskeleton. Inspired by previous work (Vines et al. 2009a), they restricted the rendering of fluid forces by presenting only the drag force to simulate the interaction with high-viscosity fluids.

Different from the above haptic devices focusing on hand-based haptic feedback, Ke and Zhu (Ke 2018; Ke et al. 2023) presented an on-leg wearable system that could generate large-scale force impacts during lower-limb interaction. By installing three pairs of ducted fans on the user's lower legs, force feedback was provided in multiple directions to simulate vertical and horizontal forces as well as dynamic interactions, such as varying force feedback based on foot depth or fluid movement.

GroundFlow (Wang et al. 2021; Han et al. 2023) is a liquid-based haptic floor system that provides multiple-flow feedback by independently controlling the inlet and outlet of the piping system. The developed system was tested in immersive scenarios such as river tracing, swimming, and bodyboarding.

Chen et al. (2024) presented a liquid-transformation system that provided hybrid tactile feedback in virtual environment. This immersive system leverages different mechanisms to alter the movement of water, thus generating experiences of water splash, flow, mist, buoyant force, etc.

Non-contact haptic devices create tactile sensations in mid-air that enable users to feel fluids without any physical contact with a device. FlowHaptics (Ratsamee et al. 2021) is a typical mid-air haptic device using air jets to reproduce the sensation of water flowing over human fingers. UltraHaptics (Carter et al. 2013) used focused ultrasound to generate a series of haptic feedback points that can be directly projected on the user’s hands. Some research (Barreiro et al. 2019, 2020; Jang and Park 2020) has been conducted to explore the potential of rendering pressure distribution on the hand using ultrasound technologies. It is worth mentioning that although previous work (Christou et al. 2022) has explored ways to enhance the sense of force directionality using contactless methods, these approaches did not reach the equivalent maturity of the kinesthetic feedback provided by contact-based devices.

In addition to the previously mentioned devices, several commercial haptic devices, such as the Phantom series and Omega series, are used for interaction with virtual fluids. Table 3 presents both haptic devices specifically developed for fluid interactions and the commercially available haptic devices adopted for applications involving haptic rendering methods for fluids. The maximum applied force and the workspace distribution of the commercial grounded haptic devices used in reviewed studies are illustrated in Fig. 2, which provides a reference for studies that develop haptic interaction technologies using existing commercial devices.

Table 3 Haptic devices used for the interaction with virtual fluids
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Fig. 2
figure 2

Maximum force and workspace distribution of grounded haptic devices

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5 Discussion

In the previous sections, we reviewed the current state-of-the-art research on haptic interaction with fluids in VE. This section presents an in-depth analysis of the reviewed studies, focusing on four key aspects: fluid simulation methods, haptic feedback modalities, evaluation approaches, and applications.

5.1 Fluid simulation methods

In the early research, haptic technologies were predominantly focused on providing feedback for rigid and deformable objects. To simulate fluid interactions, researchers relied on physically inspired models such as the mass-spring model (Mora and Lee 2008), Maxwell model (Höver et al. 2009), and bond graph (Yoo et al. 2010a). While these methods could replicate the viscosity and resistance of fluids, they had difficulty presenting the complexity and continuity of fluid motions.

As the most pivotal equations in all of theoretical fluid dynamics (Anderson 2017), the Navier–Stokes equations describe the motion of a viscous flow based on the Newton’s second law. The N–S equations is expressed in differential form as the following:

$$ \frac{{\partial \left( {\rho u} \right)}}{\partial t} + \nabla \cdot \left( {\rho u{\mathbf{V}}} \right) = - \frac{\partial p}{{\partial x}} + \rho f_{x} + \left( {F_{x} } \right)_{viscous} $$
(1)
$$ \frac{{\partial \left( {\rho v} \right)}}{\partial t} + \nabla \cdot \left( {\rho v{\mathbf{V}}} \right) = - \frac{\partial p}{{\partial y}} + \rho f_{y} + \left( {F_{y} } \right)_{viscous} $$
(2)
$$ \frac{{\partial \left( {\rho w} \right)}}{\partial t} + \nabla \cdot \left( {\rho w{\mathbf{V}}} \right) = - \frac{\partial p}{{\partial z}} + \rho f_{z} + \left( {F_{z} } \right)_{viscous} $$
(3)

where:

ρ is the density, p is the pressure, u, v, and w denote the x, y and z components of the flow velocity \({\mathbf{V}}\), the subscripts x, y and z on \(f\) and \(F\) denote the x, y and z components of the body and viscous forces, respectively,

Computational Fluid Dynamics (CFD) can deal with these nonlinear equations numerically without resorting to any geometrical or physical approximations. Hence, with the development of CFD technologies, researchers integrated CFD methods into haptic simulations to achieve accurate interactions with fluids. The Eulerian and Lagrangian approaches are the two primary methods for solving the Navier–Stokes (N–S) equations. The Eulerian approach divides the spatial region into discrete grids, with fluid properties such as density, velocity, and pressure computed at fixed points. The Lagrangian approach describes the fluid as a system of individual particles, where the motion of each particle is tracked (Blazek 2015). A notable example of the Lagrangian approach is the SPH method, which has been widely adopted for haptic simulations (Cirio et al. 2011a; Wang and Wang 2014).

Advances in CFD methods have enabled more realistic fluid interactions, including the sense of fluid resistance, buoyancy, and viscosity (Li et al. 2023). The appropriate CFD approach, whether Eulerian or Lagrangian, depends on the specific requirements of the simulation. Eulerian methods are effective for describing regular boundary conditions. However, they require significant computational resources when using finer grids to capture fluid details. On the other hand, Lagrangian methods represent fluids as discrete particles, offering greater flexibility in handling complex scenarios such as free surface problems and multiphase flows (Violeau and Issa 2007). However, using particle-based methods might lead to penetrations between fluid and solid particles since clear fluid–solid boundaries are hard to define (Monaghan and Kajtar 2009).

Several approaches have been developed to enhance computational efficiency in interactive fluid simulations. Kawai et al. (2009) introduced a real-time 3D fluid simulator using SPH method for haptic interaction. Leveraging the powerful processing capabilities of GPU, in solving N-S equations. Crane et al. (2007) implemented the 3D fluid simulations on GPU, followed by Yang et al. (2009), who proposed a parallel computing model to enhance the efficiency of interaction force calculations. To achieve real-time user experiences, Pier et al. (2011) balanced computational efficiency and fidelity by using a simplified particle-based model and CUDA technology for real-time fluid haptics. Zhang et al. (2016) improved fluid–structure coupling efficiency, building on the prototype proposed by Henmi et al. (2012). These GPU-accelerated approaches enabled real-time processing fluid interactions and offered practical solutions for applications that require high performance (Rianto et al. 2008; Rianto and Li 2009; Cirio et al. 2011b). Additionally, the rise of artificial intelligence (AI) technology has introduced new possibilities for fluid simulation acceleration. Ratsamee et al. (2021) employed a machine-learning-accelerated fluid simulation method (Tompson et al. 2017) to estimate the two-dimensional pressure distribution of water, and then controlled multiple air jets to generate airflow based on CFD results. By using AI-based methods, it was possible to predict fluid dynamics efficiently, achieving real-time simulations while maintaining accuracy.

With advancements in CFD methods, haptic techniques have been further refined to enhance fidelity in complex scenarios, such as fluid–solid coupling and multiphase fluid simulations (Zhang and Liu 2017), which have been effectively integrated into haptic interactions. Despite these significant advancements, fluid-deformable interactions are still not sufficiently addressed for haptic feedback. This limitation stems from the inherent complexity of deformable bodies, whose heterogeneity and variable material properties (Liu et al. 2019) posed challenges in haptic simulations. Previous work has employed physically inspired models (Yoo et al. 2010b) to simulate these interactions, but the developed models did not succeed in integrating haptic sensation to feel the hydrodynamic properties of the fluid flow.

5.2 Haptic feedback

Human haptic sensations can generally be categorized into two types: tactile feedback and kinesthetic feedback (Hamam et al. 2013; Huang et al. 2022). Tactile feedback encompasses sensations perceived through the skin, such as vibration (Cirio et al. 2013a), temperature (Liao et al. 2019), pressure (Ratsamee et al. 2021) and texture (Mandal et al. 2018), enabling users to feel the fine details of fluid properties. Kinesthetic feedback relates to the perception of forces and torques associated with fluid motion, providing multi-degree-of-freedom feedback that reflects the fluid resistance (Dobashi et al. 2006) and dynamics (Cirio et al. 2011a).

Previous research on haptic technologies based on different working mechanisms has revealed limitations when using individual modes of haptic feedback (Huang et al. 2022). The combination of multiple working mechanisms offers the potential to generate more realistic haptic sensations, thereby enhancing users’ immersive experiences in virtual environment. Liao et al. (2019) used peltiers and water tanks to create thermal changes with hot and cold water, and employed water valves with varying pumping frequencies to generate vibrations. Liu et al. (2020) developed a wearable haptic device that could provide multiple tactile sensations, including four vibration actuators for fluid flow perception, a cooling system for cold feelings, and a pneumatic system with eight airbags for targeted water force perception. Chen et al. (2024) used real water and mechanical elements, such as pumps, waterfalls, and bamboo ladles, to simulate various sensations of liquid splashes, weight, and resistance. This approach could create an immersive experience but primarily relies on passive feedback, as tactile sensations are generated from the natural behavior of water and mechanical forces.

The aforementioned studies utilized liquid-based haptic interfaces with various mechanisms to deliver multi-modal haptic feedback. By taking advantage of the natural behavior and versatility of liquids, these devices are capable of more accurately simulating fluid properties such as flows, temperature changes, and resistance. This allows for the creation of a richer and more immersive experience that engages multiple sensory modalities. Additionally, it is worth mentioning that Mandal et al. (2018) demonstrated the use of a force feedback haptic device to provide an illusion of an object being immersed in water, with a corresponding perception of the changing textures. This approach highlighted the potential of integrating both kinesthetic and tactile feedback to enhance the realism of virtual fluid interactions.

5.3 Evaluation of haptic technologies

The evaluation of haptic technologies plays a crucial role in verifying their effectiveness and ensuring their usability across various applications. Effective evaluation methods are essential for determining the level of performance reached by these technologies, in terms of system precision, task performance, and user experience. Abbasimoshaei et al. (2023) categorized these evaluation methods into three main types: system-centered, task-centered, and user-centered. A well-designed experimental framework for haptic systems should incorporate all three categories to provide a comprehensive evaluation. Table 2 summarizes the evaluation methods applied in existing research.

System-centered methods focus on evaluating whether a haptic system meets requirements identified during development, rather than its performance in a specific task or user scenarios. By measuring key parameters, such as the degree of freedom, frequency, force feedback value, and mechanical stiffness, etc., the overall system performance and compliance to specifications can be effectively confirmed. Samur et al. (2007) proposed a testbed-based evaluation method that integrated approaches of human factor studies to obtain a systematic haptic interface assessment. Mulot et al. presented DOLPHIN (2021), an open-source framework, that helps the design and evaluation of ultrasound haptic stimuli by controlling different rendering parameters.

Unlike system-centered methods that are used for the confirmation of system properties, task-centered methods are designed to evaluate the feasibility of developed technologies by employing simple test tasks that can be quickly understood and completed by subjects. For virtual fluid interaction, tasks such as using a virtual probe to stir the liquid (Mora and Lee 2008; Cirio et al. 2011a; Zhang and Liu 2017; Li et al. 2023) and moving a sphere in a virtual poll (Liang et al. 2016) are commonly used to assess the perception of changes in fluid viscosity, density, velocity and other properties. In non-contact haptic rendering, perceiving the pressure distribution of fluid flow (Barreiro et al. 2019, 2020; Ratsamee et al. 2021) can provide insights into subtle variations in force and pressure.

System-centered and task-centered methods offer an objective evaluation of the effectiveness of haptic technologies, focusing on technical performance and task-specific outcomes. In contrast, user-centered methods aim to measure the impact of the haptic system on the user experience, which is a subjective evaluation process. However, as one of the essential metrics for evaluating haptic techniques, there is no single standardized approach for these evaluations (Abbasimoshaei et al. 2023) due to the context of applications, individual differences and experimental purposes. Instead, various types of tests are designed depending on the specific information needed. Some methods involve comparative testing (Mandal et al. 2018) to determine the effectiveness of the developed haptic technology, while others focus on measuring specific outcomes or effects in a given context that can provide a comprehensive understanding of the benefits and limitations of the system. This issue was addressed in more details by Abbasimoshaei et al. (2023).

5.4 Applications

The rapid development of VR technologies has increased the demand for the implementation of haptic systems that enhance users’ immersion in various application areas. Giri et al. (2021) explored haptic technology from an application-based perspective and identified current challenges particularly in industrial and health science applications. Georgiou et al. (2022) presented a comprehensive review of mid-air haptic techniques covering different designs and applications. Figure 3, shows the potential applications in fluid haptics, including enhanced user experiences in entertainment, medical training, psychotherapy, and industry.

Fig. 3
figure 3

Illustrations of fluid haptics application

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One of the most straightforward examples of fluid haptics is VR gaming. Applications include painting systems (Baxter et al. 2004), cooking simulators (Cirio et al. 2011a), sports training (Ke et al. 2023), and immersive underwater environment (Liu et al. 2020), all of which provide immersive interactions between users and virtual liquids. Another typical application is medical training, where fluid haptic is employed to the training of novice physicians on basic manipulations, such as cuttings and cell injections (Rianto et al. 2008; Rianto and Li 2009), to help reducing the risk associated with real surgeries. Even in chemical industry, augmented fluid technologies were used for the training and evaluation of workers to identify hazardous fluids through the simulation of different fluid properties (Sagheb et al. 2019). In addition, with the development of WaterHCI technologies, Virtual Reality Exposure Therapy (VRET) was used to treat Aquaphobia (Misimi et al. 2020), the fear of being in water. The developed systems can capture water’s immersive qualities, such as flow dynamics and tactile sensations, while eliminating the safety risks in traditional therapies (Montoya et al. 2024).

However, due to the complexity of flow motion, natural and realistic interaction with fluids can be challenging, which requires accurate simulation of fluid dynamics, real-time haptic feedback, and stability and consistency of fluid-object interactions. Moreover, the characteristics of haptic devices, such as workspace, degrees of freedom, and mechanical resistance, also affected the fidelity of immersive interactions.

In fact, human perception of the physical world is naturally shaped by the harmonious collaboration of multiple sensory modalities. The identification of the limitations inherent to a single sensory modality has driven growing interest in multimodal sensory integration to enhance the realism of immersive experiences. Several studies have explored the combination of visual, acoustic and haptic feedback that could create more authentic and enriched VR experiences. For instance, Cirio et al. (2013a) and Cheng and Liu (2019) demonstrated that the integration of various sensory cues enabled users a better presence in virtual environment. Visual cues provide the spatial and contextual information needed for users to anticipate and comprehend physical interactions, while auditory feedback complements haptic sensations by representing material properties or dynamic events, such as collisions or liquid splashing (Cirio et al. 2013a). This multimodal sensory integration allowed reaching more immersive VR experience, especially in complex interaction scenarios like medical simulations and VR gaming.

6 Conclusions and research perspectives

This review presents a comprehensive overview of the advancements of haptic technologies for fluid interaction in virtual environment over the past two decades. It highlights the state-of-the-art research on both haptic rendering methods and the development of haptic devices. Additionally, the review presents an analytical perspective on four critical aspects: fluid simulation methods, haptic feedback modalities, evaluations of haptic systems, and their applications. The following challenges have been identified for future research in this domain:

  • While Computational Fluid Dynamics (CFD) can provide accurate simulations of fluid behaviors, translating these complicated calculations in real-time, interactive scenarios remains challenging. Achieving the requirements of precision and responsiveness often leads to trade-offs, which could limit the fidelity of haptic feedback. The popularity of Artificial Intelligence, such as machine learning and data-driven technologies, offers a potential solution through approximating complex CFD calculations while maintaining real-time interactivity.to obtain smooth and reliable haptic feedback for the interaction with fluids.

  • At present, most fluid interaction scenarios in virtual environment are limited to fluid-rigid body coupling (e.g., interactions between fluid and virtual probes). However, real-world scenarios often involve more intricate interactions, encompassing fluids, rigid bodies and deformable bodies. These interactions introduce complexities such as nonlinear deformation and dynamic coupling problems, which has been overlooked in the existing research.

  • The existing haptic devices still face limitations in reproducing the continuity, flexibility, and nonlinear characteristics of fluids. Moreover, most current systems provide single-mode haptic feedback, thereby restricting the scope of perceived haptic information by users. To overcome these limitations, the integration of multimodal haptic feedback, including thermal, vibrotactile, pressure and force feedback, offers a promising solution. However, these systems require the development of innovative control strategies and suitable mechanisms to reproduce various haptic modalities while ensuring spatial and temporal consistency of haptic sensations in the interaction with fluids.

  • With the development of WaterHCI technologies, the fluid haptic technologies have received increasing attention in immersive environment. For VR-HMD systems that require over 90 FPS for smooth interactions between users and virtual environment, the development of optimized rendering algorithms and lightweight simulation frameworks is a challenge that should be addressed in future research.

In the research perspectives, the authors will focus on the development of a new framework satisfying the requirement for accurate haptic systems with fluids and deformable bodies. The implementation of this framework is currently under development and will be validated through its application for medical diagnosis and prognosis.